• = Obtaining z as input to Rosenthal formula on previous page for a nonparametric analysis using three or more groups =

If you really want to quote an effect size for the pooled analysis ie comparing all the groups at once then you could estimate z as below (again following Field, 2005):

1. Obtain the one or two-sided p-value for the chi-square for the data from using the Kruskal-Wallis and/or chi-square test (it will have more than one df)
2. Find the z value that has the same one or two-sided p-value as that obtained just now for the chi-square. You can do this using a function in any stats package or in Excel.

For example in SPSS: suppose the two-sided p-value of my chi-square from doing either a kruskal-wallis or chi-square test is 0.02. If I run the below

COMPUTE PIN=0.02.
COMPUTE P=1-(PIN/2).
COMPUTE ZOUT=IDF.NORMAL(P,0,1).
EXE.

give s z of 2.326 so if I say have a total sample size of 40 the the effect size = 2.326/sqrt(4)= 0.367. Alternatively you could run this from the gui using compute.

If you are using a one-tailed test and say had a one-sided p=0.01 then we could instead tweak the above and use the below

COMPUTE PIN=0.01.
COMPUTE P=1-(PIN).
COMPUTE ZOUT=IDF.NORMAL(P,0,1).
EXE.

which gives a z=1.645.