If two samples are different in size, like 20 to 60, is it a good idea to apply two sample t-tests and chi-square tests?

Asked by kounoupi (577 ) 3 months ago

It’s been quite a few years since I was at uni and I have effectively forgotten everything I ever knew about statistics. So here I am.

All other prerequisites for the two sample t- test (for the continuous variables) and the chi square test (for the categorical ones) are valid. The two samples are independent, normal distribution etc etc. The only problem is that according to my old statistics book, the two samples that are to be compared need to be “equal in size”. There is no hint whatsoever about how much different in size the two samples can be.
Should I downsize the big sample to n=20 (option A) or should I go on and apply the tests (option B)? What are the pros and cons when going with option A and what when going with option B?

I am pretty sure I am going to lose on statistical power either way, but I am not sure which of the two options is the most acceptable.

Observing members: 0 Composing members: 0

If the data is continuous (or close to it), then I would use this version of the two-sample t-test. You would not have to downsize the sample.

The number of degrees of freedom is hard to calculate, I’ve always used a TI calculator that has that function built in. If you do not have a way to compute it, then you can use the smaller sample size, minus one, as a conservative estimate. In this case, df > 19.

PhiNotPi (10978 )

You may find you may have to rely on non-parametric tests. These are extremely conservative and increase the risk of type-2 errors.

Dr_Lawrence (19066 )

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