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t-test with minimum number of samples


There are two different ways to justify the use of the t-test. 
  1. Your data is normally distributed and you have at least two samples per group 
  2. You have large sample sizes in each group
If either of these cases hold, then the t-test is considered a valid test. So if you are willing to make the assumption that your data is normally distributed (which many researchers who collect small samples are), then you have nothing to worry about. 
However, someone might reasonably object that you are relying on this assumption to get your results, especially if your data is known to be skewed. Then the question of sample size required for valid inference is a very reasonable one. 
As for how large a sample size is required, unfortunately there's no real solid answer for that; the more skewed your data, the bigger the sample size required to make the approximation reasonable. 15-20 per group is usually considered reasonable large, but as with most rules of thumb, there exist counter examples: for example, in lottery ticket returns (where 1 in, say, 10,000,000 observations is an EXTREME outlier), you would literally need somewhere around 100,000,000 observations before these tests would be appropriate.

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