If a set of data is simulated from non-normal distribution and some selected tests confirm that, the p-values seem not to be the same, sometimes varying significantly.
Toni Beverin
Non-normal distribution means you have density function other than gaussian, and you have to calculate p-value for that function. If you are getting wrong results you probably are calculating p-value for wrong function.
The p-value is the probability of obtaining a test statistic result at least as extreme as the one that was actually observed.
p - value for general density function if you are looking for results equal or greater than result in point a you can calculate formula 1) and if you are looking for results equal or smaller than result in point a use formula 2):
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