R/funcao_teste_hip_T.R
In Zibetti/Plothtests: Plot Parametric Hypothesis Tests (Z, T, Chi-squared and F)
Defines functions
plot_T_test
Documented in
plot_T_test
#' Plot a two sample t-test of sample statistics
#'
#' Performs two sample t-tests for mean 1 and mean 2 (user supplied summary information). Is only applicable for the 2-sample tests (mu1-mu2).
#' alternative = "greater" is the alternative that sample mean 1 has a larger mean than sample mean 2.
#' If var.equal is "equal" then the pooled estimate of the variance is used. By default, if var.equal is "notequal" then the each sample variance is used separately and the Welch modification to the degrees of freedom is used.
#' Note: The result of Welch modification to the degrees of freedom was truncated to integer.
#'
#' @param alpha significance level for the critical limits; it must lie between zero and one
#' @param alternative a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
#' @param var.equal a char variable indicating whether to treat the two variances as being equal or notequal. If "equal" then the pooled variance is used to estimate the variance otherwise ("notequal") the Welch (or Satterthwaite) approximation to the degrees of freedom is used
#' @param n1 a single number representing the sample size of sample 1
#' @param m1 a single number representing the sample mean of sample 1
#' @param v1 a single number representing the sample variance for sample 1
#' @param n2 a single number representing the sample size of sample 2
#' @param m2 a single number representing the sample mean of sample 2
#' @param v2 a single number representing the sample variance for sample 2
#' @param delta0 a number indicating the true value of the difference in means of the two sample test.
#' @param annotations logical, show annotations in plot figure, TRUE ou FALSE (default = TRUE)
#' @param color integer, color theme for plot, from 1 to 7 so far (default = 3)
#'
#' @export
#'
#' @importFrom utils getFromNamespace
#'
#' @examples
#' plot_T_test(alpha = 0.05, alternative = "two.sided",
#' var.equal = "equal",
#' n1 = 10, m1 = 3.1, v1 = 1.5,
#' n2 = 20, m2 = 4.2, v2 = 1.7,
#' delta0 = 0,
#' annotations = TRUE,
#' color = 3)
plot_T_test = function(alpha = 0.05, alternative = "two.sided", var.equal = "equal", n1, m1, v1, n2, m2, v2, delta0 = 0, annotations = TRUE, color = 3){
## color function
tema = color_theme(color)
corCurva = tema$corCurva
corPValue = tema$corPValue
corET = tema$corET
corLinhaLimCrit = tema$corLinhaLimCrit
corAreaLimCrit = tema$corAreaLimCrit
# set function to arrow
#iArrows <- igraph:::igraph.Arrows
iArrows = getFromNamespace("igraph.Arrows", "igraph")
if ((length(alpha) != 1 || !is.finite(alpha) || alpha < 0 || alpha > 1)) # para ter efetivamente o stop é necessário { curly } em toda a função
stop("'alpha' must be a single number between 0 and 1")
if (n1 < 1 || n2 < 1)
stop("not enough 'n1 or n2' observations")
# Dados - Eixo x:
x = seq(-30,30,by=0.01)
# Variâncias - casos
if(var.equal == "equal"){
gl = n1 + n2 - 2
Sp2 = ( (n1 -1)*v1 + (n2-1)*v2 ) / (gl)
ET = ( (m1 - m2) - (delta0) ) / ( sqrt(Sp2)*sqrt(1/n1 + 1/n2) )
}
if(var.equal == "notequal"){
gld = (v1/n1 + v2/n2)^2 / ( (v1/n1)^2 / (n1-1) + (v2/n2)^2 / (n2-1) )
gl = trunc(gld)
ET = ( (m1 - m2) - (delta0) ) / ( sqrt(v1/n1 + v2/n2) )
}
# Valores das densidades
DenT = dt(x,gl) # Densidades dos valores de x
DenET = dt(ET,gl) # Densidade da estatistica amostral ET
# Bilateral ========================================================================================================
if(alternative == "two.sided"){
lic = qt(alpha/2,gl) # Limite inferior crítico
lsc = qt(1-alpha/2,gl) # Limite superior crítico
dlic = dt(lic,gl) # Densidade do Limite inferior crítico
dlsc = dt(lsc,gl) # Densidade do Limite superior crítico
# Plot da distribuicao H0
if(ET > 4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-(ET+1),ET+1),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else if(ET < -4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c((ET-1),-(ET-1)),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else{
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-4,4),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}
# área dos limites criticos alpha/2 - superior
polygon(x = c(lsc, lsc , x[x>lsc] , tail(x, n=1)), # X = conjunto dos valores de lsc até o final
y = c(0 , dlsc , DenT[x>lsc], 0), # Y = conjunto das densidades de lsc até o final
col = corAreaLimCrit, # cor do preenchimento
border = corAreaLimCrit) # cor da borda
# área dos limites criticos alpha/2 - inferior
polygon(x = c(-4 ,-4 , x[x<lic] ,lic , lic), # X = conjunto dos valores de lsc até o final
y = c( 0 ,dt(-4,gl) , DenT[x<lic] ,dlic , 0 ), # Y = conjunto das densidades de lsc até o final
col = corAreaLimCrit, # cor do preenchimento
border = corAreaLimCrit) # cor da borda
abline(v = lsc, lty = "dashed", lwd = 2, col = "darkgray")
abline(v = lic, lty = "dashed", lwd = 2, col = "darkgray")
abline(h = 0 , col = "gray" , lwd = 0.5)
points(ET, 0 , col = corET , pch = 16 , cex=1.4)
# Area do P-value
if(ET >= 0){
area_ET_cum = 1 - pt(ET, gl) # area de cauda superior : 1 - (area de -inf até estatistica amostral)
ponto_ET = qt(area_ET_cum, gl) # ponto da ET na H0 - extremidade oposta
Den_ponto_ET= dt(ponto_ET, gl) # Densidade da ET - extremidade oposta
# area do P-value superior
polygon(x = c(ET, ET , x[x>ET] , tail(x, n=1)), # X = conjunto dos valores de lsc até o final
y = c(0 , DenET , DenT[x>ET], 0), # Y = conjunto das densidades de lsc até o final
col = corPValue , density = c(30), angle = c(-45))
# area do P-value inferior
polygon(x = c(-4 ,-4 , x[x<ponto_ET] ,ponto_ET , ponto_ET), # X = conjunto dos valores de lsc até o final
y = c( 0 ,dt(-4,gl) , DenT[x<ponto_ET] ,Den_ponto_ET , 0 ), # Y = conjunto das densidades de lsc até o final
col = corPValue , density = c(30), angle = c(-45))
}
if(ET < 0){
area_ET_cum = pt(ET, gl) # area de cauda inferior :(area de 0 até estatistica amostral)
ponto_ET = qt(area_ET_cum, gl) # Ponto de ET na H0
Den_ponto_ET= dt(ponto_ET, gl) # Densidade da ET estatistica amostral bilateral
ponto_ET_2 = -1*ET # Ponto de ET na H0 - extremidade oposta
Den_ponto_ET_2 = dt(ponto_ET_2, gl) # Densidade da ET estatistica amostral bilateral - extremidade oposta
# area do P-value superior
polygon(x = c(ponto_ET_2, ponto_ET_2 , x[x>ponto_ET_2] , tail(x, n=1)), # X = conjunto dos valores de lsc até o final
y = c(0 , Den_ponto_ET_2, DenT[x>ponto_ET_2] , 0 ), # Y = conjunto das densidades de lsc até o final
col = corPValue , density = c(30), angle = c(-45))
# area do P-value inferior
polygon(x = c(-4 ,-4 , x[x<ponto_ET] ,ponto_ET , ponto_ET), # X = conjunto dos valores de lsc até o final
y = c( 0 ,dt(-4,gl) , DenT[x<ponto_ET] ,Den_ponto_ET , 0 ), # Y = conjunto das densidades de lsc até o final
col = corPValue , density = c(30), angle = c(-45))
}
Map(axis, side=1, at = round(c(lic,ET, lsc),2),
col.axis = c("gray" , corET, "gray"),
col.ticks = c("gray", corET, "gray"),
lwd = 0,
las = 1,
lwd.ticks = 2)
# plotar novamente a curva por cima
lines(x, DenT, type="l", xlab = "Statistic values", ylab = "Density", lwd = 3, col = corCurva)
## Anotações - escolha
if(annotations == TRUE){
# posição da legenda relativa ao Plot()
## obtendo os limites do plot
plot_limits = par("usr") # [1]-xini [2]-xfim [3]-yini [4]-yfim
## obtendo o centro do plot
xcent = (plot_limits[2] + plot_limits[1])/2
ycent = (plot_limits[3] + plot_limits[4])/2
## atribuindo coordendas para o print da legenda
xplot = plot_limits[2]/2
yplot = plot_limits[4] - 0.10*plot_limits[4]
# Valor de P arrow -------------------------------------
# arrow direita
iArrows(xcent , ycent, # de (x1,y1)
abs(ET) + 0.2, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = 1/(10*abs(ET)),#0.085,
width = 1,
size = 0.7)
# arrow esquerda
iArrows(xcent , ycent, # de (x1,y1)
-1*abs(ET) - 0.2, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = -1/(10*abs(ET)), #-0.085,
width = 1,
size = 0.7)
text(xcent , ycent,
label = paste("P-value =",round(2*area_ET_cum,2)),
col = corPValue,
pos = 3)
# fim Valor de P arrow ------------------------------------
# Legendas
legenda <- list( bquote( "Test Statistic = T = "~ .(round(ET,2)) ) ,
bquote( alpha == ~.(alpha) ),
bquote( "Critical limits" ~~ "[" ~ .(round(lic,2)) ~ ";" ~ .(round(lsc,2)) ~"]") )
mtext(side = 3, do.call(expression, legenda), line=-1:-3, adj=1, col=c(corET,corAreaLimCrit, "gray"))
}
}
## superior ==========================================================================================================
if(alternative == "greater"){
lsc = qt(1-alpha,gl) # Limite superior crítico
dlsc = dt(lsc,gl) # Densidade do Limite superior crítico
# Plot da distribuicao H0
if(ET > 4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-(ET+1),ET+1),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else if(ET < -4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c((ET-1),-(ET-1)),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else{
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-4,4),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}
# area do P-value
area_ET_cum = 1 - pt(ET, gl) # area de cauda superior : 1 - (area de -inf até estatistica amostral)
ponto_ET = qt(area_ET_cum, gl) # ponto da ET na H0 - extremidade oposta
Den_ponto_ET= dt(ponto_ET, gl) # Densidade da ET - extremidade oposta
# área dos limites criticos alpha - superior
polygon(x = c(lsc, lsc , x[x>lsc] , tail(x, n=1)), # X = conjunto dos valores de lsc até o final
y = c(0 , dlsc , DenT[x>lsc], 0), # Y = conjunto das densidades de lsc até o final
col = corAreaLimCrit, # cor do preenchimento
border = corAreaLimCrit ) # cor da borda
abline(v = lsc, lty = "dashed", lwd = 2, col = "darkgray")
abline(h = 0 , col = "gray" , lwd = 0.5)
points(ET, 0 , col = corET , pch = 16 , cex=1.4)
# plotar novamente a curva por cima
lines(x, DenT, type="l", xlab = "Statistic values", ylab = "Density", lwd = 3, col = corCurva)
# area do P-value superior
polygon(x = c(ET, ET , x[x>ET] , tail(x, n=1)), # X = conjunto dos valores de lsc até o final
y = c(0 , DenET , DenT[x>ET], 0), # Y = conjunto das densidades de lsc até o final
col = corPValue ,
density = c(10),
angle = c(-45),
lwd = 1.5 )
Map(axis, side=1, at = round(c(ET, lsc),2),
col.axis = c(corET, "gray"),
col.ticks = c(corET, "gray"),
lwd = 0,
las = 1,
lwd.ticks = 2)
## Anotações - escolha
if(annotations == TRUE){
# posição da legenda relativa ao Plot()
## obtendo os limites do plot
plot_limits = par("usr") # [1]-xini [2]-xfim [3]-yini [4]-yfim
## obtendo o centro do plot
xcent = (plot_limits[2] + plot_limits[1])/2
ycent = (plot_limits[3] + plot_limits[4])/2
## atribuindo coordendas para o print da legenda
xplot = plot_limits[2]/2
yplot = plot_limits[4] - 0.10*plot_limits[4]
# Valor de P arrow -------------------------------------
# arrow direita
if(ET >= 0){
iArrows(xcent , ycent, # de (x1,y1)
ET + 0.2, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = 1/(10*abs(ET)),#0.085,
width = 1,
size = 0.7)
}else{
iArrows(xcent , ycent, # de (x1,y1)
xcent + 0.5, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = 1/(10*abs(ET)),#0.085,
width = 1,
size = 0.7)
}
text(xcent , ycent,
label = paste("P-value =",round(area_ET_cum,2)),
col = corPValue,
pos = 3)
# fim Valor de P arrow ------------------------------------
# Legendas
legenda <- list( bquote( "Test Statistic = T = "~ .(round(ET,2)) ) ,
bquote( alpha == ~.(alpha) ),
bquote( "Critical limits" ~~ "[ -inf ;" ~ .(round(lsc,2)) ~"]") )
mtext(side = 3, do.call(expression, legenda), line=-1:-3, adj=1, col=c(corET,corAreaLimCrit, "gray"))
}
}
## Inferior ============================================================================================================
if(alternative == "less"){
lic = qt(alpha,gl) # Limite inferior crítico
dlic = dt(lic,gl) # Densidade no Limite inferior crítico
area_ET_cum = pt(ET, gl) # (area de 0 até estatistica amostral)
ponto_ET = qt(area_ET_cum, gl) # Ponto de ET na H0
Den_ponto_ET= dt(ponto_ET, gl) # Densidade da ET estatistica amostral bilateral
lsc = qt(1-alpha,gl) # Limite superior crítico
# Plot da distribuicao H0
if(ET > 4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-(ET+1),ET+1),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else if(ET < -4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c((ET-1),-(ET-1)),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else{
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-4,4),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}
# área do limite critico alpha - inferior
polygon(x = c(x[1] ,x[1] , x[x<lic] ,lic , lic), # X = conjunto dos valores de lsc até o final
y = c( 0 ,dt(x[1],gl) , DenT[x<lic] ,dlic , 0 ), # Y = conjunto das densidades de lsc até o final
col = corAreaLimCrit, # cor do preenchimento
border = corAreaLimCrit) # cor da borda
# plotar novamente a curva por cima
lines(x, DenT, type="l", xlab = "Statistic values", ylab = "Density", lwd = 3, col = corCurva)
# area do P-value inferior
polygon(x = c(x[1] ,x[1] , x[x<ponto_ET] ,ponto_ET ,ponto_ET), # X = conjunto dos valores de lsc até o final
y = c(0 ,dt(x[1],gl), DenT[x<ponto_ET] ,Den_ponto_ET,0 ), # Y = conjunto das densidades de lsc até o final
col = corPValue,
density = c(30),
angle = c(-45),
lwd = 1.5)
abline(v = lic, lty = "dashed", lwd = 2, col = "darkgray")
abline(h = 0 , col = "gray" , lwd = 0.5)
points(ET, 0 , col =corET , pch = 16 , cex=1.4)
Map(axis, side=1, at = round(c(lic, ET),2),
col.axis = c("gray" , corET),
col.ticks = c("gray" , corET),
lwd=0,
las=1,
lwd.ticks = 2)
## Anotações - escolha
if(annotations == TRUE){
# posição da legenda relativa ao Plot()
## obtendo os limites do plot
plot_limits = par("usr") # [1]-xini [2]-xfim [3]-yini [4]-yfim
## obtendo o centro do plot
xcent = (plot_limits[2] + plot_limits[1])/2
ycent = (plot_limits[3] + plot_limits[4])/2
## atribuindo coordendas para o print da legenda
xplot = plot_limits[2]/2
yplot = plot_limits[4] - 0.10*plot_limits[4]
# Valor de P arrow -------------------------------------
# arrow direita
if(ET >= 0){
iArrows(xcent , ycent, # de (x1,y1)
xcent - 0.5, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = -1/(10*abs(ET)),#0.085,
width = 1,
size = 0.7)
}else{
iArrows(xcent , ycent, # de (x1,y1)
ET - 0.2, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = -1/(10*abs(ET)),#0.085,
width = 1,
size = 0.7)
}
text(xcent , ycent,
label = paste("P-value =",round(area_ET_cum,2)),
col = corPValue,
pos = 3)
# fim Valor de P arrow ------------------------------------
# Legendas
legenda <- list( bquote( "Test Statistic = T = "~ .(round(ET,2)) ) ,
bquote( alpha == ~.(alpha) ),
bquote( "Critical limits" ~~ "[" ~ .(round(lic,2)) ~"; + Inf]") )
mtext(side = 3, do.call(expression, legenda), line=-1:-3, adj=1, col=c(corET,corAreaLimCrit, "gray"))
}
}
PVAL = switch(alternative,
two.sided = 2*area_ET_cum,
less = area_ET_cum,
greater = area_ET_cum)
return(list(test.statistic = ET, df = gl, p.value = PVAL))
}
# Testes --------------------------------------------------------------------------------------------------------------
Zibetti/Plothtests documentation built on Feb. 5, 2021, 8:32 p.m.
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Defines functions plot_T_test
Documented in plot_T_test
#' Plot a two sample t-test of sample statistics
#'
#' Performs two sample t-tests for mean 1 and mean 2 (user supplied summary information). Is only applicable for the 2-sample tests (mu1-mu2).
#' alternative = "greater" is the alternative that sample mean 1 has a larger mean than sample mean 2.
#' If var.equal is "equal" then the pooled estimate of the variance is used. By default, if var.equal is "notequal" then the each sample variance is used separately and the Welch modification to the degrees of freedom is used.
#' Note: The result of Welch modification to the degrees of freedom was truncated to integer.
#'
#' @param alpha significance level for the critical limits; it must lie between zero and one
#' @param alternative a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
#' @param var.equal a char variable indicating whether to treat the two variances as being equal or notequal. If "equal" then the pooled variance is used to estimate the variance otherwise ("notequal") the Welch (or Satterthwaite) approximation to the degrees of freedom is used
#' @param n1 a single number representing the sample size of sample 1
#' @param m1 a single number representing the sample mean of sample 1
#' @param v1 a single number representing the sample variance for sample 1
#' @param n2 a single number representing the sample size of sample 2
#' @param m2 a single number representing the sample mean of sample 2
#' @param v2 a single number representing the sample variance for sample 2
#' @param delta0 a number indicating the true value of the difference in means of the two sample test.
#' @param annotations logical, show annotations in plot figure, TRUE ou FALSE (default = TRUE)
#' @param color integer, color theme for plot, from 1 to 7 so far (default = 3)
#'
#' @export
#'
#' @importFrom utils getFromNamespace
#'
#' @examples
#' plot_T_test(alpha = 0.05, alternative = "two.sided",
#' var.equal = "equal",
#' n1 = 10, m1 = 3.1, v1 = 1.5,
#' n2 = 20, m2 = 4.2, v2 = 1.7,
#' delta0 = 0,
#' annotations = TRUE,
#' color = 3)
plot_T_test = function(alpha = 0.05, alternative = "two.sided", var.equal = "equal", n1, m1, v1, n2, m2, v2, delta0 = 0, annotations = TRUE, color = 3){
## color function
tema = color_theme(color)
corCurva = tema$corCurva
corPValue = tema$corPValue
corET = tema$corET
corLinhaLimCrit = tema$corLinhaLimCrit
corAreaLimCrit = tema$corAreaLimCrit
# set function to arrow
#iArrows <- igraph:::igraph.Arrows
iArrows = getFromNamespace("igraph.Arrows", "igraph")
if ((length(alpha) != 1 || !is.finite(alpha) || alpha < 0 || alpha > 1)) # para ter efetivamente o stop é necessário { curly } em toda a função
stop("'alpha' must be a single number between 0 and 1")
if (n1 < 1 || n2 < 1)
stop("not enough 'n1 or n2' observations")
# Dados - Eixo x:
x = seq(-30,30,by=0.01)
# Variâncias - casos
if(var.equal == "equal"){
gl = n1 + n2 - 2
Sp2 = ( (n1 -1)*v1 + (n2-1)*v2 ) / (gl)
ET = ( (m1 - m2) - (delta0) ) / ( sqrt(Sp2)*sqrt(1/n1 + 1/n2) )
}
if(var.equal == "notequal"){
gld = (v1/n1 + v2/n2)^2 / ( (v1/n1)^2 / (n1-1) + (v2/n2)^2 / (n2-1) )
gl = trunc(gld)
ET = ( (m1 - m2) - (delta0) ) / ( sqrt(v1/n1 + v2/n2) )
}
# Valores das densidades
DenT = dt(x,gl) # Densidades dos valores de x
DenET = dt(ET,gl) # Densidade da estatistica amostral ET
# Bilateral ========================================================================================================
if(alternative == "two.sided"){
lic = qt(alpha/2,gl) # Limite inferior crítico
lsc = qt(1-alpha/2,gl) # Limite superior crítico
dlic = dt(lic,gl) # Densidade do Limite inferior crítico
dlsc = dt(lsc,gl) # Densidade do Limite superior crítico
# Plot da distribuicao H0
if(ET > 4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-(ET+1),ET+1),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else if(ET < -4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c((ET-1),-(ET-1)),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else{
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-4,4),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}
# área dos limites criticos alpha/2 - superior
polygon(x = c(lsc, lsc , x[x>lsc] , tail(x, n=1)), # X = conjunto dos valores de lsc até o final
y = c(0 , dlsc , DenT[x>lsc], 0), # Y = conjunto das densidades de lsc até o final
col = corAreaLimCrit, # cor do preenchimento
border = corAreaLimCrit) # cor da borda
# área dos limites criticos alpha/2 - inferior
polygon(x = c(-4 ,-4 , x[x<lic] ,lic , lic), # X = conjunto dos valores de lsc até o final
y = c( 0 ,dt(-4,gl) , DenT[x<lic] ,dlic , 0 ), # Y = conjunto das densidades de lsc até o final
col = corAreaLimCrit, # cor do preenchimento
border = corAreaLimCrit) # cor da borda
abline(v = lsc, lty = "dashed", lwd = 2, col = "darkgray")
abline(v = lic, lty = "dashed", lwd = 2, col = "darkgray")
abline(h = 0 , col = "gray" , lwd = 0.5)
points(ET, 0 , col = corET , pch = 16 , cex=1.4)
# Area do P-value
if(ET >= 0){
area_ET_cum = 1 - pt(ET, gl) # area de cauda superior : 1 - (area de -inf até estatistica amostral)
ponto_ET = qt(area_ET_cum, gl) # ponto da ET na H0 - extremidade oposta
Den_ponto_ET= dt(ponto_ET, gl) # Densidade da ET - extremidade oposta
# area do P-value superior
polygon(x = c(ET, ET , x[x>ET] , tail(x, n=1)), # X = conjunto dos valores de lsc até o final
y = c(0 , DenET , DenT[x>ET], 0), # Y = conjunto das densidades de lsc até o final
col = corPValue , density = c(30), angle = c(-45))
# area do P-value inferior
polygon(x = c(-4 ,-4 , x[x<ponto_ET] ,ponto_ET , ponto_ET), # X = conjunto dos valores de lsc até o final
y = c( 0 ,dt(-4,gl) , DenT[x<ponto_ET] ,Den_ponto_ET , 0 ), # Y = conjunto das densidades de lsc até o final
col = corPValue , density = c(30), angle = c(-45))
}
if(ET < 0){
area_ET_cum = pt(ET, gl) # area de cauda inferior :(area de 0 até estatistica amostral)
ponto_ET = qt(area_ET_cum, gl) # Ponto de ET na H0
Den_ponto_ET= dt(ponto_ET, gl) # Densidade da ET estatistica amostral bilateral
ponto_ET_2 = -1*ET # Ponto de ET na H0 - extremidade oposta
Den_ponto_ET_2 = dt(ponto_ET_2, gl) # Densidade da ET estatistica amostral bilateral - extremidade oposta
# area do P-value superior
polygon(x = c(ponto_ET_2, ponto_ET_2 , x[x>ponto_ET_2] , tail(x, n=1)), # X = conjunto dos valores de lsc até o final
y = c(0 , Den_ponto_ET_2, DenT[x>ponto_ET_2] , 0 ), # Y = conjunto das densidades de lsc até o final
col = corPValue , density = c(30), angle = c(-45))
# area do P-value inferior
polygon(x = c(-4 ,-4 , x[x<ponto_ET] ,ponto_ET , ponto_ET), # X = conjunto dos valores de lsc até o final
y = c( 0 ,dt(-4,gl) , DenT[x<ponto_ET] ,Den_ponto_ET , 0 ), # Y = conjunto das densidades de lsc até o final
col = corPValue , density = c(30), angle = c(-45))
}
Map(axis, side=1, at = round(c(lic,ET, lsc),2),
col.axis = c("gray" , corET, "gray"),
col.ticks = c("gray", corET, "gray"),
lwd = 0,
las = 1,
lwd.ticks = 2)
# plotar novamente a curva por cima
lines(x, DenT, type="l", xlab = "Statistic values", ylab = "Density", lwd = 3, col = corCurva)
## Anotações - escolha
if(annotations == TRUE){
# posição da legenda relativa ao Plot()
## obtendo os limites do plot
plot_limits = par("usr") # [1]-xini [2]-xfim [3]-yini [4]-yfim
## obtendo o centro do plot
xcent = (plot_limits[2] + plot_limits[1])/2
ycent = (plot_limits[3] + plot_limits[4])/2
## atribuindo coordendas para o print da legenda
xplot = plot_limits[2]/2
yplot = plot_limits[4] - 0.10*plot_limits[4]
# Valor de P arrow -------------------------------------
# arrow direita
iArrows(xcent , ycent, # de (x1,y1)
abs(ET) + 0.2, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = 1/(10*abs(ET)),#0.085,
width = 1,
size = 0.7)
# arrow esquerda
iArrows(xcent , ycent, # de (x1,y1)
-1*abs(ET) - 0.2, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = -1/(10*abs(ET)), #-0.085,
width = 1,
size = 0.7)
text(xcent , ycent,
label = paste("P-value =",round(2*area_ET_cum,2)),
col = corPValue,
pos = 3)
# fim Valor de P arrow ------------------------------------
# Legendas
legenda <- list( bquote( "Test Statistic = T = "~ .(round(ET,2)) ) ,
bquote( alpha == ~.(alpha) ),
bquote( "Critical limits" ~~ "[" ~ .(round(lic,2)) ~ ";" ~ .(round(lsc,2)) ~"]") )
mtext(side = 3, do.call(expression, legenda), line=-1:-3, adj=1, col=c(corET,corAreaLimCrit, "gray"))
}
}
## superior ==========================================================================================================
if(alternative == "greater"){
lsc = qt(1-alpha,gl) # Limite superior crítico
dlsc = dt(lsc,gl) # Densidade do Limite superior crítico
# Plot da distribuicao H0
if(ET > 4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-(ET+1),ET+1),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else if(ET < -4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c((ET-1),-(ET-1)),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else{
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-4,4),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}
# area do P-value
area_ET_cum = 1 - pt(ET, gl) # area de cauda superior : 1 - (area de -inf até estatistica amostral)
ponto_ET = qt(area_ET_cum, gl) # ponto da ET na H0 - extremidade oposta
Den_ponto_ET= dt(ponto_ET, gl) # Densidade da ET - extremidade oposta
# área dos limites criticos alpha - superior
polygon(x = c(lsc, lsc , x[x>lsc] , tail(x, n=1)), # X = conjunto dos valores de lsc até o final
y = c(0 , dlsc , DenT[x>lsc], 0), # Y = conjunto das densidades de lsc até o final
col = corAreaLimCrit, # cor do preenchimento
border = corAreaLimCrit ) # cor da borda
abline(v = lsc, lty = "dashed", lwd = 2, col = "darkgray")
abline(h = 0 , col = "gray" , lwd = 0.5)
points(ET, 0 , col = corET , pch = 16 , cex=1.4)
# plotar novamente a curva por cima
lines(x, DenT, type="l", xlab = "Statistic values", ylab = "Density", lwd = 3, col = corCurva)
# area do P-value superior
polygon(x = c(ET, ET , x[x>ET] , tail(x, n=1)), # X = conjunto dos valores de lsc até o final
y = c(0 , DenET , DenT[x>ET], 0), # Y = conjunto das densidades de lsc até o final
col = corPValue ,
density = c(10),
angle = c(-45),
lwd = 1.5 )
Map(axis, side=1, at = round(c(ET, lsc),2),
col.axis = c(corET, "gray"),
col.ticks = c(corET, "gray"),
lwd = 0,
las = 1,
lwd.ticks = 2)
## Anotações - escolha
if(annotations == TRUE){
# posição da legenda relativa ao Plot()
## obtendo os limites do plot
plot_limits = par("usr") # [1]-xini [2]-xfim [3]-yini [4]-yfim
## obtendo o centro do plot
xcent = (plot_limits[2] + plot_limits[1])/2
ycent = (plot_limits[3] + plot_limits[4])/2
## atribuindo coordendas para o print da legenda
xplot = plot_limits[2]/2
yplot = plot_limits[4] - 0.10*plot_limits[4]
# Valor de P arrow -------------------------------------
# arrow direita
if(ET >= 0){
iArrows(xcent , ycent, # de (x1,y1)
ET + 0.2, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = 1/(10*abs(ET)),#0.085,
width = 1,
size = 0.7)
}else{
iArrows(xcent , ycent, # de (x1,y1)
xcent + 0.5, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = 1/(10*abs(ET)),#0.085,
width = 1,
size = 0.7)
}
text(xcent , ycent,
label = paste("P-value =",round(area_ET_cum,2)),
col = corPValue,
pos = 3)
# fim Valor de P arrow ------------------------------------
# Legendas
legenda <- list( bquote( "Test Statistic = T = "~ .(round(ET,2)) ) ,
bquote( alpha == ~.(alpha) ),
bquote( "Critical limits" ~~ "[ -inf ;" ~ .(round(lsc,2)) ~"]") )
mtext(side = 3, do.call(expression, legenda), line=-1:-3, adj=1, col=c(corET,corAreaLimCrit, "gray"))
}
}
## Inferior ============================================================================================================
if(alternative == "less"){
lic = qt(alpha,gl) # Limite inferior crítico
dlic = dt(lic,gl) # Densidade no Limite inferior crítico
area_ET_cum = pt(ET, gl) # (area de 0 até estatistica amostral)
ponto_ET = qt(area_ET_cum, gl) # Ponto de ET na H0
Den_ponto_ET= dt(ponto_ET, gl) # Densidade da ET estatistica amostral bilateral
lsc = qt(1-alpha,gl) # Limite superior crítico
# Plot da distribuicao H0
if(ET > 4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-(ET+1),ET+1),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else if(ET < -4){
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c((ET-1),-(ET-1)),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}else{
plot(x, DenT, type="l", xlab = "Statistic values", xlim = c(-4,4),ylab = "Density", lwd = 3, col = corCurva, xaxt='n',
main = bquote("Null Distribution :" ~ mu[1] - mu[2] == 0 ~ ", " ~ gl == ~ .(gl)))
}
# área do limite critico alpha - inferior
polygon(x = c(x[1] ,x[1] , x[x<lic] ,lic , lic), # X = conjunto dos valores de lsc até o final
y = c( 0 ,dt(x[1],gl) , DenT[x<lic] ,dlic , 0 ), # Y = conjunto das densidades de lsc até o final
col = corAreaLimCrit, # cor do preenchimento
border = corAreaLimCrit) # cor da borda
# plotar novamente a curva por cima
lines(x, DenT, type="l", xlab = "Statistic values", ylab = "Density", lwd = 3, col = corCurva)
# area do P-value inferior
polygon(x = c(x[1] ,x[1] , x[x<ponto_ET] ,ponto_ET ,ponto_ET), # X = conjunto dos valores de lsc até o final
y = c(0 ,dt(x[1],gl), DenT[x<ponto_ET] ,Den_ponto_ET,0 ), # Y = conjunto das densidades de lsc até o final
col = corPValue,
density = c(30),
angle = c(-45),
lwd = 1.5)
abline(v = lic, lty = "dashed", lwd = 2, col = "darkgray")
abline(h = 0 , col = "gray" , lwd = 0.5)
points(ET, 0 , col =corET , pch = 16 , cex=1.4)
Map(axis, side=1, at = round(c(lic, ET),2),
col.axis = c("gray" , corET),
col.ticks = c("gray" , corET),
lwd=0,
las=1,
lwd.ticks = 2)
## Anotações - escolha
if(annotations == TRUE){
# posição da legenda relativa ao Plot()
## obtendo os limites do plot
plot_limits = par("usr") # [1]-xini [2]-xfim [3]-yini [4]-yfim
## obtendo o centro do plot
xcent = (plot_limits[2] + plot_limits[1])/2
ycent = (plot_limits[3] + plot_limits[4])/2
## atribuindo coordendas para o print da legenda
xplot = plot_limits[2]/2
yplot = plot_limits[4] - 0.10*plot_limits[4]
# Valor de P arrow -------------------------------------
# arrow direita
if(ET >= 0){
iArrows(xcent , ycent, # de (x1,y1)
xcent - 0.5, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = -1/(10*abs(ET)),#0.085,
width = 1,
size = 0.7)
}else{
iArrows(xcent , ycent, # de (x1,y1)
ET - 0.2, 0.02, # até (x2,y2)
h.lwd = 2,
sh.lwd = 1,
sh.col = corPValue,
sh.lty = 2,
h.lty = 1,
curve = -1/(10*abs(ET)),#0.085,
width = 1,
size = 0.7)
}
text(xcent , ycent,
label = paste("P-value =",round(area_ET_cum,2)),
col = corPValue,
pos = 3)
# fim Valor de P arrow ------------------------------------
# Legendas
legenda <- list( bquote( "Test Statistic = T = "~ .(round(ET,2)) ) ,
bquote( alpha == ~.(alpha) ),
bquote( "Critical limits" ~~ "[" ~ .(round(lic,2)) ~"; + Inf]") )
mtext(side = 3, do.call(expression, legenda), line=-1:-3, adj=1, col=c(corET,corAreaLimCrit, "gray"))
}
}
PVAL = switch(alternative,
two.sided = 2*area_ET_cum,
less = area_ET_cum,
greater = area_ET_cum)
return(list(test.statistic = ET, df = gl, p.value = PVAL))
}
# Testes --------------------------------------------------------------------------------------------------------------
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