# What does a p value histogram that is “normally” distributed mean?

Let's say I performed 100 tests and and want to correct for multiple comparisons. Before I do so, I plot the unaltered p values in a histogram to see what the distribution looks like.

If the null were true, you would expect that a histogram of unaltered p values would be a uniform distribution. If it was right skewed, you might conclude that overall, there seems to be something real going on.

However, what if you got something like:

What does this mean?

• Based on the count values on your graph I would say you have a very small sample hence why this unusual result. You do not have enough p-values to really check how they are distributed (there is too much variation). – user2974951 Dec 21 '18 at 11:48
• Right you are correct that the sample size is small (n = 36), but despite that, I am still curious what it would mean if say n = 1000 – hlinee Dec 21 '18 at 12:24
• The interpretation would be similar to when you have right or left skewed p-values. When you have most of your p-values on the left side you would conclude that in most cases we can find an effect, if most of your p-values were on the right side you would conclude that in most cases we cannot find an effect. If most p-values were in the middle you would conclude that in most cases we cannot find an effect but we are not too sure in this (for ex. there is still 50 % chance of this outcome happening). – user2974951 Dec 21 '18 at 12:31