B5 Statistics of effect size

Once you know how, you should get into the habit of reporting statistics of effect size. For unrelated measures IVs the commonest statistics reported are Cohen's delta (d ) and partial eta squared
( ). (For more on effect size see Chapter 12 of the book. For more on reporting such statistics see also Section 4.6.13 and Section 12.3.2 of the book.)

Cohen's d is relatively easily calculated from the means and standard deviations and you can find various websites that will do the calculations for you if you cannot find it in your statistical analysis software package. The Third Edition of Pallant, one of the statistics textbooks paired with Designing and Reporting Experiments in Psychology, covers Cohen's d and eta squared in Part Five. She recommends the following website for calculating Cohen's d : http://web.uccs.edu/lbecker/Psy590/escalc3.htm

If you are using SPSS as your statistics package you will find options for adding partial eta squared to your output in various ways. For one-way ANOVA with an unrelated measures IV you can specify it as an option in the compare means analysis and for ANOVA with one or more unrelated measures IVs you can find estimates of effect size as an option in the univariate analysis of the General Linear Model (GLM) menu. It is also available as an option in all the GLM analyses (univariate, multivariate and repeated measures). If for some reason you find yourself needing to calculate it by hand you can find a simple equation to follow using an independent t test in Pallant (Third Edition) Chapter 17. (If you are unfamiliar with the term unrelated measures IV, see Section 10.2 of the book. If you are unfamiliar with terms like "one way" two way", see Section 13.3 of the book.)

Report the effect size and what it means as well as (or if you are so inclined, instead of) the outcome in terms of statistical significance. Eta squared can be expressed as the percentage of the variance explained by your IV simply by multiplying by 100. So, an eta squared of .01 is equal to 1% of the variance (.01 x 100 = 1), which is not very much, whereas an eta squared of .14 is equal to 14% of the variance (.14 x 100 = 14), which is quite a lot. Indeed, there are guidelines for estimating the magnitude of the effect. These are often cited and come from Cohen (1988):

You can cite both the magnitude of the effect and for eta squared/partial eta squared also the percentage of the variance explained by your IV.

You can find an example of how to report effect size statistics - in this case partial eta squared - in Section 12.3.2 of the book. If you are using Cohen's d instead, just substitute it for partial eta squared and interpret it as indicating the difference your IV made as a proportion of a standard deviation referring to the guidelines above. For example, a d of .48 means that your IV made almost half a standard deviation difference, which is a medium effect according to Cohen's (1988) guidelines.

Some issues to watch out for

Effect size statistics may not always be readily available for related measures IVs. (See Section 10.2 of the book if you are unfamiliar with the term related measures IV.)