I run the R code as follows:

library(oibiostat)
data("swim")
## independent two-sample pooled t test
t.test(swim$wet.suit.velocity, swim$swim.suit.velocity, 
       alternative = "two.sided", paired = FALSE, var.equal = TRUE)

#unequal variance two-sample t test
t.test(swim$wet.suit.velocity, swim$swim.suit.velocity, 
       alternative = "two.sided", paired = FALSE, var.equal = FALSE)

Which results in the same output:

    Two Sample t-test

data:  swim$wet.suit.velocity and swim$swim.suit.velocity
t = 1.3688, df = 22, p-value = 0.1849
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.03992124  0.19492124
sample estimates:
mean of x mean of y 
 1.506667  1.429167 

and

Welch Two Sample t-test

data:  swim$wet.suit开发者_运维技巧.velocity and swim$swim.suit.velocity
t = 1.3688, df = 21.974, p-value = 0.1849
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 -0.03992937  0.19492937
sample estimates:
mean of x mean of y 
 1.506667  1.429167 

The pooled two-sample t.test should be different from un-pooled one in terms of formulas.

But if I run the code as follows:

set.seed(5)
x1 = rnorm(15, 95, 20)         
x2 = rnorm(50, 110, 5)
t.test(x1, x2) # Welch
t.test(x1, x2, var.eq=T) # pooled

The outputs from both t.test are clearly different. So, I just got a coincidence of data set?

I calculate by hand and find that the output from Welch Two Sample t-test is right. I am very confused why the output of pooled t.test is wrong.

---

Edit

Like I say in comment, package oibiostat is not on CRAN, it's on GitHub. If not installed yet, run

devtools::install_github("OI-Biostat/oi_biostat_data")

And there's no need to load a package to access one of its data sets, the following will load it.

data(swim, package = "oibiostat")