Unequal variance in randomized experiments to compare treatment with control?

Question

Consider a randomized experiment to compare (one or more) treatment(s) with a control. Since groups are defined by random assignment, we should expect equal variances for a null-experiment (that is, all groups given the control.)

So unequal variance would in some sense be caused by the treatments, maybe by some interaction between treatments and (unobserved or unobservable) unit characteristics. I remember seeing a paper on this, probably references on this site --- but cannot find it now, despite much searching.

Any ideas or references?

Answer 1

Now I found the paper I was thinking about, it is Heterogeneity of Variance in Experimental Studies: A Challenge to Conventional Interpretations by Anthony S. Bryk and Stephen W. Raudenbush (Psychological Bulletin 1988, Vol. 104, No. 3, p396-404.)

Some papers following up on that one:

• Main Effects Analysis in Clinical Research: StatisticalGuidelines for Disaggregating Treatment Groups by John S. Lyons and Kenneth I. Howard.

• Heterogeneity of Variance in Clinical Data by Robert J. Grissom (Journal of Consulting and Clinical Psychology 2000, Vol. 68, No. 1, 155-165.)

• Examining heterogeneity in residual variance to detect differential response to treatments by Kim, Jinok and Seltzer, Michael (non-free for me at least.)

• One applied paper: Interpreting mood scores: clinical implications of individual differences in mood variability by Cooper C and McConville C (Br J Med Psychol. 1990 Sep;63 ( Pt 3):215-25.)

• This paper with some practical solutions is very interesting: Comparing Two Samples: Extensions of the t, Rank-Sum, and Log-Rank Tests. It was referred in this post T-tests, manova or logistic regression - how to compare two groups?

I am still interested in other references!