I tried to replicate the following simple t-test and this calculates t = -3.5985:
t.test(gktlists ~ small, data=star, var.equal=FALSE)
Here is what I did:
mean_small <- mean(star$gktlists[star$small == 1], na.rm = TRUE)
mean_large <- mean(star$gktlists[star$small == 0], na.rm = TRUE)
print(mean_small - mean_large)
var_small <- var(star$gktlists[star$small == 1], na.rm=TRUE)
var_large <- var(star$gktlists[star$small == 0], na.rm=TRUE)
len_small <- length(star$gktlists[star$small == 1])
len_large <- length(star$gktlists[star$small == 0])
(mean_large - mean_small) / sqrt(var_small / len_small + var_large / len_large)
But I get a different t-statistic, t = -3.746202. Is that only due to rounding errors or is the t.test() doing something different than I expect. What am I doing wrong?
Using sleep data, your code works actually fine for me.
> mean_small <- mean(sleep$extra[sleep$group == 1], na.rm = TRUE)
> mean_large <- mean(sleep$extra[sleep$group == 2], na.rm = TRUE)
> print(mean_small - mean_large)
[1] -1.58
> var_small <- var(sleep$extra[sleep$group == 1], na.rm=TRUE)
> var_large <- var(sleep$extra[sleep$group == 2], na.rm=TRUE)
> len_small <- length(sleep$extra[sleep$group == 1])
> len_large <- length(sleep$extra[sleep$group == 2])
> (mean_large - mean_small)/sqrt(var_small/len_small + var_large/len_large)
[1] 1.860813
> (tt <- t.test(extra ~ group, data = sleep))
Welch Two Sample t-test
data: extra by group
t = -1.8608, df = 17.776, p-value = 0.07939
alternative hypothesis: true difference in means between group 1 and group 2 is not equal to 0
95 percent confidence interval:
-3.3654832 0.2054832
sample estimates:
mean in group 1 mean in group 2
0.75 2.33
> diff(tt$estimate)
mean in group 2
1.58