## 11.4 Cohen’s *d*_{z}

_{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*= ?” to the end of your results.

_{z}A paired samples *t* found that participants’ self-reported heights were significantly lower than their measured heights (*M _{diff}* = -.148,

*SD*= 8.25),

_{diff}*t*(182) = -2.43,

*p*= .02,

*d*= -0.18.

_{z}