R/t_test.R
In fhernanb/stests: Package with useful statistical tests
Defines functions
t_test_two_equal
t_test_two_difer
t_test_one
t_test
Documented in
t_test
#' Student's t-Test using values
#'
#' This function performs the t-test for one and two samples using summarized values, not the vectors.
#'
#' @param meanx sample mean for sample x.
#' @param varx sample variance for sample x.
#' @param nx sample size for sample x.
#' @param meany sample mean for sample y.
#' @param vary sample variance for sample y.
#' @param ny sample size for sample y.
#' @param alternative a character string specifying the alternative
#' hypothesis, must be one of \code{"two.sided"} (default),
#' \code{"greater"} or \code{"less"}. You can specify just the initial letter.
#' @param mu the hypothesized number (mean) in the null hypothesis.
#' @param conf.level confidence level of the interval, by default its value is 0.95.
#' @param var.equal a logical variable indicating whether to treat the
#' two variances as being equal. If \code{TRUE} then the pooled variance
#' is used to estimate the variance otherwise the Welch (or Satterthwaite)
#' approximation to the degrees of freedom is used.
#'
#' @return A list with class \code{"htest"} containing the following
#' components:
#' \item{statistic}{the value of the statistic.}
#' \item{parameter}{the degrees of freedom for the t-statistic.}
#' \item{p.value}{the p-value for the test.}
#' \item{conf.int}{a confidence interval for the mean appropiate to the
#' alternative hypothesis.}
#' \item{estimate}{the estimated mean or difference in means depending
#' on whether it was a one-sample test or a two-sample test.}
#' \item{null.value}{the specified hypothesized value for alternative hypothesis
#' value for the mean or mean difference depending on whether it was
#' a one-sample test or a two-sample test.}
#' \item{alternative}{a character string describing the alternative hypothesis.}
#' \item{method}{a character string indicating the type of test performed.}
#'
#' @examples
#' # Examples with ONE sample
#'
#' # Example 9.2 from Walpole
#' t_test(meanx=42, varx=11.9^2, nx=12,
#' mu=50, alternative='less')
#'
#' # Example 11.5 from A. F. Siegel & C. Morgan
#' t_test(meanx=100, varx=12^2, nx=9,
#' mu=83, alternative='two.sided')
#'
#' # Example 11.6 from Murray
#' t_test(meanx=0.053, varx=0.003^2, nx=10,
#' mu=0.050, alternative='two.sided')
#'
#' # --- Examples with TWO-SAMPLES and equal variances ---
#'
#' # Example 9.3 From Walpole
#' t_test(meanx=85, varx=4^2, nx=12,
#' meany=81, vary=5^2, ny=10,
#' alternative='two.sided', mu=0, var.equal=TRUE)
#'
#' # Example 13.5 from J. Freund's
#' t_test(meanx=546, varx=31^2, nx=4,
#' meany=492, vary=26^2, ny=4,
#' alternative='two.sided', mu=0, var.equal=TRUE)
#'
#' # --- Examples with TWO-SAMPLES and different variances ---
#'
#' # Example from
#' t_test(meanx =6.8, varx=1.8^2, nx=13,
#' meany=5.3, vary=1.6^2, ny=15,
#' alternative='two.sided', mu=0, var.equal=FALSE)
#'
#' @export
t_test <- function(meanx, varx, nx,
meany=NULL, vary=NULL, ny=NULL,
alternative='two.sided', mu=0,
conf.level=0.95, var.equal=FALSE){
# Checking if the information is correct
# To check if the information about x sample is correct
if (varx <= 0)
stop(paste("The variance x must be positive", "\n", ""))
if (nx <= 0)
stop(paste("The sample size nx must be positive", "\n", ""))
if (nx %% 1 != 0)
stop(paste("The sample size nx must be integer", "\n", ""))
# To check if the user provided information about y sample
if (xor(is.null(vary), is.null(ny)))
stop("Some information about sample y is missing", "\n", "")
# To check if the information about y sample is corrected
if (! is.null(vary) & ! is.null(ny) & ! is.null(meany)) {
if (vary <= 0)
stop(paste("The variance y must be positive", "\n", ""))
if (ny <= 0)
stop(paste("The sample size ny must be positive", "\n", ""))
if (ny %% 1 != 0)
stop(paste("The sample size ny must be integer", "\n", ""))
if (is.null(meany) == TRUE)
stop(paste("Some information about y sample is missing", "\n",""))
}
# To check if the conf.level it's a number between 1 and 0
if(conf.level <= 0 || conf.level >= 1)
stop("The conf.level argument must be > 0 and < 1", "\n", "" )
if(conf.level < 0.5)
warning("Confidence levels are often close to 1, eg. 0.95")
# Argument Verification Using Partial Matching
alternative <- match.arg(arg=alternative,
choices=c("two.sided","greater","less"))
# To perform the test
if (is.null(meany) & is.null(vary) & is.null(ny))
res <- t_test_one(meanx, varx, nx, alternative, mu, conf.level)
else {
if (var.equal == TRUE)
res <- t_test_two_equal(meanx, varx, nx, meany, vary, ny,
alternative, mu, conf.level, var.equal)
if (var.equal == FALSE)
res <- t_test_two_difer(meanx, varx, nx, meany, vary, ny,
alternative, mu, conf.level, var.equal)
}
class(res) <- "htest"
res
}
#' @importFrom stats pt qt
t_test_one <- function(meanx, varx, nx, alternative, mu,
conf.level) {
alpha <- 1 - conf.level
if (alternative == 'two.sided') {
statistic <- (meanx - mu) / sqrt(varx / nx)
p.value <- 2 * pt(q=abs(statistic), df=nx-1, lower.tail=FALSE)
quantiles <- c(-qt(p=alpha/2, df=nx-1, lower.tail=FALSE),
qt(p=alpha/2, df=nx-1, lower.tail=FALSE))
conf.int <- meanx + quantiles * sqrt(varx / nx)
}
if (alternative == 'less') {
statistic <- (meanx - mu) / sqrt(varx / nx)
p.value <- pt(q=statistic, df=nx-1, lower.tail=TRUE)
conf.int <- c(-Inf,
meanx + qt(p=1-alpha, df=nx-1) * sqrt(varx / nx))
}
if (alternative == 'greater') {
statistic <- (meanx - mu) / sqrt(varx / nx)
p.value <- pt(q=statistic, df=nx-1, lower.tail=FALSE)
conf.int <- c(meanx + qt(p=alpha, df=nx-1) * sqrt(varx / nx),
Inf)
}
# To ensure that the output values are in the correct form
names(statistic) <- 't'
parameter <- nx - 1
names(parameter) <- 'df'
attr(conf.int, 'conf.level') <- conf.level
estimate <- meanx
names(estimate) <- 'mean of x'
null.value <- mu
names(null.value) <- 'mean'
method <- 'One Sample t-test'
data.name <- paste('meanx = ', meanx, ', var = ', varx, ' and nx = ', nx, sep='')
res <- list(statistic=statistic,
parameter=parameter,
p.value=p.value,
conf.int=conf.int,
estimate=estimate,
null.value=null.value,
alternative=alternative,
method=method,
data.name=data.name)
return(res)
}
#' @importFrom stats pt qt
t_test_two_difer <- function(meanx, varx, nx,
meany, vary, ny,
alternative, mu,
conf.level, var.equal) {
alpha <- 1 - conf.level
df <- (varx/nx + vary/ny)^2 / ((varx/nx)^2 / (nx-1) + (vary/ny)^2 / (ny-1))
se <- sqrt(varx/nx + vary/ny)
statistic <- (meanx - meany - mu) / se
if (alternative == 'two.sided') {
p.value <- 2 * pt(q=abs(statistic), df=df, lower.tail=FALSE)
quantiles <- c(-qt(p=alpha/2, df=df, lower.tail=FALSE),
qt(p=alpha/2, df=df, lower.tail=FALSE))
conf.int <- (meanx-meany) + quantiles * se
}
if (alternative == 'less') {
p.value <- pt(q=statistic, df=df, lower.tail=TRUE)
conf.int <- c(-Inf,
(meanx-meany) + qt(p=alpha, df=df, lower.tail=F) * se)
}
if (alternative == 'greater') {
p.value <- pt(q=statistic, df=df, lower.tail=FALSE)
conf.int <- c((meanx-meany) - qt(p=alpha, df=df, lower.tail=F) * se,
Inf)
}
# To ensure that the output values are in the correct form
names(statistic) <- 't'
parameter <- df
names(parameter) <- 'df'
attr(conf.int, 'conf.level') <- conf.level
estimate <- c(meanx, meany)
names(estimate) <- c('mean of x', 'mean of y')
null.value <- mu
names(null.value) <- 'difference in means'
method <- 'Welch Two Sample t-test'
data.name <- paste('meanx = ', meanx, ', nx = ', nx,
', meany = ', meany, ' and ny = ', ny, sep='')
res <- list(statistic=statistic,
parameter=parameter,
p.value=p.value,
conf.int=conf.int,
estimate=estimate,
null.value=null.value,
alternative=alternative,
method=method,
data.name=data.name)
return(res)
}
#' @importFrom stats pt qt
t_test_two_equal <- function(meanx, varx, nx,
meany, vary, ny,
alternative, mu,
conf.level, var.equal) {
alpha <- 1 - conf.level
df <- nx + ny - 2
sp2 <- ((nx-1) * varx + (ny-1) * vary) / df
se <- sqrt(sp2/nx + sp2/ny)
statistic <- (meanx - meany - mu) / se
if (alternative == 'two.sided') {
mu <- as.numeric(mu)
alt <- paste("true difference in means is not equal to", mu)
p.value <- 2 * pt(q=abs(statistic), df=df, lower.tail=FALSE)
quantiles <- c(-qt(p=alpha/2, df=df, lower.tail=FALSE),
qt(p=alpha/2, df=df, lower.tail=FALSE))
conf.int <- (meanx-meany) + quantiles * se
}
if (alternative == 'less') {
mu <- as.numeric(mu)
alt <- paste("true difference in means is less than", mu)
p.value <- pt(q=statistic, df=df, lower.tail=TRUE)
conf.int <- c(-Inf,
(meanx - meany) + qt(p=alpha, df=df, lower.tail=F) * se)
}
if (alternative == 'greater') {
mu <- as.numeric(mu)
alt<- paste("true difference in means is greater than", mu)
p.value <- pt(q=statistic, df=df, lower.tail=FALSE)
conf.int <- c((meanx-meany) - qt(p=alpha, df=df, lower.tail=F) * se,
Inf)
}
# To ensure that the output values are in the correct form
names(statistic) <- 't'
parameter <- df
names(parameter) <- 'df'
attr(conf.int, 'conf.level') <- conf.level
estimate <- c(meanx, meany)
names(estimate) <- c('mean of x', 'mean of y')
null.value <- mu
names(null.value) <- 'difference in means'
method <- 'Two Sample t-test'
data.name <- paste('meanx =', meanx, ', nx =', nx,
', meany =', meany, 'and ny =', ny)
res <- list(statistic = statistic,
parameter = parameter,
p.value = p.value,
conf.int = conf.int,
estimate = estimate,
null.value = null.value,
alternative = alternative,
method = method,
data.name = data.name)
return(res)
}
fhernanb/stests documentation built on March 29, 2025, 10:36 a.m.
R Package Documentation
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Defines functions t_test_two_equal t_test_two_difer t_test_one t_test
Documented in t_test
#' Student's t-Test using values
#'
#' This function performs the t-test for one and two samples using summarized values, not the vectors.
#'
#' @param meanx sample mean for sample x.
#' @param varx sample variance for sample x.
#' @param nx sample size for sample x.
#' @param meany sample mean for sample y.
#' @param vary sample variance for sample y.
#' @param ny sample size for sample y.
#' @param alternative a character string specifying the alternative
#' hypothesis, must be one of \code{"two.sided"} (default),
#' \code{"greater"} or \code{"less"}. You can specify just the initial letter.
#' @param mu the hypothesized number (mean) in the null hypothesis.
#' @param conf.level confidence level of the interval, by default its value is 0.95.
#' @param var.equal a logical variable indicating whether to treat the
#' two variances as being equal. If \code{TRUE} then the pooled variance
#' is used to estimate the variance otherwise the Welch (or Satterthwaite)
#' approximation to the degrees of freedom is used.
#'
#' @return A list with class \code{"htest"} containing the following
#' components:
#' \item{statistic}{the value of the statistic.}
#' \item{parameter}{the degrees of freedom for the t-statistic.}
#' \item{p.value}{the p-value for the test.}
#' \item{conf.int}{a confidence interval for the mean appropiate to the
#' alternative hypothesis.}
#' \item{estimate}{the estimated mean or difference in means depending
#' on whether it was a one-sample test or a two-sample test.}
#' \item{null.value}{the specified hypothesized value for alternative hypothesis
#' value for the mean or mean difference depending on whether it was
#' a one-sample test or a two-sample test.}
#' \item{alternative}{a character string describing the alternative hypothesis.}
#' \item{method}{a character string indicating the type of test performed.}
#'
#' @examples
#' # Examples with ONE sample
#'
#' # Example 9.2 from Walpole
#' t_test(meanx=42, varx=11.9^2, nx=12,
#' mu=50, alternative='less')
#'
#' # Example 11.5 from A. F. Siegel & C. Morgan
#' t_test(meanx=100, varx=12^2, nx=9,
#' mu=83, alternative='two.sided')
#'
#' # Example 11.6 from Murray
#' t_test(meanx=0.053, varx=0.003^2, nx=10,
#' mu=0.050, alternative='two.sided')
#'
#' # --- Examples with TWO-SAMPLES and equal variances ---
#'
#' # Example 9.3 From Walpole
#' t_test(meanx=85, varx=4^2, nx=12,
#' meany=81, vary=5^2, ny=10,
#' alternative='two.sided', mu=0, var.equal=TRUE)
#'
#' # Example 13.5 from J. Freund's
#' t_test(meanx=546, varx=31^2, nx=4,
#' meany=492, vary=26^2, ny=4,
#' alternative='two.sided', mu=0, var.equal=TRUE)
#'
#' # --- Examples with TWO-SAMPLES and different variances ---
#'
#' # Example from
#' t_test(meanx =6.8, varx=1.8^2, nx=13,
#' meany=5.3, vary=1.6^2, ny=15,
#' alternative='two.sided', mu=0, var.equal=FALSE)
#'
#' @export
t_test <- function(meanx, varx, nx,
meany=NULL, vary=NULL, ny=NULL,
alternative='two.sided', mu=0,
conf.level=0.95, var.equal=FALSE){
# Checking if the information is correct
# To check if the information about x sample is correct
if (varx <= 0)
stop(paste("The variance x must be positive", "\n", ""))
if (nx <= 0)
stop(paste("The sample size nx must be positive", "\n", ""))
if (nx %% 1 != 0)
stop(paste("The sample size nx must be integer", "\n", ""))
# To check if the user provided information about y sample
if (xor(is.null(vary), is.null(ny)))
stop("Some information about sample y is missing", "\n", "")
# To check if the information about y sample is corrected
if (! is.null(vary) & ! is.null(ny) & ! is.null(meany)) {
if (vary <= 0)
stop(paste("The variance y must be positive", "\n", ""))
if (ny <= 0)
stop(paste("The sample size ny must be positive", "\n", ""))
if (ny %% 1 != 0)
stop(paste("The sample size ny must be integer", "\n", ""))
if (is.null(meany) == TRUE)
stop(paste("Some information about y sample is missing", "\n",""))
}
# To check if the conf.level it's a number between 1 and 0
if(conf.level <= 0 || conf.level >= 1)
stop("The conf.level argument must be > 0 and < 1", "\n", "" )
if(conf.level < 0.5)
warning("Confidence levels are often close to 1, eg. 0.95")
# Argument Verification Using Partial Matching
alternative <- match.arg(arg=alternative,
choices=c("two.sided","greater","less"))
# To perform the test
if (is.null(meany) & is.null(vary) & is.null(ny))
res <- t_test_one(meanx, varx, nx, alternative, mu, conf.level)
else {
if (var.equal == TRUE)
res <- t_test_two_equal(meanx, varx, nx, meany, vary, ny,
alternative, mu, conf.level, var.equal)
if (var.equal == FALSE)
res <- t_test_two_difer(meanx, varx, nx, meany, vary, ny,
alternative, mu, conf.level, var.equal)
}
class(res) <- "htest"
res
}
#' @importFrom stats pt qt
t_test_one <- function(meanx, varx, nx, alternative, mu,
conf.level) {
alpha <- 1 - conf.level
if (alternative == 'two.sided') {
statistic <- (meanx - mu) / sqrt(varx / nx)
p.value <- 2 * pt(q=abs(statistic), df=nx-1, lower.tail=FALSE)
quantiles <- c(-qt(p=alpha/2, df=nx-1, lower.tail=FALSE),
qt(p=alpha/2, df=nx-1, lower.tail=FALSE))
conf.int <- meanx + quantiles * sqrt(varx / nx)
}
if (alternative == 'less') {
statistic <- (meanx - mu) / sqrt(varx / nx)
p.value <- pt(q=statistic, df=nx-1, lower.tail=TRUE)
conf.int <- c(-Inf,
meanx + qt(p=1-alpha, df=nx-1) * sqrt(varx / nx))
}
if (alternative == 'greater') {
statistic <- (meanx - mu) / sqrt(varx / nx)
p.value <- pt(q=statistic, df=nx-1, lower.tail=FALSE)
conf.int <- c(meanx + qt(p=alpha, df=nx-1) * sqrt(varx / nx),
Inf)
}
# To ensure that the output values are in the correct form
names(statistic) <- 't'
parameter <- nx - 1
names(parameter) <- 'df'
attr(conf.int, 'conf.level') <- conf.level
estimate <- meanx
names(estimate) <- 'mean of x'
null.value <- mu
names(null.value) <- 'mean'
method <- 'One Sample t-test'
data.name <- paste('meanx = ', meanx, ', var = ', varx, ' and nx = ', nx, sep='')
res <- list(statistic=statistic,
parameter=parameter,
p.value=p.value,
conf.int=conf.int,
estimate=estimate,
null.value=null.value,
alternative=alternative,
method=method,
data.name=data.name)
return(res)
}
#' @importFrom stats pt qt
t_test_two_difer <- function(meanx, varx, nx,
meany, vary, ny,
alternative, mu,
conf.level, var.equal) {
alpha <- 1 - conf.level
df <- (varx/nx + vary/ny)^2 / ((varx/nx)^2 / (nx-1) + (vary/ny)^2 / (ny-1))
se <- sqrt(varx/nx + vary/ny)
statistic <- (meanx - meany - mu) / se
if (alternative == 'two.sided') {
p.value <- 2 * pt(q=abs(statistic), df=df, lower.tail=FALSE)
quantiles <- c(-qt(p=alpha/2, df=df, lower.tail=FALSE),
qt(p=alpha/2, df=df, lower.tail=FALSE))
conf.int <- (meanx-meany) + quantiles * se
}
if (alternative == 'less') {
p.value <- pt(q=statistic, df=df, lower.tail=TRUE)
conf.int <- c(-Inf,
(meanx-meany) + qt(p=alpha, df=df, lower.tail=F) * se)
}
if (alternative == 'greater') {
p.value <- pt(q=statistic, df=df, lower.tail=FALSE)
conf.int <- c((meanx-meany) - qt(p=alpha, df=df, lower.tail=F) * se,
Inf)
}
# To ensure that the output values are in the correct form
names(statistic) <- 't'
parameter <- df
names(parameter) <- 'df'
attr(conf.int, 'conf.level') <- conf.level
estimate <- c(meanx, meany)
names(estimate) <- c('mean of x', 'mean of y')
null.value <- mu
names(null.value) <- 'difference in means'
method <- 'Welch Two Sample t-test'
data.name <- paste('meanx = ', meanx, ', nx = ', nx,
', meany = ', meany, ' and ny = ', ny, sep='')
res <- list(statistic=statistic,
parameter=parameter,
p.value=p.value,
conf.int=conf.int,
estimate=estimate,
null.value=null.value,
alternative=alternative,
method=method,
data.name=data.name)
return(res)
}
#' @importFrom stats pt qt
t_test_two_equal <- function(meanx, varx, nx,
meany, vary, ny,
alternative, mu,
conf.level, var.equal) {
alpha <- 1 - conf.level
df <- nx + ny - 2
sp2 <- ((nx-1) * varx + (ny-1) * vary) / df
se <- sqrt(sp2/nx + sp2/ny)
statistic <- (meanx - meany - mu) / se
if (alternative == 'two.sided') {
mu <- as.numeric(mu)
alt <- paste("true difference in means is not equal to", mu)
p.value <- 2 * pt(q=abs(statistic), df=df, lower.tail=FALSE)
quantiles <- c(-qt(p=alpha/2, df=df, lower.tail=FALSE),
qt(p=alpha/2, df=df, lower.tail=FALSE))
conf.int <- (meanx-meany) + quantiles * se
}
if (alternative == 'less') {
mu <- as.numeric(mu)
alt <- paste("true difference in means is less than", mu)
p.value <- pt(q=statistic, df=df, lower.tail=TRUE)
conf.int <- c(-Inf,
(meanx - meany) + qt(p=alpha, df=df, lower.tail=F) * se)
}
if (alternative == 'greater') {
mu <- as.numeric(mu)
alt<- paste("true difference in means is greater than", mu)
p.value <- pt(q=statistic, df=df, lower.tail=FALSE)
conf.int <- c((meanx-meany) - qt(p=alpha, df=df, lower.tail=F) * se,
Inf)
}
# To ensure that the output values are in the correct form
names(statistic) <- 't'
parameter <- df
names(parameter) <- 'df'
attr(conf.int, 'conf.level') <- conf.level
estimate <- c(meanx, meany)
names(estimate) <- c('mean of x', 'mean of y')
null.value <- mu
names(null.value) <- 'difference in means'
method <- 'Two Sample t-test'
data.name <- paste('meanx =', meanx, ', nx =', nx,
', meany =', meany, 'and ny =', ny)
res <- list(statistic = statistic,
parameter = parameter,
p.value = p.value,
conf.int = conf.int,
estimate = estimate,
null.value = null.value,
alternative = alternative,
method = method,
data.name = data.name)
return(res)
}
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