In the long run, the return of the stock market follows normal distribution (Roughly). Now, I am on the lookout for some signals generated by my Indicators which can give me an edge. Once I get 25-30 matches, I calculate two period forward return and if the mean is greater than 0, I try to find if the mean is statistically greater than 0. Now, although markets, in the long run, generate normal distributions with mean 0, the small sample of 30 days makes me question this assumption. Can I still use T-Test to
t-test is supposed to be used when the data is normally distributed. So, if you haven't surety about the distribution of data, you can't apply the t-test.
Mood's median test, Levene's test, One-sample sign test, etc. are available as equivalent tools for Non-normally distributed data.
In case of absense of normality in the data, t-test should not be applied. In this scenario non-parametric analysis must be carried out. Try to use Mann-Whitney or Wilcoxon tests for independent samples or repeated measures.
I hope this was useful.
It must be always a normal distribution. There are other test like Mood's median test that not required this concept.
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