11.4 Cohen’s d_z

Cohen’s d_z is a specialized form of Cohen’s d that is commonly used for paired samples t tests. You can review the video or transcript for these analysis if you need a refresher.

Unfortunately, there is no way to directly calculate Cohen’s d_z in R Commander; however, you can use the following simple formula to calculate it:

d_z = t / sqrt(df + 1)

In the lab on paired samples t tests, we obtained the following output:

From this output, we can see that t = -2.427 and df = 182. Therefore,

d_z = -2.427 / sqrt(182 + 1)

d_z = -0.179

Cohen’s d_z is produced automatically in SPSS.

These values indicates that participants’ self-reported heights were on average 0.18 standard deviations lower than their measured heights.

To report Cohen’s d_z in APA format, add “d_z = ?” to the end of your results.

A paired samples t found that participants’ self-reported heights were significantly lower than their measured heights (M_diff = -.148, SD_diff = 8.25), t(182) = -2.43, p = .02, d_z = -0.18.