Null distribution

If there was no difference between their heart rate, then the scientist would be able to say that the test statistics would follow the null distribution.

Then the scientists could determine that if there was significant difference that means the test follows the alternative distribution.

Resampling procedures, such as non-parametric or model-based bootstrap, can provide consistent estimators for the null distributions.

Improper choice of the null distribution poses significant influence on type I error and power properties in the testing process.

[5] Under a Bayesian framework, the large-scale studies allow the null distribution to be put into a probabilistic context with its non-null counterparts.

In addition, the correlation across sampling units and unobserved covariates may lead to wrong theoretical null distribution.

[6] Permutation methods are frequently used in multiple testing to obtain an empirical null distribution generated from data.