The power is in general a function of the possible distributions, often determined by a parameter, under the alternative hypothesis.

We test z as a standard normal under the null hypothesis of no expression difference.

The test involves the calculation of a statistic, usually called U, whose distribution under the null hypothesis is known.

Under the hypothesis of the previous lemma, (indeed, the lemma shows that ).

The only required condition is that X has finite moment under the null hypothesis.

Under the null hypothesis, the probability of cancer death in each group is p .

Low values of the likelihood ratio mean that the observed result was less likely to occur under the null hypothesis as compared to the alternative.

We also fitted the model under the null hypothesis that there is no major gene with a single normal distribution.

These are the parameter values under the null hypothesis.

Under the null hypothesis the probability of death from all causes is p + k in each group.