Estimating the null distribution There may be various ways to estimate the null distribution 0 .

We used a permutation test to generate an empirical null distribution of for all word pairs with N 10.

This shifts the alternative distribution further away from the null distribution and thus increases power.

How extreme the observed test statistic is will be judged by counting the number of times that more extreme values are obtained from the null distribution.

In Clest, the observed similarity statistics are compared across numbers of clusters k by considering their distance from their estimated expected value under the null distribution.

In cases where the tests are not independent, the null distribution of X is more complicated.

In an F-test, the null distribution is an F-distribution.

A total of 100,000 iterations were done with each data set to create null distributions of random information content.

The observed information values were then compared to the null distributions to infer their probabilities.

"On the null distribution of the Kruskal-Wallis statistic".