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A significance test of interaction in 2 x K designs with proportions

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Doi: 10.20982/tqmp.03.1.p001

Michael, George A.
Keywords: Statistical test , Test of proportions
(no sample data)   (Appendix)

When investigating the deficits of a single patient, psychologists usually compare his/her performance in one or more tests to the performance of a control group. This can be done for any kind of variables, provided (i) that the design does not require the investigation of interactions between two or more factors, (ii) that the comparison between two or more individuals is not desired, and (iii) that the collection of the control data is possible. Yet, researchers are constantly interested in assessing interactions in the performance of an individual, and in the comparison of two or more individuals for investigating double dissociations or the efficiency of different methods of therapy, etc. They also may desire to investigate cases where only extremely simple and easy tasks can be performed, where ceiling effects are observed in the performance of the controls, and thus the case-controls comparison is impossible. The available statistical tools for the analysis of intra-individual or inter-individual performance (mainly with proportions) do not offer the possibility to assess interaction, they are not appropriate when some cells may contain 0 or 1 proportions, and when the sample size is small. Here, we present the Q’ test which may be used to test the hypothesis of equal proportions and proportion differences in 2 x K designs, offering therefore the possibility for researchers to investigate the main effects and interaction. This test can be used for any sample size and even when the data contains extreme proportions. Finally, a procedure of multiple comparisons described in this paper may be used to locate statistically significant sources of variance and differences.

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