# R code for two sample t-test in case of equal variances

In R, how can I perform a two sample t-test in the case of equal variances?

My actual problem is to compare different algorithms for length measurements in machine vision.

I have studied Applied Statistics and Probability for Engineers by Montgomery & Runger and I have tried to implement the test in R and compare the results to the R command t.test.

This is my code:

# Douglas C. Montgomery, George C. Runger
# Applied Statistics and Probability for Engineers
# Third Edition
# 10-3.1 Hypotheses Tests for a Difference in Means, Variances Unknown, p.337
# Case 1: sigma_1^2 = sigma_2^2 = sigma^2
#
two_sample_t_test_equal_variance <- function(x1,x2,Delta_0,alpha)
{
n1 <- length(x1)
n2 <- length(x2)
dof <- n1+n2-2
S1_squared <- var(x1)
S2_squared <- var(x2)
#pooled estimator:
Sp_squared <- ((n1-1)*S1_squared + (n2-1)*S2_squared)/(n1+n2-2)
x1_bar <- mean(x1)
x2_bar <- mean(x2)
Sp <- sqrt(Sp_squared)
t0 <- (x1_bar - x2_bar - Delta_0)/(Sp*sqrt(1/n1+1/n2))
t_half_alpha_dof <- -qt(alpha/2,dof)
reject_H0 <- (t0 > t_half_alpha_dof || t0 < - t_half_alpha_dof)
if ( reject_H0 ) {
cat("Reject H0 (alpha =",alpha,").\nH0 is mu1 - mu2 =", Delta_0, "\n\n" )
} else {
cat("Cannot reject H0 (alpha =",alpha,").\nH0 is mu1 - mu2 =", Delta_0, "\n\n" )
}

test_result <- t.test(x1, x2, alternative="two.sided", mu=Delta_0,
paired=FALSE, var.equal = TRUE )

accept_H0_by_R <- (test_result$p.value > alpha) if ( reject_H0 != !accept_H0_by_R ) { cat("WARNING: R t.test gives a different answer for accepting H0.\n" ) } rel_error_warn <- 0.01 if ( abs(test_result$statistic - t0)/abs(test_result\$statistic) > rel_error_warn ) {
cat("WARNING: t0 relative error is >", rel_error_warn, "\n"  )
}
}

# data from EXAMPLE 10-5, p.339
cat1<-c(91.50, 94.18, 92.18, 95.39, 91.79, 89.07, 94.72, 89.21)
cat2<-c(89.19, 90.95, 90.46, 93.21, 97.19, 97.04, 91.07, 92.75)
two_sample_t_test_equal_variance(cat1,cat2,0,0.05)


Is my invocation of t.test correct for the case at hand?

Is there any error in the code?

I tagged the question with "homework" even if I am not at school since more than 10 years and I am self-studying statistics for job-related reasons.

Thank you. Alessandro

• Are you aware that there is already a function in R doing that ? Try help(t.test). – steffen Jun 29 '11 at 10:15
• @steffen Yes, I am aware. I included in the code my invocation of t.test and I would like to know whether it is correct. – Alessandro Jacopson Jun 29 '11 at 10:22
• @uvts_csv Sorry, did not read the question properly :( – steffen Jun 29 '11 at 10:29