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Detecting a lack of association: An equivalence testing approach
Author(s) -
Goertzen Jason R.,
Cribbie Robert A.
Publication year - 2010
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711009x475853
Subject(s) - association (psychology) , type i and type ii errors , equivalence (formal languages) , sample size determination , test (biology) , association test , statistics , statistical hypothesis testing , econometrics , independence (probability theory) , statistical power , sample (material) , psychology , computer science , mathematics , chromatography , gene , genotype , single nucleotide polymorphism , psychotherapist , biology , paleontology , biochemistry , chemistry , discrete mathematics
Researchers often test for a lack of association between variables. A lack of association is usually established by demonstrating a non‐significant relationship with a traditional test (e.g., Pearson's r ). However, for logical as well as statistical reasons, such conclusions are problematic. In this paper, we discuss and compare the empirical Type I error and power rates of three lack of association tests. The results indicate that large, sometimes very large, sample sizes are required for the test statistics to be appropriate. What is especially problematic is that the required sample sizes may exceed what is practically feasible for the conditions that are expected to be common among researchers in psychology. This paper highlights the importance of using available lack of association tests, instead of traditional tests of association, for demonstrating the independence of variables, and qualifies the conditions under which these tests are appropriate.