Nothing
R/test_of_hypothesis.R
In leem: Laboratory of Teaching to Statistics and Mathematics
#' #' Test of hypothesis
#' #'
#' #' Performs hypothesis testing for various parameters of one or more populations
#' #'
#' #' @param x R object. See in details.
#' #' @param y an optional (non-empty) numeric vector of data values.
#' #' @param test character value. The options are: \code{"ttest"}, \code{"ztest"}, \code{"ptest"}, \code{"chitest"}, \code{"ftest"}, \code{"anova"}, \code{"friedman"}, \code{"kruskal"}, \code{"mann whitney"}.
#' #' @param h0 numeric value. The hypothesized parameter.
#' #' @param prop a logical indicating whether you want to use the proportion test of not. Default is \code{prop=FALSE}.
#' #' @param alternative a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
#' #' @param alpha significance level of the test
#' #' @param exact a logical indicating whether you want to use the exact test or not. Default is \code{exact=TRUE}.
#' #' @param correct a logical indicating whether Yates' continuity correction should be applied where possible. This argument must be used when \code{exact = FALSE}.
#' #' @param paired a logical indicating whether you want a paired t-test. Valid only for \code{test="ttest"}.
#' #' @param paired a logical indicating whether you want a paired t-test. Valid only for \code{test="ttest"}.
#' #' @param plot a logical indicating whether you want a graph indicating the regions of rejection or not of the null hypothesis, as well as the test decision.
#' #' @examples
#' #' # Null hypothesis
#' #' nullhyp <- h0 <- 90
#' #' # Simulation
#' #' set.seed(10)
#' #' data <- rnorm(30, 100, 10)
#' #' # Test of hypothesis
#' #' th(data, h0 = h0, sd = 10, plot = TRUE)
#' #'
#' #' @import crayon
#' #' @export
#' th <- function(x, y = NULL, test = "ztest", h0, prop = FALSE,
#' delta = 0, p, pa,
#' alternative = c("two.sided","L", "less", "greater","G"),
#' alpha = 0.05, exact = TRUE,
#' correct = FALSE, paired = FALSE, plot = FALSE, ...) {
#'
#' alternative <- match.arg(alternative)
#' argaddit <- list(...)
#'
#' if (missing(x)) {
#' xfile <- file.choose(new = TRUE)
#' x <- read.table(xfile, header = TRUE)
#' }
#' if (any(test == c("ztest", "z", "Z", "normal"))) {
#' if(prop == TRUE){
#' if (!any(names(argaddit) == "pa")) {
#' pa <- readline("Insert the value of population sample part? ")
#' pa <- as.numeric(pa)
#' } else pa <- argaddit$pa
#' if (missing(p)) {
#' p <- readline("Insert the value of proportion? ")
#' p <- as.numeric(p)
#' }else p <- argaddit$p
#' }else{
#' if (is.null(y)) {
#' if (!any(names(argaddit) == "sd")) {
#' sdev <- readline(paste0(gettext("Enter the value of population standard deviation:", domain = "R-leem"), " "))
#' sdev <- as.numeric(sdev)
#' } else sdev <- argaddit$sd
#' if (missing(h0)) {
#' h0 <- readline(paste0(gettext("Enter the value of null hypothesis:"), " "))
#' h0 <- as.numeric(h0)
#' }
#' } else {
#' if (!any(names(argaddit) == "sd")) {
#' sdev <- c(as.numeric(readline(paste0(gettext("Enter the standard deviation value of population 1:")), " ")),
#' as.numeric(readline(paste0(gettext("Enter the standard deviation value of population 2:")), " ")))
#' } else if(length(argaddit$sd) < 1){
#' sdev <- c(as.numeric(readline(paste0(gettext("Enter the standard deviation value of population 1:")), " ")),
#' as.numeric(readline(paste0(gettext("Enter the standard deviation value of population 2:")), " ")))
#' } else sdev <- argaddit$sd
#' if (sdev[1] > length(x) || sdev[2] > length(y)){
#' stop("Incorrect standard deviantion argument for 2 populations", call. = FALSE, domain = "R-leem")
#' }
#' if ((length(x) > length(y) && sdev[1] <= sdev[2])||((length(x) < length(y) && sdev[1] >= sdev[2]))){
#' stop("Incorrect standard deviantion argument for 2 populations", call. = FALSE, domain = "R-leem")
#' }
#' }
#' }
#' if (any(alternative == c("two.sided", "t", "T"))) {
#' if (is.null(y)) {
#' if (prop == TRUE) {
#' title <- paste(gettext(" One Sample z-test proportion (Two-sided test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext(" H0: p= ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' althyp <- paste(gettext(" H1: p != ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' pa <- pa/n
#' ztest <- round( (( pa - p ) / ( sqrt( (p * ( 1-p) ) / n ) )) , 2)
#' ztab <- round(qnorm(1 - (alpha)/2), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' h0 <- p
#' } else {
#' title <- paste(" ", gettext("One Sample z-test (Two-sided test)", domain = "R-leem"), "\n")
#' nullhyp <- paste(" ", gettext("H0: mu = ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' althyp <- paste(" ", gettext("H1: mu != ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' signlevel <- paste(" ", gettext("alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' ztest <- round((mean(x) - h0) / (sdev /sqrt(n)), 2)
#' ztab <- round(qnorm(1 - (alpha)/2), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' }
#' if (ztest >= ztab[2]) {
#' decision <- paste(gettext("As ztest = ", domain = "R-leem"),
#' ztest, " > |ztab =", abs(ztab[2]), " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext("As ztest =", domain = "R-leem"), " ",
#' ztest, " > ztab =", ztab[2])
#' decision2 <- paste(gettext("As p-value = ", domain = "R-leem"),
#' round(pvalue, 5), " < alpha = ", alpha, " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = " ")
#' conclusion <- paste(gettext("We observed by the Z Test that the null hypothesis was rejected, at the significance level of", domain = "R-leem"),
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = " ")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#' } else {
#' decision <- paste(" ", gettext("As ztest =", domain = "R-leem"), " ",
#' abs(ztest), " < ztab = ", abs(ztab[2]), " ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(" ", gettext("As ztest =", domain = "R-leem"),
#' ztest, " < ztab = ", ztab[2])
#' decision2 <- paste(" ", gettext("As p-value =", domain = "R-leem"), " ",
#' round(pvalue, 5), " ", "> alpha = ", alpha,
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' conclusion <- paste(" ", gettext("We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of", domain = "R-leem"), " ",
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#' }
#' else {
#' title <- paste(gettext(" two Sample z-test (Two-sided test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext(" H0: mu1 = mu2 ", domain = "R-leem"),sep ="")
#' althyp <- paste(gettext(" H1: mu1 != mu2", domain = "R-leem"),sep ="")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha ,2),sep = "")
#' n <- length(x)
#' n1 <- length(y)
#' ztest <- round(((mean(x) - mean(y))/sqrt(((sdev[1]^2)/n)-((sdev[2]^2)/n1))), 2)
#' ztab <- round(qnorm(1 - (alpha)/2), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' if (abs(ztest) >= abs(ztab[2])) {
#' decision <- paste(gettext("As ztest = ", domain = "R-leem"),
#' abs(ztest), "| > |ztab = ", abs(ztab[2]),
#' gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' pvalue, " < alpha = ", alpha,
#' gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| > |ztab = ", abs(ztab[2]), '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#' } else {
#' decision <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| < |ztab = ", abs(ztab[2]),
#' gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' pvalue, " > alpha = ", alpha,
#' gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| < |ztab = ", abs(ztab[2]), '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#' }
#' if (plot == TRUE) {
#' par(mar = c(10,4,4,4))
#' x <- seq(- 4 * 1, ztab[1], by = 0.01)
#' z <- seq(ztab[2], 4, by = 0.01)
#' y <- seq( - 4, + 4, by = 0.01)
#' fx <- dnorm(x, mean = 0, sd = 1)
#' fz <- dnorm(z,mean = 0, sd = 1)
#' fy <- dnorm(y, mean = 0, sd = 1)
#' curve(dnorm(x, mean = 0, sd = 1), - 4 , + 4 ,
#' ylim = c(0.0, 1.2 * max(fx,fy,fz)), xlab = "",
#' ylab = "", lwd = 5, axes = FALSE)
#' polygon(c(y, rev(y)),
#' c(fy, rep(0, length(fy))),
#' col="#99ccff")
#' polygon(c(x, rev(x)),
#' c(fx, rep(0, length(fx))),
#' col="#cc0000")
#' polygon(c(z,rev(z)), c(fz,rep(0,length(fz))),
#' col="#cc0000" )
#' abline(v = ztab[1], lty=2, col = "#cc0000")
#' abline(v = ztab[2], lty=2, col = "#cc0000")
#' abline(v = ztest, lty=2, col = "blue")
#' cpoint <- gettext("Critical point", domain = "R-leem")
#' text(-2.5, 0.3, substitute(bold(cpoint), list(cpoint = cpoint)))
#' arrows(ztab[1], 0.14, -2.3, 0.27, length = 0.15)
#' text(2.5, 0.3, substitute(bold(cpoint), list(cpoint = cpoint)))
#' arrows(ztab[2] ,0.14,2.3, 0.27, length = 0.15)
#' testatistico <- gettext("test \nstatistic", domain = "R-leem")
#' text(ztest, 0.4, substitute(bold(testatistico), list(testatistico = testatistico)), col = "blue")
#' aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' #aux1 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/10000
#' axis(side = 1, at = c(ztab[1],ztab[2]), font = 2, labels = FALSE,
#' col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#' axis(side=1, at=as.character(c( - 4, ztab[1])), tick = TRUE, lwd = 1,
#' col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' axis(side=1, at=as.character(c(ztab[2], + 4)), tick = TRUE, lwd = 1,
#' col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' axis(side = 1, at = c(ztab[1],ztab[2]), lwd = 0,
#' col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#' axis(side = 1, at = ztest, lwd = 0,
#' col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = -0.001)
#' axis(side = 1, at = ztest, tick = TRUE, lwd = 1,
#' col="blue", lwd.ticks = 1, labels = FALSE)
#'
#' if (prop == TRUE) {
#' titulo <- gettext("Test of proportion: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' } else {
#' titulo <- gettext("Test of hypothesis: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' }
#' aceitah0 <- gettext("ACCEPT", domain = "R-leem")
#' text(0,0.1,substitute(bold(aceitah0)~H[0], list(aceitah0 = aceitah0)), font = 2)
#' text(ztab[1] - 1 , 0.1, expression("RR"*H[0]), font = 2)
#' text(ztab[2] + 1 ,0.1,expression("RR"*H[0]), font = 2)
#' passo1 <- gettext("Step 1: Hypothesis", domain = "R-leem")
#' mtext(substitute(passo1, list(passo1 = passo1)), side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' mtext(text = substitute(H[0]:~mu==h0,list(h0 = round(h0, 2))), side = 1, line = 4.2, adj = 0.05)
#' mtext(text = substitute(H[1]:~mu!=h0,list(h0 = round(h0, 2))), side = 1, line = 5, adj = 0.05)
#' passo2 <- gettext("Step 2: Significante level", domain = "R-leem")
#' mtext(substitute(passo2, list(passo2 = passo2)), side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' mtext(text = substitute(alpha==alfa,list(alfa = round(alpha, 2))), side = 1, line = 7, adj = 0.05)
#' passo3 <- gettext("Step 3: Rule of decision", domain = "R-leem")
#' mtext(substitute(passo3, list(passo3 = passo3)), side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' mtext(decisionplot, side = 1, line = 4, adj = 1)
#' passo4 <- gettext("Step 4: Conclusion", domain = "R-leem")
#' mtext(substitute(passo4, list(passo4 = passo4)), side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' if (abs(ztest) >= abs(ztab[2])) {
#' mtext(substitute(H[0]~conclusionplot, list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' } else {
#' mtext(substitute(conclusionplot~H[0], list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' }
#'
#' }
#' }
#' if (any(alternative == c("less", "l", "L"))) {
#' if (is.null(y)) {
#' if (prop == TRUE) {
#' title <- paste(gettext("One Sample z-test proportion (Less test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext("H0: p >= ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' althyp <- paste(gettext(" H1: p < ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' pa <- pa/n
#' ztest <- round( (( pa - p ) / ( sqrt( (p * ( 1-p) ) / n ) )) , 2)
#' ztab <- round(qnorm(1 - (alpha)), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = T)
#' h0 <- p
#' } else {
#' title <- paste(gettext("One Sample z-test (Less test)", domain = "R-leem"), "\n")
#' nullhyp <- paste(" ", gettext("H0: mu >= ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' althyp <- paste(" ", gettext("H1: mu < ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' signlevel <- paste(" ", gettext("alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' ztest <- round((mean(x) - h0) / (sdev /sqrt(n)), 2)
#' ztab <- round(qnorm(1 - alpha), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' }
#' if (abs(ztest) >= abs(ztab[2])) {
#' decision <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| > |ztab = ", abs(ztab[2]), "| ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' round(pvalue, 5), " < alpha = ", alpha,
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' ztest, "| > |ztab = ", ztab[1], '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#'
#' } else {
#' decision <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| < |ztab = ", abs(ztab[2]),
#' "| ", gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' round(pvalue, 5), " > alpha = ", alpha, "| ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' ztest, "| < |ztab = ", ztab[1], '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#' }
#' else{
#' title <- paste(gettext(" two Sample z-test (Less-sided test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext(" H0: mu1 >= mu2 ", domain = "R-leem"),sep ="")
#' althyp <- paste(gettext(" H1: mu1 < mu2", domain = "R-leem"),sep ="")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha ,2),sep = "")
#' n <- length(x)
#' n1 <- length(y)
#' ztest <- round((mean(x) - mean(y)) /sqrt((sdev[1]^2/n)-(sdev[2]^2 /n1)), 2)
#' ztab <- round(qnorm(1 - (alpha)), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' if (abs(ztest) >= abs(ztab[2])) {
#' decision <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| > |ztab = ", abs(ztab[2]),
#' gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' pvalue, " < alpha = ", alpha,
#' gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' ztest, "| > |ztab = ", ztab[1], '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' } else {
#' decision <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| < |ztab = ", abs(ztab[2]),
#' gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' pvalue, " > alpha = ", alpha,
#' gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' ztest, "| < |ztab = ", ztab[1], '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#' }
#' if (plot == TRUE) {
#' par(mar = c(10,4,4,4))
#' x <- seq(- 4 , ztab[1], by = 0.01)
#' y <- seq(ztab[1],+ 4, by = 0.01)
#' fx <- dnorm(x, mean = 0, sd = 1)
#' fy <- dnorm(y, mean = 0, sd = 1)
#' curve(dnorm(x, mean = 0, sd = 1), - 4 , + 4 ,
#' ylim = c(0, 1.2*max(fx,fy)), xlab = "",
#' ylab = "", lwd = 5, axes = FALSE)
#' polygon(c(y, rev(y)),
#' c(fy, rep(0, length(fy))),
#' col="#99ccff")
#' polygon(c(x, rev(x)),
#' c(fx, rep(0, length(fx))),
#' col="#cc0000")
#' abline(v = ztab[1], lty=2, col = "red")
#' text(-2.5, 0.3, expression(bold("Critical point")))
#' arrows(ztab[1] ,0.14, -2.3, 0.28, , length = 0.15)
#' abline(v = ztest, lty=2, col = "blue")
#' aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#'
#'
#' axis(side = 1, at = c(ztab[1], 4), font = 2, labels = FALSE, lwd.ticks = 0,
#' col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#'
#' axis(side=1, at=as.character(c( -4, ztab[1])), tick = TRUE, lwd = 1,
#' col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#'
#' axis(side = 1, at = c("",ztab[1]), lwd = 0,
#' col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#'
#' axis(side=1, at=as.character(c( "", ztab[1])), tick = TRUE, labels = FALSE,
#' lwd.ticks = 1, col="#cc0000")
#'
#' axis(side = 1, at = ztest, lwd = 0,
#' col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = -0.001)
#' axis(side = 1, at = ztest, tick = TRUE, lwd = 1,
#' col="blue", lwd.ticks = 1, labels = FALSE)
#'
#'
#' if (prop == TRUE) {
#' titulo <- gettext("Test of proportion: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' } else {
#' titulo <- gettext("Test of hypothesis: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' }
#' aceitah0 <- gettext("ACCEPT", domain = "R-leem")
#' text(0,0.1,substitute(bold(aceitah0)~H[0], list(aceitah0 = aceitah0)), font = 2)
#' text(-2.5, 0.1, expression(bold("RRH0")))
#' arrows(ztest, 0.27, 1.7, 0.37, length = 0.15)
#' text(2, 0.39, expression(bold("ztest")))
#' passo01 <- gettext("Step 1: Hypothesis", domain = "R-leem")
#' mtext(substitute(passo01, list(passo01 = passo01)), side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' mtext(text = substitute(H[0]>=h0, list(h0=round(h0, 2))) , side = 1, line = 4.2, adj = 0.05)
#' mtext(text = substitute(H[1]<h0, list(h0=round(h0, 2))) , side = 1, line = 5, adj = 0.05)
#' passo02 <- gettext("Step 2: Significante level", domain = "R-leem")
#' mtext(substitute(passo02, list(passo02 = passo02)), side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' mtext(text = substitute(alpha == alfa, list(alfa = alpha)) , side = 1, line = 7, adj = 0.05)
#' passo03 <- gettext("Step 3: Rule of decision", domain = "R-leem")
#' mtext(substitute(passo03, list(passo03 = passo03)), side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' mtext(decisionplot, side = 1, line = 4, adj = 1)
#' passo04 <- gettext("Step 4: Conclusion", domain = "R-leem")
#' mtext(substitute(passo04, list(passo04 = passo04)), side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' if (abs(ztest) >= abs(ztab[2])) {
#' mtext(substitute(H[0]~conclusionplot, list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' } else {
#' mtext(substitute(conclusionplot~H[0], list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' }
#' }
#' }
#' if (any(alternative == c("greater", "g", "G"))) {
#' if (is.null(y)) {
#' if (prop == TRUE) {
#' title <- paste(gettext("One Sample z-test proportion (Greater test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext(" H0: p <= ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' althyp <- paste(gettext(" H1: p > ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' pa <- pa/n
#' ztest <- round( (( pa - p ) / ( sqrt( (p * ( 1-p) ) / n ) )) , 2)
#' ztab <- round(qnorm(1 - (alpha)), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = F)
#' h0 <- p
#' } else {
#' title <- paste(" ", gettext("One Sample z-test (Greater test)", domain = "R-leem"), " ")
#' nullhyp <- paste(gettext(" H0: mu <= ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' althyp <- paste(gettext(" H1: mu > ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' ztest <- round((mean(x) - h0) / (sdev /sqrt(n)), 2)
#' ztab <- round(qnorm(1 - alpha), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' }
#' if (ztest >= ztab[2]) {
#' decision <- paste(" ", gettext("As ztest =", domain = "R-leem"), " ",
#' abs(ztest), " > ztab = ", abs(ztab[2]), " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decision2 <- paste(" ", gettext("As p-value =", domain = "R-leem"),
#' round(pvalue, 5), " < alpha =", alpha, " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(" ", gettext("As ztest =", domain = "R-leem"), " ",
#' ztest, "> ztab = ", ztab[2])
#' conclusion <- paste(" ", gettext("We observed by the Z Test that the null hypothesis was rejected, at the significance level of", domain = "R-leem"),
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#' } else {
#' decision <- paste(gettext("As ztest =", domain = "R-leem"), " ",
#' ztest, " < ztab = ", ztab[2], " ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext("As p-value =", domain = "R-leem"), " ",
#' round(pvalue, 5), " > alpha = ", alpha, " ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext("As ztest = ", domain = "R-leem"),
#' ztest, " < ztab = ", ztab[2])
#' conclusion <- paste(gettext("We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of", domain = "R-leem"),
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#' }
#' else {
#' title <- paste(gettext(" two Sample z-test (Greater-sided test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext(" H0: mu1 <= mu2 ", domain = "R-leem"),sep ="")
#' althyp <- paste(gettext(" H1: mu1 > mu2", domain = "R-leem"),sep ="")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha ,2),sep = "")
#' n <- length(x)
#' n1 <- length(y)
#' ztest <- round((mean(x) - mean(y)) /sqrt((sdev[1]^2/n)-(sdev[2]^2 /n1)), 2)
#' ztab <- round(qnorm(1 - (alpha)), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = TRUE)
#'
#' if (ztest >= ztab[2]) {
#' decision <- paste(" ", gettext("As ztest = ", domain = "R-leem"),
#' ztest, " > ztab = ", ztab[2], " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext("As p-value = ", domain = "R-leem"),
#' round(pvalue, 5), " < alpha = ", alpha, " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(" ", gettext("As ztest =", domain = "R-leem"),
#' ztest, " > ztab = ", ztab[2])
#' conclusion <- paste(gettext("We observed by the Z Test that the null hypothesis was rejected, at the significance level of", domain = "R-leem"),
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' } else {
#' decision <- paste(" ", gettext("As ztest = ", domain = "R-leem"),
#' ztest, " < ztab = ", ztab[2], " ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decision2 <- paste(" ", gettext("As p-value = ", domain = "R-leem"),
#' round(pvalue, 5), " > alpha = ", alpha, " ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext("As ztest =", domain = "R-leem"), " ",
#' ztest, " < ztab = ", ztab[2])
#' conclusion <- paste(gettext("We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of", domain = "R-leem"),
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#'
#' }
#' if (plot == TRUE) {
#' par(mar = c(10,4,4,4))
#' x <- seq(- 4 , ztab[2], by = 0.01)
#' y <- seq(ztab[2],+ 4, by = 0.01)
#' fx <- dnorm(x, mean = 0, sd = 1)
#' fy <- dnorm(y, mean = 0, sd = 1)
#' if (ztest >= 4) {
#' curve(dnorm(x, mean = 0, sd = 1), - 4 , ztest + 1,
#' ylim = c(0, 1.2*max(fx,fy)), ylab = "", xlab = "",
#' lwd = 5, axes = FALSE)
#' }
#' if (ztest <= -4) {
#' curve(dnorm(x, mean = 0, sd = 1), ztest - 1 , 4,
#' ylim = c(0, 1.2*max(fx,fy)), ylab = "", xlab = "",
#' lwd = 5, axes = FALSE)
#' }
#' if (ztest < 4 & ztest > -4) {
#' curve(dnorm(x, mean = 0, sd = 1), - 4 , 4,
#' ylim = c(0, 1.2*max(fx,fy)), ylab = "", xlab = "",
#' lwd = 5, axes = FALSE)
#' }
#'
#'
#' polygon(c(y, rev(y)),
#' c(fy, rep(0, length(fy))),
#' col="#cc0000")
#' polygon(c(x, rev(x)),
#' c(fx, rep(0, length(fx))),
#' col="#99ccff")
#' abline(v = ztab[2], lty=2, col = "red")
#' abline(v = ztest, lty=2, col = "blue")
#' pcritico <- gettext("Critical point", domain = "R-leem")
#' text(2.5, 0.3, substitute(bold(pcritico), list(pcritico = pcritico)))
#' arrows(ztab[2], 0.14, 2.3, 0.28, length = 0.10)
#' aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#'
#' if (ztest > 4) {
#' axis(side=1, at=as.character(c( ztab[2], ztest + 1)), tick = TRUE, lwd = 1,
#' col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' } else {
#' axis(side=1, at=as.character(c( ztab[2], 4)), tick = TRUE, lwd = 1,
#' col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' }
#'
#' if (ztest < -4) {
#' axis(side = 1, at = c(ztest - 1, ztab[2]), font = 2, labels = FALSE, lwd.ticks = 0,
#' col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#' } else {
#' axis(side = 1, at = c(-4, ztab[2]), font = 2, labels = FALSE, lwd.ticks = 0,
#' col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#' }
#'
#' axis(side = 1, at = c("",ztab[2]), lwd = 0,
#' col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#'
#' axis(side=1, at=as.character(c( "", ztab[2])), tick = TRUE, labels = FALSE,
#' lwd.ticks = 1, col="#cc0000")
#' axis(side = 1, at = ztest, lwd = 0,
#' col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = -0.001)
#' axis(side = 1, at = ztest, tick = TRUE, lwd = 1,
#' col="blue", lwd.ticks = 1, labels = FALSE)
#'
#'
#' if (prop == TRUE) {
#' titulo <- gettext("Test of proportion: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' } else {
#' titulo <- gettext("Test of hypothesis: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' }
#' aceitah0 <- gettext("ACCEPT", domain = "R-leem")
#' text(0,0.1,substitute(bold(aceitah0)~H[0], list(aceitah0 = aceitah0)), font = 2)
#' text(2.5, 0.1, expression(bold("RRH0")))
#' arrows(ztest, 0.1, 3, 0.37, length = 0.1)
#' text(3, 0.39, expression(bold("ztest")))
#' passo01 <- gettext("Step 1: Hypothesis", domain = "R-leem")
#' mtext(substitute(passo01, list(passo01 = passo01)), side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' mtext(text = substitute(H[0]<=h0, list(h0=round(h0, 2))) , side = 1, line = 4.2, adj = 0.05)
#' mtext(text = substitute(H[1]>h0, list(h0=round(h0, 2))) , side = 1, line = 5, adj = 0.05)
#' passo02 <- gettext("Step 2: Significante level", domain = "R-leem")
#' mtext(substitute(passo02, list(passo02 = passo02)), side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' mtext(text = substitute(alpha == alfa, list(alfa = alpha)) , side = 1, line = 7, adj = 0.05)
#' passo03 <- gettext("Step 3: Rule of decision", domain = "R-leem")
#' mtext(substitute(passo03, list(passo03 = passo03)), side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' mtext(decisionplot, side = 1, line = 4, adj = 1)
#' passo04 <- gettext("Step 4: Conclusion", domain = "R-leem")
#' mtext(substitute(passo04, list(passo04 = passo04)), side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' if (ztest >= ztab[2]) {
#' mtext(substitute(H[0]~conclusionplot, list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' } else {
#' mtext(substitute(conclusionplot~H[0], list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' }
#' }
#' }
#' }
#' # if (any(test == c("ttest", "t", "T", "tstudent"))) {
#' # df <- length(x) - 1
#' # nu <- df
#' # nu <- as.numeric(nu)
#' # sdev <- df
#' # if (missing(h0)) {
#' # h0 <- readline("Insert the value of null hypothesis: ")
#' # h0 <- as.numeric(h0)
#' # }
#' # if (any(alternative == c("two.sided", "t", "T"))) {
#' # if (is.null(y)) {
#' # title <- paste(gettext(" One Sample t-test (Two-sided test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu = ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # althyp <- paste(gettext(" H1: mu != ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' # sep = "")
#' # n <- length(x)
#' # ttest <- round((mean(x) - h0) / (sdev /sqrt(n)), 2)
#' # if (alternative == "two.sided"){
#' # ttab <- round(qt(1 - (alpha)/2, df = nu), 2)
#' # } else {
#' # ttab <- round(qt(1 - alpha, df = nu), 2)
#' # }
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df = nu, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]), '|')
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("H0 was rejected.", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),"|")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("No evidence to reject the H0. ", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # else{
#' # n1 <- length(x)
#' # n2 <- length(y)
#' # if(n1 == n2){
#' # df <- n1+n2-2
#' # sp <- ((n1-1)*var(x) + (n2-1)*var(y))/df
#' # }else{
#' # df <- ((sd(x)^2/n1)^2 + 2*(sd(x)^2/n1)*(sd(y)^2/n2) + (sd(y)^2/n2)^2)/((((sd(x)^2/n1)^2)/(n1-1))+(((sd(y)^2/n2)^2)/(n2-1)))
#' # sp <- sqrt(((sd(x)^2)/n1)+((sd(y)^2)/n2))
#' # }
#' # title <- paste(gettext(" Two Sample t-test (Two-sided test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu1 = mu2", domain = "R-leem"), sep = "")
#' # althyp <- paste(gettext(" H1: mu1 != mu2", domain = "R-leem"), sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2), sep = "")
#' # ttest <- round((mean(x) - mean(y)) / sqrt(sp*(1/n1+1/n2)), 2)
#' # ttab <- round(qt(1 - (alpha)/2, df), 2)
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "" )
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]), '|')
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" H0 was rejected", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),"|")
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" No evidence to reject the H0 ", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # if (plot == TRUE) {
#' # par(mar = c(10,4,4,4))
#' # x <- seq(- 4 * 1, ttab[1], by = 0.01)
#' # z <- seq(ttab[2], 4, by = 0.01)
#' # y <- seq( - 4, + 4, by = 0.01)
#' # fx <- dt(x, df = nu)
#' # fz <- dt(z,df = nu)
#' # fy <- dt(y, df = nu)
#' # curve(dt(x, df = nu), - 4, + 4,
#' # ylim = c(0.0, 1.2 * max(fx,fy,fz)),xlab = "X",
#' # ylab = expression(f[X](x)),
#' # panel.first = grid(col="gray90"), lwd = 5)
#' # polygon(c(y, rev(y)),
#' # c(fy, rep(0, length(fy))),
#' # col="#99ccff")
#' # polygon(c(x, rev(x)),
#' # c(fx, rep(0, length(fx))),
#' # col="#cc0000")
#' # polygon(c(z,rev(z)), c(fz,rep(0,length(fz))),
#' # col="#cc0000")
#' # abline(v = ttab[1], lty=2, col = "red")
#' # abline(v = ttab[2], lty=2, col = "red")
#' # abline(v = ttest, lty=2, col = "blue")
#' # text(-2.5, 0.3, expression(bold("Critical point")))
#' # arrows(ttab[1] ,0.14, -2.3, 0.27)
#' # text(2.5, 0.3, expression(bold("Critical point")))
#' # arrows(ttab[2] ,0.14, 2.3, 0.27)
#' # aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' # axis(side = 1, at = c(ttab[1],ttab[2]), font = 2, labels = FALSE,
#' # col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#' # axis(side=1, at=as.character(c( - 4, ttab[1])), tick = TRUE, lwd = 1,
#' # col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' # axis(side=1, at=as.character(c(ttab[2], + 4)), tick = TRUE, lwd = 1,
#' # col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' # axis(side = 1, at = c(ttab[1],ttab[2]), lwd = 0,
#' # col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#' # axis(side = 1, at = ttest, lwd = 0,
#' # col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = aux2)
#' # axis(side = 1, at = ttest, tick = TRUE, lwd = 1,
#' # col="blue", lwd.ticks = 1, labels = FALSE)
#' # title("Test of hypothesis: T-Test.")
#' # text(0,0.1, expression(bold("ACCEPT H0" )))
#' # text(ttab[1] - 1 , 0.1, expression(bold("RRH0")))
#' # text(ttab[2] + 1 ,0.1, expression(bold("RRH0")))
#' # arrows(ttest, 0.27, -1.5, 0.33)
#' # text(-1.7, 0.35, expression(bold("ttest")))
#' # mtext("Step 1: Hypothesis", side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' # mtext(text = nullhyp , side = 1, line = 4, adj = 0)
#' # mtext(text = althyp , side = 1, line = 5, adj = 0)
#' #
#' # mtext("Step 2: Significante level", side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' # mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' # mtext(text = signlevel , side = 1, line = 7, adj = 0)
#' #
#' # mtext("Step 3: Rule of decision", side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' # mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' # mtext(decisionplot, side = 1, line = 4, adj = 1)
#' #
#' # mtext("Step 4: Conclusion", side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' # mtext(conclusionplot, side = 1, line = 7, adj = 1)
#' # }
#' # }
#' # if (any(alternative == c("less", "l", "L"))) {
#' # if (is.null(y)) {
#' # title <- paste(gettext(" One Sample t-test (Less test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu = ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # althyp <- paste(gettext(" H1: mu != ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' # sep = "")
#' # n <- length(x)
#' # ttest <- round((mean(x) - h0) / (nu /sqrt(n)), 2)
#' # ttab <- round(dt(df = nu, 1 - alpha), 2)
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df = nu, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # "|")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("H0 was rejected.", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = |", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]), "|")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("No evidence to reject H0.", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # else{
#' # n1 <- length(x)
#' # n2 <- length(y)
#' # df <- n1+n2-2
#' # sp <- ((n1-1)*var(x) + (n2-1)*var(y))/df
#' # title <- paste(gettext(" Two Sample t-test (Less test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu1 >= mu2", domain = "R-leem"),
#' # sep = "")
#' # althyp <- paste(gettext(" H1: mu1 < mu2", domain = "R-leem"),
#' # sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' # sep = "")
#' # ttest <- round((mean(x) - mean(y)) / sqrt(sp*(1/n1+1/n2)), 2)
#' # ttab <- round(dt(df, 1 - alpha), 2)
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]), '|')
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" H0 was rejected", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]), '|')
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" No evidence to reject the H0 ", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # if (plot == TRUE) {
#' # par(mar = c(10,4,4,4))
#' # x <- seq(- 4 , ttab[1], by = 0.01)
#' # y <- seq(ttab[1],+ 4, by = 0.01)
#' # fx <- dt(x, df = nu)
#' # fy <- dt(y, df = nu)
#' # curve(dt(x, df = nu), - 4 , + 4 ,
#' # ylim = c(0, 1.2*max(fx,fy)), ylab = expression(f[X](x)), xlab="X",
#' # panel.first = grid(col="gray90"), lwd = 5)
#' # polygon(c(y, rev(y)),
#' # c(fy, rep(0, length(fy))),
#' # col="#99ccff")
#' # polygon(c(x, rev(x)),
#' # c(fx, rep(0, length(fx))),
#' # col="#cc0000")
#' # abline(v = ttab[1], lty=2, col = "red")
#' # abline(v = ttest, lty=2, col = "blue")
#' # text(-2.5, 0.3, expression(bold("Critical point")))
#' # arrows(ttab[1] ,0.14, -2.1, 0.28)
#' # aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' #
#' #
#' # axis(side = 1, at = c(ttab[1], 4), font = 2, labels = FALSE, lwd.ticks = 0,
#' # col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#' # axis(side=1, at=as.character(c( -4, ttab[1])),
#' # col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' # axis(side=1, at=as.character(c( "", ttab[1])), tick = TRUE, labels = FALSE,
#' # lwd.ticks = 1, col="#cc0000")
#' # axis(side = 1, at = c("",ttab[1]), lwd = 0,
#' # col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#' # axis(side = 1, at = ttest, lwd = 0,
#' # col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = aux2)
#' # axis(side = 1, at = ttest, tick = TRUE, lwd = 1,
#' # col="blue", lwd.ticks = 1, labels = FALSE)
#' #
#' #
#' # title("Test of hypothesis: T-Test.")
#' # text(0, 0.1, expression(bold("ACCEPT H0")))
#' # text(-2.5, 0.1, expression(bold("RRH0")))
#' # arrows(ttest , 0.27, -2.1, 0.38)
#' # text(-2.3, 0.4, expression(bold("ttest")))
#' # mtext("Step 1: Hypothesis", side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' # mtext(text = nullhyp , side = 1, line = 4, adj = 0)
#' # mtext(text = althyp , side = 1, line = 5, adj = 0)
#' #
#' # mtext("Step 2: Significante level", side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' # mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' # mtext(text = signlevel , side = 1, line = 7, adj = 0)
#' #
#' # mtext("Step 3: Rule of decision", side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' # mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' # mtext(decisionplot, side = 1, line = 4, adj = 1)
#' #
#' # mtext("Step 4: Conclusion", side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' # mtext(conclusionplot, side = 1, line = 7, adj = 1)
#' # }
#' # }
#' # if (any(alternative == c("greater", "g", "G"))) {
#' # if (is.null(y)) {
#' # title <- paste(gettext(" One Sample t-test (Greater test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu = ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # althyp <- paste(gettext(" H1: mu != ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' # sep = "")
#' # n <- length(x)
#' # ttest <- round((mean(x) - h0) / (nu /sqrt(n)), 2)
#' # ttab <- round(qt(df = nu,1 - alpha), 2)
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df = nu, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),"|")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("H0 was rejected.", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),'|')
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("No evidence to reject the H0.", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # else{
#' # n1 <- length(x)
#' # n2 <- length(y)
#' # df <- n1+n2-2
#' # sp <- ((n1-1)*var(x) + (n2-1)*var(y))/df
#' # title <- paste(gettext(" Two Sample z-test (Greater test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu1 <= mu2", domain = "R-leem"),
#' # sep = "")
#' # althyp <- paste(gettext(" H1: mu1 > mu2", domain = "R-leem"),
#' # sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' # sep = "")
#' # ttest <- round((mean(x) - mean(y)) / sqrt(sp*(1/n1+1/n2)), 2)
#' # ttab <- round(dt(df, 1 - alpha), 2)
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]), '|')
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" H0 was rejected", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]), '|')
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" No evidence to reject the H0 ", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # if(plot == TRUE){
#' # par(mar = c(10,4,4,4))
#' # x <- seq(- 4 , ttab[2], by = 0.01)
#' # y <- seq(ttab[2],+ 4, by = 0.01)
#' # fx <- dt(x, df = nu)
#' # fy <- dt(y, df = nu)
#' # curve(dt(x, df = nu), - 4 , + 4 ,
#' # ylim = c(0, 1.2*max(fx,fy)), ylab = expression(f[X](x)), xlab="X",
#' # panel.first = grid(col="gray90"), lwd = 5)
#' # polygon(c(y, rev(y)),
#' # c(fy, rep(0, length(fy))),
#' # col="#cc0000")
#' # polygon(c(x, rev(x)),
#' # c(fx, rep(0, length(fx))),
#' # col="#559ee8")
#' # abline(v = ttab[2], lty=2, col = "red")
#' # abline(v = ttest, lty=2, col = "blue")
#' # text(2.5, 0.3, expression(bold("Critical point")))
#' # arrows(ttab[2] ,0.14,2.3, 0.27)
#' # aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' #
#' #
#' #
#' # axis(side = 1, at = c(-4, ttab[2]), font = 2, labels = FALSE,
#' # lwd.ticks = 0, col = "#559ee8")
#' #
#' # axis(side=1, at=as.character(c( ttab[2], 4)), tick = TRUE, labels = FALSE,
#' # lwd.ticks = 0,col="#cc0000")
#' #
#' # axis(side=1, at=as.character(c( "", ttab[2])), tick = TRUE, labels = FALSE,
#' # lwd.ticks = 1, col="#cc0000")
#' #
#' # axis(side = 1, at = c("",ttab[2]), lwd = 0,
#' # col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#' #
#' #
#' # axis(side = 1, at = ttest, lwd = 0,
#' # col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = aux2)
#' # axis(side = 1, at = ttest, tick = TRUE, lwd = 1,
#' # col="blue", lwd.ticks = 1, labels = FALSE)
#' #
#' #
#' #
#' # title("Test of hypothesis: T-Test.")
#' # text(0, 0.1, expression(bold("ACCEPT H0")))
#' # text(2.5, 0.1, expression(bold("RRH0")))
#' # arrows(ttest ,0.27, -2, 0.37)
#' # text(-2, 0.4, expression(bold("ttest")))
#' # mtext("Step 1: Hypothesis", side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' # mtext(text = nullhyp , side = 1, line = 4, adj = 0)
#' # mtext(text = althyp , side = 1, line = 5, adj = 0)
#' #
#' # mtext("Step 2: Significante level", side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' # mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' # mtext(text = signlevel , side = 1, line = 7, adj = 0)
#' #
#' # mtext("Step 3: Rule of decision", side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' # mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' # mtext(decisionplot, side = 1, line = 4, adj = 1)
#' #
#' # mtext("Step 4: Conclusion", side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' # mtext(conclusionplot, side = 1, line = 7, adj = 1)
#' # }
#' # }
#' # }
#' # if (any(test == c("chisqtest", "chisq", "CHI", "chisquared"))) {
#' # if (any(alternative == c("less", "l", "L"))) {
#' # if (is.null(y)) {
#' # aux_x <- x
#' # sd <- sd(x)
#' # df <- length(x)-1
#' # if (missing(h0)) {
#' # h0 <- readline("Insert the value of null hypothesis: ")
#' # h0 <- as.numeric(h0)
#' # }
#' # if (!any(names(argaddit) == "s")) {
#' # s <- readline("Insert the value of population variance: ")
#' # s <- as.numeric(s)
#' # } else s <- argaddit$s
#' # title <- paste(gettext(" One Sample Chi-Squared Test (Unilateral Test) \n", domain = "R-leem"))
#' #
#' #
#' # nullhyp <- paste(gettext(" H0: sigma^2 = ", domain = "R-leem"), round(h0, 2), sep = "")
#' # althyp <- paste(gettext(" H1: sigma^2 != ", domain = "R-leem"), round(h0, 2), sep = "")
#' # signlevel <- paste(gettext(" Alpha = ", domain = "R-leem"), round(alpha, 2), sep = "")
#' #
#' #
#' # chitest <- round((df*s)/h0, 2)
#' # chitab <- round(qchisq((1-alpha), df, lower.tail = FALSE), 2)
#' # pvalue <- 2 * pchisq(abs(chitest), df, lower.tail = FALSE)
#' # if (abs(chitest) <= abs(chitab)) {
#' # decision <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | < | CP = ", abs(chitab),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < Alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | < | CP = ", abs(chitab), '|')
#' # conclusion <- paste(gettext(" We observed by the Chi-Squared Test that hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("H0 was rejected.", domain = "R-leem"))
#' #
#' # } else {
#' # decision <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | > | CP = ", abs(chitab),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > Alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | > | CP = ", abs(chitab), '|')
#' # conclusion <- paste(gettext(" We observed by the Chi-Squared Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("No evidence to reject H0.", domain = "R-leem"))
#' # }
#' # results <- list(chitest = chitest, chitab = chitab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # else{
#' # stop("Em desenvolvimento", .call = FALSE, domain = "R-leem")
#' # }
#' # if (plot == TRUE) {
#' # par(mar = c(11,4,4,4))
#' # minimo <- if (chitest <= (-4) * df) chitest - 4 * df else 0
#' # maximo <- if (chitest > 4 * df) chitest + 4 * df else 4 * df
#' # x <- seq(minimo, chitab, by = 0.01)
#' # y <- seq(chitab, maximo, by = 0.01)
#' # fx <- dchisq(x, df)
#' # fy <- dchisq(y, df)
#' # main <- substitute(atop(bold("One Sample Chi-Squared Test (Unilateral Test)"),chi[c]^2 == frac((n-1)*s^2,sigma^2)), list(h0 = h0))
#' # curve(dchisq(x, df), minimo, maximo,
#' # ylim = c(0, 1.2*max(fx,fy)), ylab = expression(f[X](x)), xlab="",
#' # panel.first = grid(col="gray90"), main = main)
#' # polygon(c(y, rev(y)),
#' # c(fy, rep(0, length(fy))),
#' # col="#99ccff")
#' # polygon(c(x, rev(x)),
#' # c(fx, rep(0, length(fx))),
#' # col="gray")
#' # abline(v = chitab, lty=2, col = "#880000")
#' #
#' #
#' # #text(chitab, 0.8*max(fx,fy), expression(bold("CRITICAL POINT")), col = "#880000")
#' # #text(chitest, 0.8*max(fx,fy), expression(bold("CHISQTEST")), col = "blue")
#' # legend(chitest, 0.8*max(fx, fy), bg = "#010199", cex=0.8, box.col = "#010199",
#' # legend = expression(bold("STATISTICAL TEST(ST) ")), text.col = "white")
#' # legend(chitab, 0.9*max(fx, fy), bg = "#880000", cex=0.8, box.col = "#880000",
#' # legend = expression(bold("CRITICAL POINT(CP) ")), text.col = "white")
#' #
#' #
#' # abline(v = chitest, lty=2, col = "#010199")
#' # aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' # axis(side = 1, at = as.character(c(0, chitab)),
#' # col = "#888888", col.axis = "#888888", labels = FALSE)
#' # axis(side = 1, at = as.character(c(chitab, auxmaximo*10)),
#' # col = "#559ee8", col.axis = "#559ee8", labels = FALSE)
#' # axis(side = 1, at = chitab, tick = TRUE,
#' # col.ticks = "#880000", lwd.ticks = 1, labels = FALSE)
#' # axis(side = 1, at = chitab, tick = FALSE,
#' # font = 2, col.axis="#880000", pos = aux2)
#' # axis(side = 1, at = chitest, tick = FALSE,
#' # font = 2, col.axis="#010199", pos = aux2)
#' # axis(side = 1, at = chitest, tick = TRUE,
#' # col.ticks = "#010199", lwd.ticks = 1, labels = FALSE)
#' #
#' #
#' # legend("topleft", cex = 0.9, box.col = "black", bg = "#e0e0e0",
#' # legend = c("REJECT H0", "ACCEPT H0"), fill = c("gray", "#559ee8"))
#' #
#' #
#' #
#' # mtext("Step 1: Hypothesis", side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' # mtext(text = substitute(~~H[0]:~sigma^2 >= h0, list(h0 = h0)) , side = 1, line = 4.3, adj = 0)
#' # mtext(text =substitute(~~H[1]:~sigma^2 < h0, list(h0 = h0)), side = 1, line = 5.3, adj = 0)
#' # mtext("Step 2: Significante level", side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' # mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' # mtext(text = signlevel , side = 1, line = 7, adj = 0)
#' #
#' # mtext("Step 3: Rule of decision", side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' # mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' # mtext(decisionplot, side = 1, line = 4.3, adj = 1)
#' #
#' # mtext("Step 4: Conclusion", side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' # mtext(conclusionplot, side = 1, line = 7, adj = 1)
#' # }
#' #
#' # }
#' # if (any(alternative == c("greater", "g", "G"))) {
#' # if (is.null(y)) {
#' # aux_x <- x
#' # sd <- sd(x)
#' # df <- length(x)-1
#' # if (missing(h0)) {
#' # h0 <- readline("Insert the value of null hypothesis: ")
#' # h0 <- as.numeric(h0)
#' # }
#' # if (!any(names(argaddit) == "s")) {
#' # s <- readline("Insert the value of population variance: ")
#' # s <- as.numeric(s)
#' # } else s <- argaddit$s
#' # title <- paste(gettext(" One Sample Chi-Squared Test(Unilateral Test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: sgima^2 = ", domain = "R-leem"), round(h0, 2), sep = "")
#' # althyp <- paste(gettext(" H1: sigma^2 != ", domain = "R-leem"), round(h0, 2), sep = "")
#' # signlevel <- paste(gettext(" Alpha = ", domain = "R-leem"), round(alpha, 2), sep = "")
#' #
#' # chitest <- round((df*s)/h0, 2)
#' # chitab <- round(qchisq(1 - alpha, df), 2)
#' # pvalue <- 2 * pchisq(abs(chitest), df, lower.tail = TRUE)
#' # if (abs(chitest) >= abs(chitab)) {
#' # decision <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | > | CP = ", abs(chitab),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < Alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | > | CP = ", abs(chitab), '|')
#' # conclusion <- paste(gettext(" We observed by the Chi-Squared Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("H0 was rejected.", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | < | CP = ", abs(chitab),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > Alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | < | CP = ", abs(chitab), '|')
#' # conclusion <- paste(gettext(" We observed by the Chi-Squared Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("No evidence to reject H0.", domain = "R-leem"))
#' # }
#' # } else{
#' # stop("Em desenvolvimento", .call = FALSE, domain = "R-leem")
#' # }
#' # results <- list(chitest = chitest, chitab = chitab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # if (plot == TRUE) {
#' # par(mar = c(11,4,4,4))
#' # main <- substitute(atop(bold("One Sample Chi-Squared Test (Greater Test)"),chi[c]^2 == frac((n-1)*s^2,sigma^2)), list(h0 = h0))
#' # minimo <- if (chitest <= (-4) * df) chitest - 4 * df else 0
#' # maximo <- if (chitest > 4 * df) chitest + 4 * df else 4 * df
#' # x <- seq(minimo, chitab, by = 0.01)
#' # y <- seq(chitab, maximo, by = 0.01)
#' # fx <- dchisq(x, df)
#' # fy <- dchisq(y, df)
#' # curve(dchisq(x, df), minimo, maximo,
#' # ylim = c(0, 1.2*max(fx,fy)), ylab = expression(f[X](x)), xlab="X",
#' # panel.first = grid(col="gray90"), main = main)
#' # polygon(c(y, rev(y)),
#' # c(fy, rep(0, length(fy))),
#' # col="gray")
#' # polygon(c(x, rev(x)),
#' # c(fx, rep(0, length(fx))),
#' # col="#99ccff")
#' # abline(v = chitab, lty=2, col = "#880000")
#' #
#' #
#' # #text(chitab, 0.8*max(fx,fy), expression(bold("CRITICAL POINT")), col = "#880000")
#' # #text(chitest, 0.8*max(fx,fy), expression(bold("CHISQTEST")), col = "blue")
#' # legend(chitest, 0.8*max(fx, fy), bg = "#010199", cex=0.8, box.col = "#010199",
#' # legend = expression(bold("STATISTICAL TEST(ST) ")), text.col = "white")
#' # legend(chitab, 0.9*max(fx, fy), bg = "#880000", cex=0.8, box.col = "#880000",
#' # legend = expression(bold("CRITICAL POINT(CP) ")), text.col = "white")
#' #
#' #
#' # abline(v = chitest, lty=2, col = "#010199")
#' # aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' # axis(side = 1, at = as.character(c(0, chitab)),
#' # col = "#888888", col.axis = "#888888", labels = FALSE)
#' # axis(side = 1, at = as.character(c(chitab, auxmaximo*10)),
#' # col = "#559ee8", col.axis = "#559ee8", labels = FALSE)
#' # axis(side = 1, at = chitab, tick = TRUE,
#' # col.ticks = "#880000", lwd.ticks = 1, labels = FALSE)
#' # axis(side = 1, at = chitab, tick = FALSE,
#' # font = 2, col.axis="#880000", pos = aux2)
#' # axis(side = 1, at = chitest, tick = FALSE,
#' # font = 2, col.axis="#010199", pos = aux2)
#' # axis(side = 1, at = chitest, tick = TRUE,
#' # col.ticks = "#010199", lwd.ticks = 1, labels = FALSE)
#' #
#' #
#' # legend("topleft", cex = 0.9, box.col = "black", bg = "#e0e0e0",
#' # legend = c("REJECT H0", "ACCEPT H0"), fill = c("gray", "#559ee8"))
#' #
#' #
#' #
#' # mtext("Step 1: Hypothesis", side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' # mtext(text = substitute(~~H[0]:~sigma^2 <= h0, list(h0 = h0)) , side = 1, line = 4.3, adj = 0)
#' # mtext(text =substitute(~~H[1]:~sigma^2 > h0, list(h0 = h0)), side = 1, line = 5.3, adj = 0)
#' #
#' # mtext("Step 2: Significante level", side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' # mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' # mtext(text = signlevel , side = 1, line = 7, adj = 0)
#' #
#' # mtext("Step 3: Rule of decision", side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' # mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' # mtext(decisionplot, side = 1, line = 4, adj = 1)
#' #
#' # mtext("Step 4: Conclusion", side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' # mtext(conclusionplot, side = 1, line = 7, adj = 1)
#' # }
#' # }
#' # }
#' # if (any(test == c("ftest", "f", "F"))){
#' #
#' # stop("Em desenvolvimento", .call = FALSE, domain = "R-leem")
#' # }
#' attr(results, "output") <- "htest"
#' class(results) <- "leem"
#' results
#' }
#'
#'
#'
#'
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#' #' Test of hypothesis
#' #'
#' #' Performs hypothesis testing for various parameters of one or more populations
#' #'
#' #' @param x R object. See in details.
#' #' @param y an optional (non-empty) numeric vector of data values.
#' #' @param test character value. The options are: \code{"ttest"}, \code{"ztest"}, \code{"ptest"}, \code{"chitest"}, \code{"ftest"}, \code{"anova"}, \code{"friedman"}, \code{"kruskal"}, \code{"mann whitney"}.
#' #' @param h0 numeric value. The hypothesized parameter.
#' #' @param prop a logical indicating whether you want to use the proportion test of not. Default is \code{prop=FALSE}.
#' #' @param alternative a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.
#' #' @param alpha significance level of the test
#' #' @param exact a logical indicating whether you want to use the exact test or not. Default is \code{exact=TRUE}.
#' #' @param correct a logical indicating whether Yates' continuity correction should be applied where possible. This argument must be used when \code{exact = FALSE}.
#' #' @param paired a logical indicating whether you want a paired t-test. Valid only for \code{test="ttest"}.
#' #' @param paired a logical indicating whether you want a paired t-test. Valid only for \code{test="ttest"}.
#' #' @param plot a logical indicating whether you want a graph indicating the regions of rejection or not of the null hypothesis, as well as the test decision.
#' #' @examples
#' #' # Null hypothesis
#' #' nullhyp <- h0 <- 90
#' #' # Simulation
#' #' set.seed(10)
#' #' data <- rnorm(30, 100, 10)
#' #' # Test of hypothesis
#' #' th(data, h0 = h0, sd = 10, plot = TRUE)
#' #'
#' #' @import crayon
#' #' @export
#' th <- function(x, y = NULL, test = "ztest", h0, prop = FALSE,
#' delta = 0, p, pa,
#' alternative = c("two.sided","L", "less", "greater","G"),
#' alpha = 0.05, exact = TRUE,
#' correct = FALSE, paired = FALSE, plot = FALSE, ...) {
#'
#' alternative <- match.arg(alternative)
#' argaddit <- list(...)
#'
#' if (missing(x)) {
#' xfile <- file.choose(new = TRUE)
#' x <- read.table(xfile, header = TRUE)
#' }
#' if (any(test == c("ztest", "z", "Z", "normal"))) {
#' if(prop == TRUE){
#' if (!any(names(argaddit) == "pa")) {
#' pa <- readline("Insert the value of population sample part? ")
#' pa <- as.numeric(pa)
#' } else pa <- argaddit$pa
#' if (missing(p)) {
#' p <- readline("Insert the value of proportion? ")
#' p <- as.numeric(p)
#' }else p <- argaddit$p
#' }else{
#' if (is.null(y)) {
#' if (!any(names(argaddit) == "sd")) {
#' sdev <- readline(paste0(gettext("Enter the value of population standard deviation:", domain = "R-leem"), " "))
#' sdev <- as.numeric(sdev)
#' } else sdev <- argaddit$sd
#' if (missing(h0)) {
#' h0 <- readline(paste0(gettext("Enter the value of null hypothesis:"), " "))
#' h0 <- as.numeric(h0)
#' }
#' } else {
#' if (!any(names(argaddit) == "sd")) {
#' sdev <- c(as.numeric(readline(paste0(gettext("Enter the standard deviation value of population 1:")), " ")),
#' as.numeric(readline(paste0(gettext("Enter the standard deviation value of population 2:")), " ")))
#' } else if(length(argaddit$sd) < 1){
#' sdev <- c(as.numeric(readline(paste0(gettext("Enter the standard deviation value of population 1:")), " ")),
#' as.numeric(readline(paste0(gettext("Enter the standard deviation value of population 2:")), " ")))
#' } else sdev <- argaddit$sd
#' if (sdev[1] > length(x) || sdev[2] > length(y)){
#' stop("Incorrect standard deviantion argument for 2 populations", call. = FALSE, domain = "R-leem")
#' }
#' if ((length(x) > length(y) && sdev[1] <= sdev[2])||((length(x) < length(y) && sdev[1] >= sdev[2]))){
#' stop("Incorrect standard deviantion argument for 2 populations", call. = FALSE, domain = "R-leem")
#' }
#' }
#' }
#' if (any(alternative == c("two.sided", "t", "T"))) {
#' if (is.null(y)) {
#' if (prop == TRUE) {
#' title <- paste(gettext(" One Sample z-test proportion (Two-sided test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext(" H0: p= ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' althyp <- paste(gettext(" H1: p != ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' pa <- pa/n
#' ztest <- round( (( pa - p ) / ( sqrt( (p * ( 1-p) ) / n ) )) , 2)
#' ztab <- round(qnorm(1 - (alpha)/2), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' h0 <- p
#' } else {
#' title <- paste(" ", gettext("One Sample z-test (Two-sided test)", domain = "R-leem"), "\n")
#' nullhyp <- paste(" ", gettext("H0: mu = ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' althyp <- paste(" ", gettext("H1: mu != ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' signlevel <- paste(" ", gettext("alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' ztest <- round((mean(x) - h0) / (sdev /sqrt(n)), 2)
#' ztab <- round(qnorm(1 - (alpha)/2), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' }
#' if (ztest >= ztab[2]) {
#' decision <- paste(gettext("As ztest = ", domain = "R-leem"),
#' ztest, " > |ztab =", abs(ztab[2]), " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext("As ztest =", domain = "R-leem"), " ",
#' ztest, " > ztab =", ztab[2])
#' decision2 <- paste(gettext("As p-value = ", domain = "R-leem"),
#' round(pvalue, 5), " < alpha = ", alpha, " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = " ")
#' conclusion <- paste(gettext("We observed by the Z Test that the null hypothesis was rejected, at the significance level of", domain = "R-leem"),
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = " ")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#' } else {
#' decision <- paste(" ", gettext("As ztest =", domain = "R-leem"), " ",
#' abs(ztest), " < ztab = ", abs(ztab[2]), " ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(" ", gettext("As ztest =", domain = "R-leem"),
#' ztest, " < ztab = ", ztab[2])
#' decision2 <- paste(" ", gettext("As p-value =", domain = "R-leem"), " ",
#' round(pvalue, 5), " ", "> alpha = ", alpha,
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' conclusion <- paste(" ", gettext("We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of", domain = "R-leem"), " ",
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#' }
#' else {
#' title <- paste(gettext(" two Sample z-test (Two-sided test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext(" H0: mu1 = mu2 ", domain = "R-leem"),sep ="")
#' althyp <- paste(gettext(" H1: mu1 != mu2", domain = "R-leem"),sep ="")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha ,2),sep = "")
#' n <- length(x)
#' n1 <- length(y)
#' ztest <- round(((mean(x) - mean(y))/sqrt(((sdev[1]^2)/n)-((sdev[2]^2)/n1))), 2)
#' ztab <- round(qnorm(1 - (alpha)/2), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' if (abs(ztest) >= abs(ztab[2])) {
#' decision <- paste(gettext("As ztest = ", domain = "R-leem"),
#' abs(ztest), "| > |ztab = ", abs(ztab[2]),
#' gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' pvalue, " < alpha = ", alpha,
#' gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| > |ztab = ", abs(ztab[2]), '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#' } else {
#' decision <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| < |ztab = ", abs(ztab[2]),
#' gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' pvalue, " > alpha = ", alpha,
#' gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| < |ztab = ", abs(ztab[2]), '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#' }
#' if (plot == TRUE) {
#' par(mar = c(10,4,4,4))
#' x <- seq(- 4 * 1, ztab[1], by = 0.01)
#' z <- seq(ztab[2], 4, by = 0.01)
#' y <- seq( - 4, + 4, by = 0.01)
#' fx <- dnorm(x, mean = 0, sd = 1)
#' fz <- dnorm(z,mean = 0, sd = 1)
#' fy <- dnorm(y, mean = 0, sd = 1)
#' curve(dnorm(x, mean = 0, sd = 1), - 4 , + 4 ,
#' ylim = c(0.0, 1.2 * max(fx,fy,fz)), xlab = "",
#' ylab = "", lwd = 5, axes = FALSE)
#' polygon(c(y, rev(y)),
#' c(fy, rep(0, length(fy))),
#' col="#99ccff")
#' polygon(c(x, rev(x)),
#' c(fx, rep(0, length(fx))),
#' col="#cc0000")
#' polygon(c(z,rev(z)), c(fz,rep(0,length(fz))),
#' col="#cc0000" )
#' abline(v = ztab[1], lty=2, col = "#cc0000")
#' abline(v = ztab[2], lty=2, col = "#cc0000")
#' abline(v = ztest, lty=2, col = "blue")
#' cpoint <- gettext("Critical point", domain = "R-leem")
#' text(-2.5, 0.3, substitute(bold(cpoint), list(cpoint = cpoint)))
#' arrows(ztab[1], 0.14, -2.3, 0.27, length = 0.15)
#' text(2.5, 0.3, substitute(bold(cpoint), list(cpoint = cpoint)))
#' arrows(ztab[2] ,0.14,2.3, 0.27, length = 0.15)
#' testatistico <- gettext("test \nstatistic", domain = "R-leem")
#' text(ztest, 0.4, substitute(bold(testatistico), list(testatistico = testatistico)), col = "blue")
#' aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' #aux1 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/10000
#' axis(side = 1, at = c(ztab[1],ztab[2]), font = 2, labels = FALSE,
#' col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#' axis(side=1, at=as.character(c( - 4, ztab[1])), tick = TRUE, lwd = 1,
#' col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' axis(side=1, at=as.character(c(ztab[2], + 4)), tick = TRUE, lwd = 1,
#' col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' axis(side = 1, at = c(ztab[1],ztab[2]), lwd = 0,
#' col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#' axis(side = 1, at = ztest, lwd = 0,
#' col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = -0.001)
#' axis(side = 1, at = ztest, tick = TRUE, lwd = 1,
#' col="blue", lwd.ticks = 1, labels = FALSE)
#'
#' if (prop == TRUE) {
#' titulo <- gettext("Test of proportion: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' } else {
#' titulo <- gettext("Test of hypothesis: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' }
#' aceitah0 <- gettext("ACCEPT", domain = "R-leem")
#' text(0,0.1,substitute(bold(aceitah0)~H[0], list(aceitah0 = aceitah0)), font = 2)
#' text(ztab[1] - 1 , 0.1, expression("RR"*H[0]), font = 2)
#' text(ztab[2] + 1 ,0.1,expression("RR"*H[0]), font = 2)
#' passo1 <- gettext("Step 1: Hypothesis", domain = "R-leem")
#' mtext(substitute(passo1, list(passo1 = passo1)), side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' mtext(text = substitute(H[0]:~mu==h0,list(h0 = round(h0, 2))), side = 1, line = 4.2, adj = 0.05)
#' mtext(text = substitute(H[1]:~mu!=h0,list(h0 = round(h0, 2))), side = 1, line = 5, adj = 0.05)
#' passo2 <- gettext("Step 2: Significante level", domain = "R-leem")
#' mtext(substitute(passo2, list(passo2 = passo2)), side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' mtext(text = substitute(alpha==alfa,list(alfa = round(alpha, 2))), side = 1, line = 7, adj = 0.05)
#' passo3 <- gettext("Step 3: Rule of decision", domain = "R-leem")
#' mtext(substitute(passo3, list(passo3 = passo3)), side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' mtext(decisionplot, side = 1, line = 4, adj = 1)
#' passo4 <- gettext("Step 4: Conclusion", domain = "R-leem")
#' mtext(substitute(passo4, list(passo4 = passo4)), side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' if (abs(ztest) >= abs(ztab[2])) {
#' mtext(substitute(H[0]~conclusionplot, list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' } else {
#' mtext(substitute(conclusionplot~H[0], list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' }
#'
#' }
#' }
#' if (any(alternative == c("less", "l", "L"))) {
#' if (is.null(y)) {
#' if (prop == TRUE) {
#' title <- paste(gettext("One Sample z-test proportion (Less test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext("H0: p >= ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' althyp <- paste(gettext(" H1: p < ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' pa <- pa/n
#' ztest <- round( (( pa - p ) / ( sqrt( (p * ( 1-p) ) / n ) )) , 2)
#' ztab <- round(qnorm(1 - (alpha)), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = T)
#' h0 <- p
#' } else {
#' title <- paste(gettext("One Sample z-test (Less test)", domain = "R-leem"), "\n")
#' nullhyp <- paste(" ", gettext("H0: mu >= ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' althyp <- paste(" ", gettext("H1: mu < ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' signlevel <- paste(" ", gettext("alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' ztest <- round((mean(x) - h0) / (sdev /sqrt(n)), 2)
#' ztab <- round(qnorm(1 - alpha), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' }
#' if (abs(ztest) >= abs(ztab[2])) {
#' decision <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| > |ztab = ", abs(ztab[2]), "| ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' round(pvalue, 5), " < alpha = ", alpha,
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' ztest, "| > |ztab = ", ztab[1], '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#'
#' } else {
#' decision <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| < |ztab = ", abs(ztab[2]),
#' "| ", gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' round(pvalue, 5), " > alpha = ", alpha, "| ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' ztest, "| < |ztab = ", ztab[1], '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#' }
#' else{
#' title <- paste(gettext(" two Sample z-test (Less-sided test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext(" H0: mu1 >= mu2 ", domain = "R-leem"),sep ="")
#' althyp <- paste(gettext(" H1: mu1 < mu2", domain = "R-leem"),sep ="")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha ,2),sep = "")
#' n <- length(x)
#' n1 <- length(y)
#' ztest <- round((mean(x) - mean(y)) /sqrt((sdev[1]^2/n)-(sdev[2]^2 /n1)), 2)
#' ztab <- round(qnorm(1 - (alpha)), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' if (abs(ztest) >= abs(ztab[2])) {
#' decision <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| > |ztab = ", abs(ztab[2]),
#' gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' pvalue, " < alpha = ", alpha,
#' gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' ztest, "| > |ztab = ", ztab[1], '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' } else {
#' decision <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' abs(ztest), "| < |ztab = ", abs(ztab[2]),
#' gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' pvalue, " > alpha = ", alpha,
#' gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext(" As |ztest = ", domain = "R-leem"),
#' ztest, "| < |ztab = ", ztab[1], '|')
#' conclusion <- paste(gettext(" We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#' }
#' if (plot == TRUE) {
#' par(mar = c(10,4,4,4))
#' x <- seq(- 4 , ztab[1], by = 0.01)
#' y <- seq(ztab[1],+ 4, by = 0.01)
#' fx <- dnorm(x, mean = 0, sd = 1)
#' fy <- dnorm(y, mean = 0, sd = 1)
#' curve(dnorm(x, mean = 0, sd = 1), - 4 , + 4 ,
#' ylim = c(0, 1.2*max(fx,fy)), xlab = "",
#' ylab = "", lwd = 5, axes = FALSE)
#' polygon(c(y, rev(y)),
#' c(fy, rep(0, length(fy))),
#' col="#99ccff")
#' polygon(c(x, rev(x)),
#' c(fx, rep(0, length(fx))),
#' col="#cc0000")
#' abline(v = ztab[1], lty=2, col = "red")
#' text(-2.5, 0.3, expression(bold("Critical point")))
#' arrows(ztab[1] ,0.14, -2.3, 0.28, , length = 0.15)
#' abline(v = ztest, lty=2, col = "blue")
#' aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#'
#'
#' axis(side = 1, at = c(ztab[1], 4), font = 2, labels = FALSE, lwd.ticks = 0,
#' col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#'
#' axis(side=1, at=as.character(c( -4, ztab[1])), tick = TRUE, lwd = 1,
#' col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#'
#' axis(side = 1, at = c("",ztab[1]), lwd = 0,
#' col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#'
#' axis(side=1, at=as.character(c( "", ztab[1])), tick = TRUE, labels = FALSE,
#' lwd.ticks = 1, col="#cc0000")
#'
#' axis(side = 1, at = ztest, lwd = 0,
#' col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = -0.001)
#' axis(side = 1, at = ztest, tick = TRUE, lwd = 1,
#' col="blue", lwd.ticks = 1, labels = FALSE)
#'
#'
#' if (prop == TRUE) {
#' titulo <- gettext("Test of proportion: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' } else {
#' titulo <- gettext("Test of hypothesis: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' }
#' aceitah0 <- gettext("ACCEPT", domain = "R-leem")
#' text(0,0.1,substitute(bold(aceitah0)~H[0], list(aceitah0 = aceitah0)), font = 2)
#' text(-2.5, 0.1, expression(bold("RRH0")))
#' arrows(ztest, 0.27, 1.7, 0.37, length = 0.15)
#' text(2, 0.39, expression(bold("ztest")))
#' passo01 <- gettext("Step 1: Hypothesis", domain = "R-leem")
#' mtext(substitute(passo01, list(passo01 = passo01)), side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' mtext(text = substitute(H[0]>=h0, list(h0=round(h0, 2))) , side = 1, line = 4.2, adj = 0.05)
#' mtext(text = substitute(H[1]<h0, list(h0=round(h0, 2))) , side = 1, line = 5, adj = 0.05)
#' passo02 <- gettext("Step 2: Significante level", domain = "R-leem")
#' mtext(substitute(passo02, list(passo02 = passo02)), side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' mtext(text = substitute(alpha == alfa, list(alfa = alpha)) , side = 1, line = 7, adj = 0.05)
#' passo03 <- gettext("Step 3: Rule of decision", domain = "R-leem")
#' mtext(substitute(passo03, list(passo03 = passo03)), side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' mtext(decisionplot, side = 1, line = 4, adj = 1)
#' passo04 <- gettext("Step 4: Conclusion", domain = "R-leem")
#' mtext(substitute(passo04, list(passo04 = passo04)), side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' if (abs(ztest) >= abs(ztab[2])) {
#' mtext(substitute(H[0]~conclusionplot, list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' } else {
#' mtext(substitute(conclusionplot~H[0], list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' }
#' }
#' }
#' if (any(alternative == c("greater", "g", "G"))) {
#' if (is.null(y)) {
#' if (prop == TRUE) {
#' title <- paste(gettext("One Sample z-test proportion (Greater test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext(" H0: p <= ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' althyp <- paste(gettext(" H1: p > ", domain = "R-leem"), round(p, 2),
#' sep = "")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' pa <- pa/n
#' ztest <- round( (( pa - p ) / ( sqrt( (p * ( 1-p) ) / n ) )) , 2)
#' ztab <- round(qnorm(1 - (alpha)), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = F)
#' h0 <- p
#' } else {
#' title <- paste(" ", gettext("One Sample z-test (Greater test)", domain = "R-leem"), " ")
#' nullhyp <- paste(gettext(" H0: mu <= ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' althyp <- paste(gettext(" H1: mu > ", domain = "R-leem"), round(h0, 2),
#' sep = "")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' sep = "")
#' n <- length(x)
#' ztest <- round((mean(x) - h0) / (sdev /sqrt(n)), 2)
#' ztab <- round(qnorm(1 - alpha), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = FALSE)
#' }
#' if (ztest >= ztab[2]) {
#' decision <- paste(" ", gettext("As ztest =", domain = "R-leem"), " ",
#' abs(ztest), " > ztab = ", abs(ztab[2]), " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decision2 <- paste(" ", gettext("As p-value =", domain = "R-leem"),
#' round(pvalue, 5), " < alpha =", alpha, " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(" ", gettext("As ztest =", domain = "R-leem"), " ",
#' ztest, "> ztab = ", ztab[2])
#' conclusion <- paste(" ", gettext("We observed by the Z Test that the null hypothesis was rejected, at the significance level of", domain = "R-leem"),
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#' } else {
#' decision <- paste(gettext("As ztest =", domain = "R-leem"), " ",
#' ztest, " < ztab = ", ztab[2], " ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext("As p-value =", domain = "R-leem"), " ",
#' round(pvalue, 5), " > alpha = ", alpha, " ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext("As ztest = ", domain = "R-leem"),
#' ztest, " < ztab = ", ztab[2])
#' conclusion <- paste(gettext("We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of", domain = "R-leem"),
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#' }
#' else {
#' title <- paste(gettext(" two Sample z-test (Greater-sided test) \n", domain = "R-leem"))
#' nullhyp <- paste(gettext(" H0: mu1 <= mu2 ", domain = "R-leem"),sep ="")
#' althyp <- paste(gettext(" H1: mu1 > mu2", domain = "R-leem"),sep ="")
#' signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha ,2),sep = "")
#' n <- length(x)
#' n1 <- length(y)
#' ztest <- round((mean(x) - mean(y)) /sqrt((sdev[1]^2/n)-(sdev[2]^2 /n1)), 2)
#' ztab <- round(qnorm(1 - (alpha)), 2)
#' ztab <- round(c(-ztab, ztab), 2)
#' pvalue <- 2 * pnorm(abs(ztest), lower.tail = TRUE)
#'
#' if (ztest >= ztab[2]) {
#' decision <- paste(" ", gettext("As ztest = ", domain = "R-leem"),
#' ztest, " > ztab = ", ztab[2], " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decision2 <- paste(gettext("As p-value = ", domain = "R-leem"),
#' round(pvalue, 5), " < alpha = ", alpha, " ",
#' gettext("then reject H0!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(" ", gettext("As ztest =", domain = "R-leem"),
#' ztest, " > ztab = ", ztab[2])
#' conclusion <- paste(gettext("We observed by the Z Test that the null hypothesis was rejected, at the significance level of", domain = "R-leem"),
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("No evidence to reject", domain = "R-leem"))
#' } else {
#' decision <- paste(" ", gettext("As ztest = ", domain = "R-leem"),
#' ztest, " < ztab = ", ztab[2], " ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decision2 <- paste(" ", gettext("As p-value = ", domain = "R-leem"),
#' round(pvalue, 5), " > alpha = ", alpha, " ",
#' gettext("then H0 is not rejected!", domain = "R-leem"), sep = "")
#' decisionplot <- paste(gettext("As ztest =", domain = "R-leem"), " ",
#' ztest, " < ztab = ", ztab[2])
#' conclusion <- paste(gettext("We observed by the Z Test that there is no evidence to reject the H0 hypothesis, at the significance level of", domain = "R-leem"),
#' " ", round(alpha * 100),
#' gettext("% probability", domain = "R-leem"), sep = "")
#' conclusionplot <- paste(gettext("was rejected", domain = "R-leem"))
#' }
#' results <- list(ztest = ztest, ztab = ztab, pvalue = pvalue, test = test,
#' alternative = alternative, title = title, nullhyp = nullhyp,
#' althyp = althyp, signlevel = signlevel, decision = decision,
#' decision2 = decision2, conclusion = conclusion)
#'
#' }
#' if (plot == TRUE) {
#' par(mar = c(10,4,4,4))
#' x <- seq(- 4 , ztab[2], by = 0.01)
#' y <- seq(ztab[2],+ 4, by = 0.01)
#' fx <- dnorm(x, mean = 0, sd = 1)
#' fy <- dnorm(y, mean = 0, sd = 1)
#' if (ztest >= 4) {
#' curve(dnorm(x, mean = 0, sd = 1), - 4 , ztest + 1,
#' ylim = c(0, 1.2*max(fx,fy)), ylab = "", xlab = "",
#' lwd = 5, axes = FALSE)
#' }
#' if (ztest <= -4) {
#' curve(dnorm(x, mean = 0, sd = 1), ztest - 1 , 4,
#' ylim = c(0, 1.2*max(fx,fy)), ylab = "", xlab = "",
#' lwd = 5, axes = FALSE)
#' }
#' if (ztest < 4 & ztest > -4) {
#' curve(dnorm(x, mean = 0, sd = 1), - 4 , 4,
#' ylim = c(0, 1.2*max(fx,fy)), ylab = "", xlab = "",
#' lwd = 5, axes = FALSE)
#' }
#'
#'
#' polygon(c(y, rev(y)),
#' c(fy, rep(0, length(fy))),
#' col="#cc0000")
#' polygon(c(x, rev(x)),
#' c(fx, rep(0, length(fx))),
#' col="#99ccff")
#' abline(v = ztab[2], lty=2, col = "red")
#' abline(v = ztest, lty=2, col = "blue")
#' pcritico <- gettext("Critical point", domain = "R-leem")
#' text(2.5, 0.3, substitute(bold(pcritico), list(pcritico = pcritico)))
#' arrows(ztab[2], 0.14, 2.3, 0.28, length = 0.10)
#' aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#'
#' if (ztest > 4) {
#' axis(side=1, at=as.character(c( ztab[2], ztest + 1)), tick = TRUE, lwd = 1,
#' col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' } else {
#' axis(side=1, at=as.character(c( ztab[2], 4)), tick = TRUE, lwd = 1,
#' col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' }
#'
#' if (ztest < -4) {
#' axis(side = 1, at = c(ztest - 1, ztab[2]), font = 2, labels = FALSE, lwd.ticks = 0,
#' col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#' } else {
#' axis(side = 1, at = c(-4, ztab[2]), font = 2, labels = FALSE, lwd.ticks = 0,
#' col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#' }
#'
#' axis(side = 1, at = c("",ztab[2]), lwd = 0,
#' col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#'
#' axis(side=1, at=as.character(c( "", ztab[2])), tick = TRUE, labels = FALSE,
#' lwd.ticks = 1, col="#cc0000")
#' axis(side = 1, at = ztest, lwd = 0,
#' col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = -0.001)
#' axis(side = 1, at = ztest, tick = TRUE, lwd = 1,
#' col="blue", lwd.ticks = 1, labels = FALSE)
#'
#'
#' if (prop == TRUE) {
#' titulo <- gettext("Test of proportion: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' } else {
#' titulo <- gettext("Test of hypothesis: Z-Test", domain = "R-leem")
#' title(substitute(titulo, list(titulo = titulo)))
#' }
#' aceitah0 <- gettext("ACCEPT", domain = "R-leem")
#' text(0,0.1,substitute(bold(aceitah0)~H[0], list(aceitah0 = aceitah0)), font = 2)
#' text(2.5, 0.1, expression(bold("RRH0")))
#' arrows(ztest, 0.1, 3, 0.37, length = 0.1)
#' text(3, 0.39, expression(bold("ztest")))
#' passo01 <- gettext("Step 1: Hypothesis", domain = "R-leem")
#' mtext(substitute(passo01, list(passo01 = passo01)), side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' mtext(text = substitute(H[0]<=h0, list(h0=round(h0, 2))) , side = 1, line = 4.2, adj = 0.05)
#' mtext(text = substitute(H[1]>h0, list(h0=round(h0, 2))) , side = 1, line = 5, adj = 0.05)
#' passo02 <- gettext("Step 2: Significante level", domain = "R-leem")
#' mtext(substitute(passo02, list(passo02 = passo02)), side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' mtext(text = substitute(alpha == alfa, list(alfa = alpha)) , side = 1, line = 7, adj = 0.05)
#' passo03 <- gettext("Step 3: Rule of decision", domain = "R-leem")
#' mtext(substitute(passo03, list(passo03 = passo03)), side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' mtext(decisionplot, side = 1, line = 4, adj = 1)
#' passo04 <- gettext("Step 4: Conclusion", domain = "R-leem")
#' mtext(substitute(passo04, list(passo04 = passo04)), side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' if (ztest >= ztab[2]) {
#' mtext(substitute(H[0]~conclusionplot, list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' } else {
#' mtext(substitute(conclusionplot~H[0], list(conclusionplot = conclusionplot)), side = 1, line = 7.1, adj = 1)
#' }
#' }
#' }
#' }
#' # if (any(test == c("ttest", "t", "T", "tstudent"))) {
#' # df <- length(x) - 1
#' # nu <- df
#' # nu <- as.numeric(nu)
#' # sdev <- df
#' # if (missing(h0)) {
#' # h0 <- readline("Insert the value of null hypothesis: ")
#' # h0 <- as.numeric(h0)
#' # }
#' # if (any(alternative == c("two.sided", "t", "T"))) {
#' # if (is.null(y)) {
#' # title <- paste(gettext(" One Sample t-test (Two-sided test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu = ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # althyp <- paste(gettext(" H1: mu != ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' # sep = "")
#' # n <- length(x)
#' # ttest <- round((mean(x) - h0) / (sdev /sqrt(n)), 2)
#' # if (alternative == "two.sided"){
#' # ttab <- round(qt(1 - (alpha)/2, df = nu), 2)
#' # } else {
#' # ttab <- round(qt(1 - alpha, df = nu), 2)
#' # }
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df = nu, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]), '|')
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("H0 was rejected.", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),"|")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("No evidence to reject the H0. ", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # else{
#' # n1 <- length(x)
#' # n2 <- length(y)
#' # if(n1 == n2){
#' # df <- n1+n2-2
#' # sp <- ((n1-1)*var(x) + (n2-1)*var(y))/df
#' # }else{
#' # df <- ((sd(x)^2/n1)^2 + 2*(sd(x)^2/n1)*(sd(y)^2/n2) + (sd(y)^2/n2)^2)/((((sd(x)^2/n1)^2)/(n1-1))+(((sd(y)^2/n2)^2)/(n2-1)))
#' # sp <- sqrt(((sd(x)^2)/n1)+((sd(y)^2)/n2))
#' # }
#' # title <- paste(gettext(" Two Sample t-test (Two-sided test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu1 = mu2", domain = "R-leem"), sep = "")
#' # althyp <- paste(gettext(" H1: mu1 != mu2", domain = "R-leem"), sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2), sep = "")
#' # ttest <- round((mean(x) - mean(y)) / sqrt(sp*(1/n1+1/n2)), 2)
#' # ttab <- round(qt(1 - (alpha)/2, df), 2)
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "" )
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]), '|')
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" H0 was rejected", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),"|")
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" No evidence to reject the H0 ", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # if (plot == TRUE) {
#' # par(mar = c(10,4,4,4))
#' # x <- seq(- 4 * 1, ttab[1], by = 0.01)
#' # z <- seq(ttab[2], 4, by = 0.01)
#' # y <- seq( - 4, + 4, by = 0.01)
#' # fx <- dt(x, df = nu)
#' # fz <- dt(z,df = nu)
#' # fy <- dt(y, df = nu)
#' # curve(dt(x, df = nu), - 4, + 4,
#' # ylim = c(0.0, 1.2 * max(fx,fy,fz)),xlab = "X",
#' # ylab = expression(f[X](x)),
#' # panel.first = grid(col="gray90"), lwd = 5)
#' # polygon(c(y, rev(y)),
#' # c(fy, rep(0, length(fy))),
#' # col="#99ccff")
#' # polygon(c(x, rev(x)),
#' # c(fx, rep(0, length(fx))),
#' # col="#cc0000")
#' # polygon(c(z,rev(z)), c(fz,rep(0,length(fz))),
#' # col="#cc0000")
#' # abline(v = ttab[1], lty=2, col = "red")
#' # abline(v = ttab[2], lty=2, col = "red")
#' # abline(v = ttest, lty=2, col = "blue")
#' # text(-2.5, 0.3, expression(bold("Critical point")))
#' # arrows(ttab[1] ,0.14, -2.3, 0.27)
#' # text(2.5, 0.3, expression(bold("Critical point")))
#' # arrows(ttab[2] ,0.14, 2.3, 0.27)
#' # aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' # axis(side = 1, at = c(ttab[1],ttab[2]), font = 2, labels = FALSE,
#' # col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#' # axis(side=1, at=as.character(c( - 4, ttab[1])), tick = TRUE, lwd = 1,
#' # col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' # axis(side=1, at=as.character(c(ttab[2], + 4)), tick = TRUE, lwd = 1,
#' # col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' # axis(side = 1, at = c(ttab[1],ttab[2]), lwd = 0,
#' # col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#' # axis(side = 1, at = ttest, lwd = 0,
#' # col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = aux2)
#' # axis(side = 1, at = ttest, tick = TRUE, lwd = 1,
#' # col="blue", lwd.ticks = 1, labels = FALSE)
#' # title("Test of hypothesis: T-Test.")
#' # text(0,0.1, expression(bold("ACCEPT H0" )))
#' # text(ttab[1] - 1 , 0.1, expression(bold("RRH0")))
#' # text(ttab[2] + 1 ,0.1, expression(bold("RRH0")))
#' # arrows(ttest, 0.27, -1.5, 0.33)
#' # text(-1.7, 0.35, expression(bold("ttest")))
#' # mtext("Step 1: Hypothesis", side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' # mtext(text = nullhyp , side = 1, line = 4, adj = 0)
#' # mtext(text = althyp , side = 1, line = 5, adj = 0)
#' #
#' # mtext("Step 2: Significante level", side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' # mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' # mtext(text = signlevel , side = 1, line = 7, adj = 0)
#' #
#' # mtext("Step 3: Rule of decision", side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' # mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' # mtext(decisionplot, side = 1, line = 4, adj = 1)
#' #
#' # mtext("Step 4: Conclusion", side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' # mtext(conclusionplot, side = 1, line = 7, adj = 1)
#' # }
#' # }
#' # if (any(alternative == c("less", "l", "L"))) {
#' # if (is.null(y)) {
#' # title <- paste(gettext(" One Sample t-test (Less test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu = ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # althyp <- paste(gettext(" H1: mu != ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' # sep = "")
#' # n <- length(x)
#' # ttest <- round((mean(x) - h0) / (nu /sqrt(n)), 2)
#' # ttab <- round(dt(df = nu, 1 - alpha), 2)
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df = nu, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # "|")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("H0 was rejected.", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = |", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]), "|")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("No evidence to reject H0.", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # else{
#' # n1 <- length(x)
#' # n2 <- length(y)
#' # df <- n1+n2-2
#' # sp <- ((n1-1)*var(x) + (n2-1)*var(y))/df
#' # title <- paste(gettext(" Two Sample t-test (Less test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu1 >= mu2", domain = "R-leem"),
#' # sep = "")
#' # althyp <- paste(gettext(" H1: mu1 < mu2", domain = "R-leem"),
#' # sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' # sep = "")
#' # ttest <- round((mean(x) - mean(y)) / sqrt(sp*(1/n1+1/n2)), 2)
#' # ttab <- round(dt(df, 1 - alpha), 2)
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]), '|')
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" H0 was rejected", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]), '|')
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" No evidence to reject the H0 ", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # if (plot == TRUE) {
#' # par(mar = c(10,4,4,4))
#' # x <- seq(- 4 , ttab[1], by = 0.01)
#' # y <- seq(ttab[1],+ 4, by = 0.01)
#' # fx <- dt(x, df = nu)
#' # fy <- dt(y, df = nu)
#' # curve(dt(x, df = nu), - 4 , + 4 ,
#' # ylim = c(0, 1.2*max(fx,fy)), ylab = expression(f[X](x)), xlab="X",
#' # panel.first = grid(col="gray90"), lwd = 5)
#' # polygon(c(y, rev(y)),
#' # c(fy, rep(0, length(fy))),
#' # col="#99ccff")
#' # polygon(c(x, rev(x)),
#' # c(fx, rep(0, length(fx))),
#' # col="#cc0000")
#' # abline(v = ttab[1], lty=2, col = "red")
#' # abline(v = ttest, lty=2, col = "blue")
#' # text(-2.5, 0.3, expression(bold("Critical point")))
#' # arrows(ttab[1] ,0.14, -2.1, 0.28)
#' # aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' #
#' #
#' # axis(side = 1, at = c(ttab[1], 4), font = 2, labels = FALSE, lwd.ticks = 0,
#' # col.axis = "#cc0000", col.ticks = "#cc0000", col = "#559ee8")
#' # axis(side=1, at=as.character(c( -4, ttab[1])),
#' # col="#cc0000", font = 2, lwd.ticks = 0, labels = FALSE)
#' # axis(side=1, at=as.character(c( "", ttab[1])), tick = TRUE, labels = FALSE,
#' # lwd.ticks = 1, col="#cc0000")
#' # axis(side = 1, at = c("",ttab[1]), lwd = 0,
#' # col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#' # axis(side = 1, at = ttest, lwd = 0,
#' # col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = aux2)
#' # axis(side = 1, at = ttest, tick = TRUE, lwd = 1,
#' # col="blue", lwd.ticks = 1, labels = FALSE)
#' #
#' #
#' # title("Test of hypothesis: T-Test.")
#' # text(0, 0.1, expression(bold("ACCEPT H0")))
#' # text(-2.5, 0.1, expression(bold("RRH0")))
#' # arrows(ttest , 0.27, -2.1, 0.38)
#' # text(-2.3, 0.4, expression(bold("ttest")))
#' # mtext("Step 1: Hypothesis", side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' # mtext(text = nullhyp , side = 1, line = 4, adj = 0)
#' # mtext(text = althyp , side = 1, line = 5, adj = 0)
#' #
#' # mtext("Step 2: Significante level", side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' # mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' # mtext(text = signlevel , side = 1, line = 7, adj = 0)
#' #
#' # mtext("Step 3: Rule of decision", side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' # mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' # mtext(decisionplot, side = 1, line = 4, adj = 1)
#' #
#' # mtext("Step 4: Conclusion", side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' # mtext(conclusionplot, side = 1, line = 7, adj = 1)
#' # }
#' # }
#' # if (any(alternative == c("greater", "g", "G"))) {
#' # if (is.null(y)) {
#' # title <- paste(gettext(" One Sample t-test (Greater test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu = ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # althyp <- paste(gettext(" H1: mu != ", domain = "R-leem"), round(h0, 2),
#' # sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' # sep = "")
#' # n <- length(x)
#' # ttest <- round((mean(x) - h0) / (nu /sqrt(n)), 2)
#' # ttab <- round(qt(df = nu,1 - alpha), 2)
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df = nu, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),"|")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("H0 was rejected.", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),'|')
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("No evidence to reject the H0.", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # else{
#' # n1 <- length(x)
#' # n2 <- length(y)
#' # df <- n1+n2-2
#' # sp <- ((n1-1)*var(x) + (n2-1)*var(y))/df
#' # title <- paste(gettext(" Two Sample z-test (Greater test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: mu1 <= mu2", domain = "R-leem"),
#' # sep = "")
#' # althyp <- paste(gettext(" H1: mu1 > mu2", domain = "R-leem"),
#' # sep = "")
#' # signlevel <- paste(gettext(" alpha = ", domain = "R-leem"), round(alpha, 2),
#' # sep = "")
#' # ttest <- round((mean(x) - mean(y)) / sqrt(sp*(1/n1+1/n2)), 2)
#' # ttab <- round(dt(df, 1 - alpha), 2)
#' # ttab <- round(c(-ttab, ttab), 2)
#' # pvalue <- 2 * pt(df, abs(ttest), lower.tail = FALSE)
#' # if (abs(ttest) >= abs(ttab[2])) {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| > |ttab = ", abs(ttab[2]), '|')
#' # conclusion <- paste(gettext(" We observed by the t Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" H0 was rejected", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As |ttest = ", domain = "R-leem"),
#' # abs(ttest), "| < |ttab = ", abs(ttab[2]), '|')
#' # conclusion <- paste(gettext(" We observed by the t Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext(" No evidence to reject the H0 ", domain = "R-leem"))
#' # }
#' # results <- list(ttest = ttest, ttab = ttab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # if(plot == TRUE){
#' # par(mar = c(10,4,4,4))
#' # x <- seq(- 4 , ttab[2], by = 0.01)
#' # y <- seq(ttab[2],+ 4, by = 0.01)
#' # fx <- dt(x, df = nu)
#' # fy <- dt(y, df = nu)
#' # curve(dt(x, df = nu), - 4 , + 4 ,
#' # ylim = c(0, 1.2*max(fx,fy)), ylab = expression(f[X](x)), xlab="X",
#' # panel.first = grid(col="gray90"), lwd = 5)
#' # polygon(c(y, rev(y)),
#' # c(fy, rep(0, length(fy))),
#' # col="#cc0000")
#' # polygon(c(x, rev(x)),
#' # c(fx, rep(0, length(fx))),
#' # col="#559ee8")
#' # abline(v = ttab[2], lty=2, col = "red")
#' # abline(v = ttest, lty=2, col = "blue")
#' # text(2.5, 0.3, expression(bold("Critical point")))
#' # arrows(ttab[2] ,0.14,2.3, 0.27)
#' # aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' #
#' #
#' #
#' # axis(side = 1, at = c(-4, ttab[2]), font = 2, labels = FALSE,
#' # lwd.ticks = 0, col = "#559ee8")
#' #
#' # axis(side=1, at=as.character(c( ttab[2], 4)), tick = TRUE, labels = FALSE,
#' # lwd.ticks = 0,col="#cc0000")
#' #
#' # axis(side=1, at=as.character(c( "", ttab[2])), tick = TRUE, labels = FALSE,
#' # lwd.ticks = 1, col="#cc0000")
#' #
#' # axis(side = 1, at = c("",ttab[2]), lwd = 0,
#' # col = "#cc0000", font = 2, tick = FALSE, col.axis="#cc0000", pos = aux2)
#' #
#' #
#' # axis(side = 1, at = ttest, lwd = 0,
#' # col = "blue", font = 2, tick = TRUE, col.axis="blue", pos = aux2)
#' # axis(side = 1, at = ttest, tick = TRUE, lwd = 1,
#' # col="blue", lwd.ticks = 1, labels = FALSE)
#' #
#' #
#' #
#' # title("Test of hypothesis: T-Test.")
#' # text(0, 0.1, expression(bold("ACCEPT H0")))
#' # text(2.5, 0.1, expression(bold("RRH0")))
#' # arrows(ttest ,0.27, -2, 0.37)
#' # text(-2, 0.4, expression(bold("ttest")))
#' # mtext("Step 1: Hypothesis", side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' # mtext(text = nullhyp , side = 1, line = 4, adj = 0)
#' # mtext(text = althyp , side = 1, line = 5, adj = 0)
#' #
#' # mtext("Step 2: Significante level", side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' # mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' # mtext(text = signlevel , side = 1, line = 7, adj = 0)
#' #
#' # mtext("Step 3: Rule of decision", side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' # mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' # mtext(decisionplot, side = 1, line = 4, adj = 1)
#' #
#' # mtext("Step 4: Conclusion", side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' # mtext(conclusionplot, side = 1, line = 7, adj = 1)
#' # }
#' # }
#' # }
#' # if (any(test == c("chisqtest", "chisq", "CHI", "chisquared"))) {
#' # if (any(alternative == c("less", "l", "L"))) {
#' # if (is.null(y)) {
#' # aux_x <- x
#' # sd <- sd(x)
#' # df <- length(x)-1
#' # if (missing(h0)) {
#' # h0 <- readline("Insert the value of null hypothesis: ")
#' # h0 <- as.numeric(h0)
#' # }
#' # if (!any(names(argaddit) == "s")) {
#' # s <- readline("Insert the value of population variance: ")
#' # s <- as.numeric(s)
#' # } else s <- argaddit$s
#' # title <- paste(gettext(" One Sample Chi-Squared Test (Unilateral Test) \n", domain = "R-leem"))
#' #
#' #
#' # nullhyp <- paste(gettext(" H0: sigma^2 = ", domain = "R-leem"), round(h0, 2), sep = "")
#' # althyp <- paste(gettext(" H1: sigma^2 != ", domain = "R-leem"), round(h0, 2), sep = "")
#' # signlevel <- paste(gettext(" Alpha = ", domain = "R-leem"), round(alpha, 2), sep = "")
#' #
#' #
#' # chitest <- round((df*s)/h0, 2)
#' # chitab <- round(qchisq((1-alpha), df, lower.tail = FALSE), 2)
#' # pvalue <- 2 * pchisq(abs(chitest), df, lower.tail = FALSE)
#' # if (abs(chitest) <= abs(chitab)) {
#' # decision <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | < | CP = ", abs(chitab),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < Alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | < | CP = ", abs(chitab), '|')
#' # conclusion <- paste(gettext(" We observed by the Chi-Squared Test that hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("H0 was rejected.", domain = "R-leem"))
#' #
#' # } else {
#' # decision <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | > | CP = ", abs(chitab),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > Alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | > | CP = ", abs(chitab), '|')
#' # conclusion <- paste(gettext(" We observed by the Chi-Squared Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("No evidence to reject H0.", domain = "R-leem"))
#' # }
#' # results <- list(chitest = chitest, chitab = chitab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # }
#' # else{
#' # stop("Em desenvolvimento", .call = FALSE, domain = "R-leem")
#' # }
#' # if (plot == TRUE) {
#' # par(mar = c(11,4,4,4))
#' # minimo <- if (chitest <= (-4) * df) chitest - 4 * df else 0
#' # maximo <- if (chitest > 4 * df) chitest + 4 * df else 4 * df
#' # x <- seq(minimo, chitab, by = 0.01)
#' # y <- seq(chitab, maximo, by = 0.01)
#' # fx <- dchisq(x, df)
#' # fy <- dchisq(y, df)
#' # main <- substitute(atop(bold("One Sample Chi-Squared Test (Unilateral Test)"),chi[c]^2 == frac((n-1)*s^2,sigma^2)), list(h0 = h0))
#' # curve(dchisq(x, df), minimo, maximo,
#' # ylim = c(0, 1.2*max(fx,fy)), ylab = expression(f[X](x)), xlab="",
#' # panel.first = grid(col="gray90"), main = main)
#' # polygon(c(y, rev(y)),
#' # c(fy, rep(0, length(fy))),
#' # col="#99ccff")
#' # polygon(c(x, rev(x)),
#' # c(fx, rep(0, length(fx))),
#' # col="gray")
#' # abline(v = chitab, lty=2, col = "#880000")
#' #
#' #
#' # #text(chitab, 0.8*max(fx,fy), expression(bold("CRITICAL POINT")), col = "#880000")
#' # #text(chitest, 0.8*max(fx,fy), expression(bold("CHISQTEST")), col = "blue")
#' # legend(chitest, 0.8*max(fx, fy), bg = "#010199", cex=0.8, box.col = "#010199",
#' # legend = expression(bold("STATISTICAL TEST(ST) ")), text.col = "white")
#' # legend(chitab, 0.9*max(fx, fy), bg = "#880000", cex=0.8, box.col = "#880000",
#' # legend = expression(bold("CRITICAL POINT(CP) ")), text.col = "white")
#' #
#' #
#' # abline(v = chitest, lty=2, col = "#010199")
#' # aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' # axis(side = 1, at = as.character(c(0, chitab)),
#' # col = "#888888", col.axis = "#888888", labels = FALSE)
#' # axis(side = 1, at = as.character(c(chitab, auxmaximo*10)),
#' # col = "#559ee8", col.axis = "#559ee8", labels = FALSE)
#' # axis(side = 1, at = chitab, tick = TRUE,
#' # col.ticks = "#880000", lwd.ticks = 1, labels = FALSE)
#' # axis(side = 1, at = chitab, tick = FALSE,
#' # font = 2, col.axis="#880000", pos = aux2)
#' # axis(side = 1, at = chitest, tick = FALSE,
#' # font = 2, col.axis="#010199", pos = aux2)
#' # axis(side = 1, at = chitest, tick = TRUE,
#' # col.ticks = "#010199", lwd.ticks = 1, labels = FALSE)
#' #
#' #
#' # legend("topleft", cex = 0.9, box.col = "black", bg = "#e0e0e0",
#' # legend = c("REJECT H0", "ACCEPT H0"), fill = c("gray", "#559ee8"))
#' #
#' #
#' #
#' # mtext("Step 1: Hypothesis", side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' # mtext(text = substitute(~~H[0]:~sigma^2 >= h0, list(h0 = h0)) , side = 1, line = 4.3, adj = 0)
#' # mtext(text =substitute(~~H[1]:~sigma^2 < h0, list(h0 = h0)), side = 1, line = 5.3, adj = 0)
#' # mtext("Step 2: Significante level", side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' # mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' # mtext(text = signlevel , side = 1, line = 7, adj = 0)
#' #
#' # mtext("Step 3: Rule of decision", side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' # mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' # mtext(decisionplot, side = 1, line = 4.3, adj = 1)
#' #
#' # mtext("Step 4: Conclusion", side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' # mtext(conclusionplot, side = 1, line = 7, adj = 1)
#' # }
#' #
#' # }
#' # if (any(alternative == c("greater", "g", "G"))) {
#' # if (is.null(y)) {
#' # aux_x <- x
#' # sd <- sd(x)
#' # df <- length(x)-1
#' # if (missing(h0)) {
#' # h0 <- readline("Insert the value of null hypothesis: ")
#' # h0 <- as.numeric(h0)
#' # }
#' # if (!any(names(argaddit) == "s")) {
#' # s <- readline("Insert the value of population variance: ")
#' # s <- as.numeric(s)
#' # } else s <- argaddit$s
#' # title <- paste(gettext(" One Sample Chi-Squared Test(Unilateral Test) \n", domain = "R-leem"))
#' # nullhyp <- paste(gettext(" H0: sgima^2 = ", domain = "R-leem"), round(h0, 2), sep = "")
#' # althyp <- paste(gettext(" H1: sigma^2 != ", domain = "R-leem"), round(h0, 2), sep = "")
#' # signlevel <- paste(gettext(" Alpha = ", domain = "R-leem"), round(alpha, 2), sep = "")
#' #
#' # chitest <- round((df*s)/h0, 2)
#' # chitab <- round(qchisq(1 - alpha, df), 2)
#' # pvalue <- 2 * pchisq(abs(chitest), df, lower.tail = TRUE)
#' # if (abs(chitest) >= abs(chitab)) {
#' # decision <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | > | CP = ", abs(chitab),
#' # gettext("| then reject H0!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " < Alpha = ", alpha,
#' # gettext(" then reject H0!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | > | CP = ", abs(chitab), '|')
#' # conclusion <- paste(gettext(" We observed by the Chi-Squared Test that the hypothesis H0 was rejected, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("H0 was rejected.", domain = "R-leem"))
#' # } else {
#' # decision <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | < | CP = ", abs(chitab),
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decision2 <- paste(gettext(" As p-value = ", domain = "R-leem"),
#' # pvalue, " > Alpha = ", alpha,
#' # gettext("| then H0 is not rejected!", domain = "R-leem"), sep = "")
#' # decisionplot <- paste(gettext(" As | ST = ", domain = "R-leem"),
#' # abs(chitest), " | < | CP = ", abs(chitab), '|')
#' # conclusion <- paste(gettext(" We observed by the Chi-Squared Test that there is no evidence to reject the H0 hypothesis, at the significance level of ", domain = "R-leem"),
#' # round(alpha * 100),
#' # gettext("% probability", domain = "R-leem"), sep = "")
#' # conclusionplot <- paste(gettext("No evidence to reject H0.", domain = "R-leem"))
#' # }
#' # } else{
#' # stop("Em desenvolvimento", .call = FALSE, domain = "R-leem")
#' # }
#' # results <- list(chitest = chitest, chitab = chitab, pvalue = pvalue, test = test,
#' # alternative = alternative, title = title, nullhyp = nullhyp,
#' # althyp = althyp, signlevel = signlevel, decision = decision,
#' # decision2 = decision2, conclusion = conclusion)
#' # if (plot == TRUE) {
#' # par(mar = c(11,4,4,4))
#' # main <- substitute(atop(bold("One Sample Chi-Squared Test (Greater Test)"),chi[c]^2 == frac((n-1)*s^2,sigma^2)), list(h0 = h0))
#' # minimo <- if (chitest <= (-4) * df) chitest - 4 * df else 0
#' # maximo <- if (chitest > 4 * df) chitest + 4 * df else 4 * df
#' # x <- seq(minimo, chitab, by = 0.01)
#' # y <- seq(chitab, maximo, by = 0.01)
#' # fx <- dchisq(x, df)
#' # fy <- dchisq(y, df)
#' # curve(dchisq(x, df), minimo, maximo,
#' # ylim = c(0, 1.2*max(fx,fy)), ylab = expression(f[X](x)), xlab="X",
#' # panel.first = grid(col="gray90"), main = main)
#' # polygon(c(y, rev(y)),
#' # c(fy, rep(0, length(fy))),
#' # col="gray")
#' # polygon(c(x, rev(x)),
#' # c(fx, rep(0, length(fx))),
#' # col="#99ccff")
#' # abline(v = chitab, lty=2, col = "#880000")
#' #
#' #
#' # #text(chitab, 0.8*max(fx,fy), expression(bold("CRITICAL POINT")), col = "#880000")
#' # #text(chitest, 0.8*max(fx,fy), expression(bold("CHISQTEST")), col = "blue")
#' # legend(chitest, 0.8*max(fx, fy), bg = "#010199", cex=0.8, box.col = "#010199",
#' # legend = expression(bold("STATISTICAL TEST(ST) ")), text.col = "white")
#' # legend(chitab, 0.9*max(fx, fy), bg = "#880000", cex=0.8, box.col = "#880000",
#' # legend = expression(bold("CRITICAL POINT(CP) ")), text.col = "white")
#' #
#' #
#' # abline(v = chitest, lty=2, col = "#010199")
#' # aux2 <- par("usr")[3]-(par("usr")[4] - par("usr")[3])/20
#' # axis(side = 1, at = as.character(c(0, chitab)),
#' # col = "#888888", col.axis = "#888888", labels = FALSE)
#' # axis(side = 1, at = as.character(c(chitab, auxmaximo*10)),
#' # col = "#559ee8", col.axis = "#559ee8", labels = FALSE)
#' # axis(side = 1, at = chitab, tick = TRUE,
#' # col.ticks = "#880000", lwd.ticks = 1, labels = FALSE)
#' # axis(side = 1, at = chitab, tick = FALSE,
#' # font = 2, col.axis="#880000", pos = aux2)
#' # axis(side = 1, at = chitest, tick = FALSE,
#' # font = 2, col.axis="#010199", pos = aux2)
#' # axis(side = 1, at = chitest, tick = TRUE,
#' # col.ticks = "#010199", lwd.ticks = 1, labels = FALSE)
#' #
#' #
#' # legend("topleft", cex = 0.9, box.col = "black", bg = "#e0e0e0",
#' # legend = c("REJECT H0", "ACCEPT H0"), fill = c("gray", "#559ee8"))
#' #
#' #
#' #
#' # mtext("Step 1: Hypothesis", side = 1, line = 3, adj = 0, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 3, adj = 0, col = "#0099ff")
#' # mtext(text = substitute(~~H[0]:~sigma^2 <= h0, list(h0 = h0)) , side = 1, line = 4.3, adj = 0)
#' # mtext(text =substitute(~~H[1]:~sigma^2 > h0, list(h0 = h0)), side = 1, line = 5.3, adj = 0)
#' #
#' # mtext("Step 2: Significante level", side = 1, line = 6, adj = 0, col = "#0099ff", font = 2)
#' # mtext("_____________________", side = 1, line = 6, adj = 0, col = "#0099ff")
#' # mtext(text = signlevel , side = 1, line = 7, adj = 0)
#' #
#' # mtext("Step 3: Rule of decision", side = 1, line = 3, adj = 1, col = "#0099ff", font = 2)
#' # mtext("____________________", side = 1, line = 3, adj = 1, col = "#0099ff")
#' # mtext(decisionplot, side = 1, line = 4, adj = 1)
#' #
#' # mtext("Step 4: Conclusion", side = 1, line = 6, adj = 1, col = "#0099ff", font = 2)
#' # mtext("________________", side = 1, line = 6, adj = 1, col = "#0099ff")
#' # mtext(conclusionplot, side = 1, line = 7, adj = 1)
#' # }
#' # }
#' # }
#' # if (any(test == c("ftest", "f", "F"))){
#' #
#' # stop("Em desenvolvimento", .call = FALSE, domain = "R-leem")
#' # }
#' attr(results, "output") <- "htest"
#' class(results) <- "leem"
#' results
#' }
#'
#'
#'
#'
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