# Introduction to Effect Size

In the above discussion on standardized scores, we pointed out that comparisons can be made much easier when things are measured on the same scale.  The problem of measuring the same thing on different scales is also a problem when we want to examine the differences between groups.  Say, for example, that a researcher conducts an experiment using a pretest and a posttest administered after some treatment is given (The d statistic works equally well when an experimental and a control group is used).

She can determine the difference between the pretest score and the posttest score by simple subtraction.  The resulting difference is only meaningful in terms of the scale used.  We can compute a measure of effect size that allows us to consider the magnitude of the difference in terms of standard deviation units.

While there are several variations on measures of effect size, a statistic known as d is one of the most common.  The d statistic is sometimes referred to as a standardized mean difference statistic.  Because it is scaled in standard deviation units, the range of d is usually between -3.0 and +3.0.  Note that if d equals zero, then there is no effect.  The farther d is from zero, the larger the effect size.  The strength is not affected by whether the result is positive or negative—only the magnitude matters.

While many researchers argue against attaching labels to effect sizes, a sort of naming convention has nevertheless developed.  It is common to interpret and effect size (d) of 0.5 or greater as a “large” effect, effect sizes between 0.3 and 0.5 as “moderate,” and effect sizes between 0.1 and 0.3 as small.  Effect sizes less than 0.1 are considered trivial.

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