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For example, if I have 12 participants who responded in a particular way to a task, and 7 participants who responded a different way. I want to compare the response time between these two 'groups' of respondents. Will having an unequal sample size impact the t-test?

Does the independent t-test make assumptions about sample size? If so, would a non-parametric test be more appropriate?

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  • $\begingroup$ The t test assumes both variables have normal distributions and for very large sample sizes the normal approximation works. In small sample sizes like yours you need to get the degrees of freedom right. For your case it would be n+m-2 degrees of freedom where n=12 and m=7 giving a total of 17 degrees of freedom. The Wilcoxon rank sum test is a nonparametric method that applies to your case but would lose power. $\endgroup$ – Michael R. Chernick Mar 27 '17 at 16:53
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It doesn't make assumptions about sample size. However, the test is not robust to violations of homogeneity of variance with unequal n. Consider using the Welch test. Response time often has considerable positive skew so you can usually gain power with a transformation such as log(x). The t test is conservative with skewed distributions so a significant difference with skewed distributions is interpretable.

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