Various effect sizes have been proposed. However, different effect size measures are suitable for different types of data, and the interpretations of effect sizes are generally arbitrary and remain problematic.
In this article, the concepts of contrast variable, its standardized mean (SMCV) and c + -probability are explored to link together the commonly used effect sizes including the probabilistic index and ratios of mean difference to variability. A contrast variable can provide both a probabilistic meaning and an index of signal-to-noise ratio to interpret the strength of a comparison, which offers us a strong base to classify the strength of a comparison. Contrast variable, SMCV and c + -probability not only give interpretations to both Cohen’s and McLean’s criteria but also work effectively and consistently for either relationship or group comparison in either independent or correlated situations and in either two or more than 2 groups.
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