Statistical and psychometric utilities

for psychotherapy and counselling research

Information written and mounted by Chris Evans (Email to: on, last updated All information mounted under a Creative Commons License. Please respect the licence but feel free to reuse anything here within the terms that licence allows. Creative Commons License

New 09.x.14 statistical significance of the difference between two independent Cronbach alpha values

If you use the same multi-item instrument in two different samples you should really look to see if the internal reliabilities are the same before testing other things and just assuming that reliability is the same. Generally there won't be a difference or one that is only trivial (which may be statistically significant if you have huge samples) but this can be important if you are using the measure in very different samples, for example using a body image measure in very different cultures or even perhaps using a measure of something gender sensitive like body image in men and women and comparing your sample parameters. In these sorts of situations, as we showed rather nicely I think a long time ago (Evans, Dolan & Toriola (1997). Detection of intra- and cross-cultural non-equivalence by simple methods in cross-cultural research: evidence from a study of eating attitudes in Nigeria and Britain. Eating and Weight Disorders, 2, 67-78) a good diagnostic check that will detect problems is to test the Cronbach alpha values in each sample. While all the major statistics packages give alpha, and SPSS has actually given it a 95% confidence interval for ages now, none of them as far as I know offer a test of the difference between two alpha values despite Feldt having worked out the parametric statistics of the test in 1969 (for a summary see Feldt, Woodruff & Salih (1987). Statistical inference for coefficient alpha. Applied Psychological Measurement, 11(1):93-103). I've finally found time to put up an online that carries out Feldt's test, see

New 31.vii.14. The problem of subgroup mean differences in correlation, regression and factor analyses

I've had a running discussion over some years now with a good colleague about the problems of conducting exploratory factor analyses (EFA) or Principal Component Analyses (PCA) on variables where there may be groups within the data which may have the same population factor/component structure in the correlations between the variables but where there are perhaps large mean differences between groups on some of the variables to be analysed. I quite often get sent papers to peer review that apply factor analytic methods or PCA to data within which there perhaps clearly is, or may well be, quite large subgroup mean differences. I'm putting this bit of simulation work, done using my beloved R <>

New 21.x.10 and earlier privacy policy program that plots the "Clinically Significant Change" (CSC) cutting points given clinical and non-clinical means and standard deviations. Useful to grasp the logic as it applies to particular measures.

Even older stuff!

I'll try to mount more interactive R programs here shortly. Like almost everything on this website, all these utilities are mounted here licensed under a Creative Commons License. Creative Commons License