How do I compute Cohen's d in SPSS?

Cohen's d represents the difference between a pair of group means expressed in terms of the average group standard deviation.

Cohen's d = $$\frac{\mbox{difference in group means}}{\mbox{average group sd}} $$

This may be worked out using the routine of Smithson which is located in the demo file in the power talk given as part of the [:StatsCourse2009:Graduate Statistics Courses 2009.] Alternatively the average group sd is equal to the square root of the Mean Square Error outputted using the ONEWAY procedure in SPSS and dividing this into the difference in the two means which can be obtained using the means procedure. For example for comparing the two age 'pr' group means we can run the below

ONEWAY
  age BY pr
  /MISSING ANALYSIS.
MEANS
  TABLES=age  BY pr
  /CELLS MEAN COUNT STDDEV  .

You can alternatively use SPSS Output Management Syntax (OMS) as shown [:FAQ/omscd:here] to compute Cohen's d which converts the tabular output in SPSS procedures into data files which may then be manipulated to give statistics of interest.

Howell (2013, p.643) gives a formula for the standard error of d equal to

$$sqrt{\frac{1}{n1}+\frac{1}{n2}+\frac{d^text{2}}{2(n1+n2)}}$$

for sample sizes n1 and n2 and a Cohens' d equal to d. The denominator on the right hand side becomes 2n1 if the standard deviation of the control group is used to compute d (Howell 2013 quoting Gleser and Olkin, 2009).

References

Gleser LJ and Olkin I (2009). Stochastically dependent effect sizes. In H. Cooper. LV Hedges & JC Valentine (Eds.). The handbook of research synthesis and meta-analysis. New York:Russell Sage Foundation.

Howell DC (2013) Statistical methods for psychology. 8th Edition. International edition. Wadsworth:Belmont,CA.