I have to test the difference between two samples which were selected via stratified randomization. The problem is that the samples are not independent due to randomization was stratified.

How should I conduct the test?


There are 80 patients. They were strafified by weight into four groups, each containing 20 observations. There are 4 treatments A,B,C,D. 5 patients from each group were randomly assigned to each of the four treatments.

The question is how to compare these treatments?

Weight is known to be the most important factor influencing the desease. The researcher tries to "adjust for weight", i.e., to provide "balance" of weights among the treatments.

The problem in comparing treatments for each weight separately is that we will then have only 5 observations per group.

  • $\begingroup$ Can you say more about your situation & the randomization procedure you used? $\endgroup$ Jun 25, 2015 at 18:26
  • $\begingroup$ Are you wondering if some treatments will only work / work differently for some weight classes? Or are you just trying to control for the influence of weight? $\endgroup$ Jun 25, 2015 at 18:44
  • $\begingroup$ It seems that nobody knows how to account for this correlation in two sample tests? $\endgroup$
    – Viktor
    Jun 27, 2015 at 16:06

1 Answer 1


You needn't run separate ANOVAs within each strata. In essence, you have blocked on weight. You can just run a two-way (i.e., 4x4) factorial ANOVA. You don't have to worry about whether the blocking variable is significant or not, it just exists to reduce the error variance. It should enhance your statistical power.

  • $\begingroup$ I need an analog for ANOVA for the case when the observations (or residuals) are not normal. Will the Scheirer-Ray-Hare test be suitable here? Are there any implementations of the test in R? $\endgroup$
    – Viktor
    Jul 1, 2015 at 9:49
  • $\begingroup$ As long as you believe your response data to be meaningfully ordered, you can use ordinal logistic regression; see here. $\endgroup$ Jul 1, 2015 at 13:21

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