English: Non language-specific illustration of the small p-values that can appear when performing multiple hypothesis testing.

30 samples of 10 dots of random color (blue or red) are observed. On each sample, a two-tailed binomial test of the null hypothesis that blue and red are equally probable is performed. The possible p-values for this test are shown on the first row as a function of the number of blue and red dots in the sample.

Although the 30 samples were all simulated under the null, one of the resulting p-values is very small (p = 0.0215) which would produce a false rejection (an incorrect conclusion that red is more probable than blue) at the typical level 0.05 in the absence of correction.

This is a similar story to xkcd comic "Significant".