Section 2: Interpreting the effect size

When they summarize these studies into an effect size of Cohen's d = .33, how big an effect are we talking about? How much does knowing a child was included in the corporal punishment group vs the non-corporal punishment group help me predict their outcomes?

• If you look at this primer Download this primeron Cohen's d, you will see that an effect size of .33 suggests two overlapping distributions of child outcomes. It also explains how we gauge small, medium, and large effect sizes. So how big an effect is .33?

The primer contains a table on interpreting effect size. In this table, .3 is the closest we can get to .33. Think of the "control group" as the non-spanked group and the "experimental group" as the spanked group. Note that with an effect size of .3, the probability that you could guess which kids had been spanked and which had not based on their outcomes (e.g., aggression, relationship with parents, etc.) is 56%. Compare this to a 50/50 guess. With an effect size of .3, there is a 58% chance that a child picked at random from the corporal punishment group will have a higher negative outcome score than a child picked at random from the control group Compare this to a 50/50 probability if spanking had no effect.

Another way to visualize this is with this example calculator https://rpsychologist.com/d3/cohend/Links to an external site.

I will ask you to work through some exercises with this calculator in the Section 2 Assessment. Of note, his calculator is based on the idea that there are two groups--a control group which is lower on something positive (like endurance) and a treatment group which is higher on something positive (like endurance). But in our example about corporal punishment, the higher scores for the children exposed to corporal punishment mean that they are higher on things like aggression. So below I have rewritten the "Common Language Explanation" this calculator provides for OUR example, using aggression as the outcome, and .33 as Cohen's d (the effect size shown in the meta analysis).

With a Cohen's d of 0.33, 62.9% of the children in the corporal punishment group are estimated to be above the MEAN of the children in the non-corporal punishment group on a measure of aggression (Note, this also indicates that 37.1% of the corporal punishment children will be BELOW the mean of the non corporal punishment group on scores of aggression). Read that first sentence carefully: this does NOT indicate that 62.9% of corporal punishment children will have higher scores than non-corporal punishment children. With a Cohen's d of .33, 86.9% of the children in the two groups will have overlapping scores. Note, this means that only 13.1% of the scores in the two distributions will not overlap. Similar to the table with the .3 example, there is a 59.2% chance that a child picked at random from the corporal punishment group will have a higher negative outcome score than a child picked at random from the control group .

Question 12 pts

1) According the the primer on Cohen's d, how big an effect is .33?

a) somewhere between a medium and large effect