Article

The Single Latin Square Design in Psychological Research

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Abstract

The expected value of mean square concept is used to determine the effects of the presence of interactions in the single Latin square design onF tests. The results indicate that as the number of random effects included in the experiment increase, moreF tests are unbiased, and that some of these are validF tests. However, whenF test bias does occur it is almost always of a negative nature so that the conclusions stated are conservative ones. PositiveF test bias may occur when the triple interaction is extant and when zero or one random variate is included in the experiment.

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The conceptual model, designed and implemented in context of this work, requires to be proved and validated. Furthermore, shortcomings and limitations of the approach should be enlightened to enable future work for the community on this topic.
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In an earlier paper, a method of analysis, due to Neyman and now known generally as variance component analysis, was used to examineF-test bias for experimental designs in education of the randomized block type. The same method is now applied to studyF-test bias for designs of the Latin square type. The results, in general, disprove the view that, for a valid application of Latin square techniques, it is necessary that all interactions are zero.
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