The composite hypothesis states that Haldane's rule in different subdivisions has different causes.

Definition (likelihood ratio test for composite hypotheses)

A composite hypothesis formulation would be that the examinee's ability is in the region above the cutscore or the region below the cutscore.

Note that this is a point hypothesis formulation rather than a composite hypothesis formulation that is more conceptually appropriate.

The Karlin-Rubin theorem can be regarded as an extension of the Neyman-Pearson lemma for composite hypotheses.

Currently, the most popular explanation for Haldane's rule is the composite hypothesis, which divides Haldane's rule into multiple subdivisions, including sterility, inviability, male heterogamety, and female heterogamety.

Careful treatments of point hypotheses for subsets of parameters do consider them as composite hypotheses and study how the p-value for a fixed critical value of the test statistic varies with the parameters that are not specified by the null hypothesis.

A composite hypothesis holds that early language took the form of part gestural and part vocal mimesis (imitative 'song-and-dance'), combining modalities because all signals (like those of apes and monkeys) still needed to be costly in order to be intrinsically convincing.