
Hypothesis Tests and Simulation Envelopes 389
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Simple null hypothesis Composite null hypothesis
Data Data
Null model
Fitted null model
Simulations from null model Simulations from fitted model
Figure 10.4. Why Monte Carlo tests are typically conservative when the null hypothe sis is com-
posite. Left column: simple null hypothe sis; Right column: composite null hypothesis. The Monte
Carlo test compare s the observed value (dot) with simulated values (vertical bars). For a simple
null hypothesis, the simulated values are generated from the null distribution, and the test is exact.
For a composite null hypothesis, simulated ...