Before we can consider various issues and procedures in the cumulation of research results, we must become quite explicit about the meaning of the concept "results of a study." It is easiest to begin with what we do not mean. We do not mean the prose conclusion drawn by the investigator and reported in the abstract, the results, or the discussion section of the research report. We also do not mean the results of an omnibus F test with df > 1 in the numerator or an omnibus X2 test with df > 1. (These omnibus tests address vague questions that are rarely, if ever, of scientific interest.)
What we do mean is the answer to the question: What is the relationship between any variable X and any variable Y? The variables X and Y are chosen with only the constraint that their relationship be of interest to us. The answer to this question should normally come in two parts: (1) the estimate of the magnitude of the relationship (the effect size), and (2) an indication of the accuracy, precision, or stability of the estimated effect size (as in a confidence interval placed around the effect size estimate). An alternative to the second part of the answer is one not intrinsi
MILLER ANALOGIES TEST
cally more useful, but one more consistent with the existing practices of researchers; that is, the examination of the significance level of the difference between the obtained effect size and the effect size expected under the null hypothesis (usually an effect size of zero). If the significance level is employed, it should always be reported accurately and never as "significant" or "not significant."
Because a complete reporting of the results of a study requires the report of both the effect size and level of statistical significance, it is useful to make explicit the relationship between these quantities. The general relationship is given by:
Test of Significance = Size of Effect x Size of Study
In other words, the larger the study in terms of the number of sampling units, the more significant the results will be. This is true unless the size of the effect is truly zero, in which case a larger study will not produce a result that is any more significant than a smaller study. However, effect magnitudes of zero are not encountered very often.
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