Common Errors in Statistics (and How to Avoid Them), 4th Edition

TEST ASSUMPTIONS

As noted in previous chapters, before any statistical test can be performed and a p-value or confidence interval be derived, we must first establish all of the following:

1. That the sample was selected at random from the population or from specific subsets (strata) of the population of interest.

2. That subjects were assigned to treatments at random.

3. That observations and observers are free of bias.

To these guidelines, we now add the following:

4. That all assumptions are satisfied.

Every statistical procedure relies on certain assumptions for correctness. Errors in testing hypotheses come about either because the assumptions underlying the chosen test are not satisfied, or because the chosen test is less powerful than other competing procedures. We shall study each of these lapses in turn.

Virtually all statistical procedures rely on the assumption that the observations are independent.

Virtually all statistical procedures require that at least one of the following successively weaker assumptions be satisfied under the null hypothesis:

1. The observations are identically distributed and their distribution is known.

2. The observations are exchangeable, that is, their joint distribution remains unchanged when the labels on the observations are exchanged.

3. The observations are drawn from populations in which a specific parameter is the same across the populations.

The first assumption is the strongest assumption. If it is true, the following two ...