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I teach A level and Undergrad Foundation Biology. We are applying 2-tailed 2-sample t-test for unequal variance (this bit is directly prescribed from the exam boards):

$$|T| = \frac{|\bar{X}_1-\bar{X}_2|}{\sqrt{\frac{S_1 \cdot S_1}{n_1}+\frac{S_2 \cdot S_2}{n_2}}}.$$

However, we are calculating degrees of freedom using $n_1+n_2-2$ which should really only be for equal variance.

However, as students will likely have identical or similar sample sizes, and are also likely to have relatively similar variances, is it appropriate to use this calculation for d.f. in this situation?

Ben
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Mandy Wallington
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  • I have edited this question to put it into LaTex format, to make it easier to read. The equation can be simplified by expressing $S_1 \cdot S_1 = S_1^2$ and $S_2 \cdot S_2 = S_2^2$, but I have not done this, since I wanted to remain faithful to the way the OP has written the equation. – Ben May 04 '18 at 00:13
  • It would only be an approximation but close to the true value. So I think you can use it. – sww May 03 '18 at 23:38
  • Possible duplicate of [Unequal sample sizes in t test with homogeneity of variance](https://stats.stackexchange.com/questions/166680/unequal-sample-sizes-in-t-test-with-homogeneity-of-variance) – Jeremy Miles May 04 '18 at 01:33

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