# standard error of difference

I have two groups

As the picture shows I have two groups. I shall perform a two-tailed t test. The correct SE (standard error of difference) is 2,77. Please help me with the formula to calculate this. How do I calculate to get an SE of 2.77?

• If you look up the t-test on wikipedia if gives the formula you need.. See en.wikipedia.org/wiki/… ... its. the denominator of the t-statistic there – Glen_b Sep 10 '17 at 21:29
• please see the help center in relation to homework style questions and edit your question (not just to add the tag it mentions, but to follow the other guidelines in relation to those kinds of questions) – Glen_b Sep 10 '17 at 21:33

As glen_b pointed out in the comments, the pooled standard error (i.e. standard error of difference) depends on whether you assume the groups variances to be equal or not. If equal, with unequal sample sizes (which will yield 2.77) and using your notation, the calculation is:

$$\sqrt{\frac{(n_1 - 1) \cdot \text{SD}_1^2 + (n_2 - 1) \cdot \text{SD}_2^2}{(n_1 + n_2 - 2)}} \cdot \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}$$

In R:

n1  <- 114186
n2  <- 60472
sd1 <- 532
sd2 <- 585
sqrt(((n1 - 1) * sd1^2 + (n2 - 1) * sd2^2) / (n1 + n2 - 2)) * sqrt(1/n1 + 1/n2)
[1] 2.770799


If unequal, you need to replace $$\text{SD}$$ with an estimate of the pooled standard deviation, using Satterthwaite's approximation.