# SAGE Journal Articles

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**Summary/Abstract: **Most of the debates around statistical testing suffer from a failure to identify clearly the features specific to the theories invented by Fisher and by Neyman and Pearson. These features are outlined. The hybrids of Fisher’s and Neyman-Pearson’s theory are briefly addressed. The lack of random sampling and its consequences for statistical inference are also highlighted, leading to the recommendation to dispense with inferences and perform approximate randomization tests instead. A possible scheme for the appraisal of substantive hypotheses is offered, the corroboration of which is a necessary prerequisite for scientific explanations and predictions. The scheme is partly based on the Neyman-Pearson theory. This theory, though not perfect, is superior to its competitors, especially when examining substantive hypotheses. The many statistical and extra-statistical decisions prior to experimentation and the inevitable subjectivity of our research endeavors are emphasized. If feasible, statistical problems should be discussed from an extra-statistical methodological/epistemological viewpoint.

#### Questions to Consider

1. According to Hager, what are some of the differences between Fisher’s theory of significance testing and Neyman and Pearson’s theory of testing statistical hypotheses?

2. With randomization tests the results are:

- very generalizable.
- valid only for the one experiment.
- slightly biased.
- valid for a class of experiments.

3. _______ hypotheses refer solely to random variables whereas _______ hypotheses typically are conjectures about unobservable hypothetical entities, states, processes, and the relationship(s) between the concepts.

- Substantive; statistical
- Statistical; substantive
- Directional; bidirectional
- One-tailed; two-tailed

**Summary/Abstract: **Randomization tests are usually represented as strategies for determining significance through the comparison of the value of an obtained test statistic with a distribution of such values associated with every possible random assignment of subjects to treatments. Randomization tests can, however, also be conducted on the basis of a subset of all possible assignments and justified through the concept of a *permutation group *as defined by Chung and Fraser (1958). This idea is useful in acquiring a deeper understanding of randomization tests and in facilitating the development of new classes of tests.

**Questions to Consider**

1. Describe the importance of a reference set for a randomization test.

2. A(n) _______ group is a collection of rearranging operations that produce the same set when applied to elements in the collection, regardless of the initial element to which the operations are applied.

- randomization
- elemental
- permutation
- combination

3. The reference set, under the null hypothesis, is the same as it would have been if any of the alternative randomizations associated with the data permutations in the reference set had been the __________ randomization.

- obtained
- estimated
- approximated
- theoretical