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I have a trial with 8 groups. Each group experienced one of two treatments - four groups got treatment A & 4 got B. Within each group, the dependent variable was measured 4 times.

Unfortunately, the dependent variable is not normally distributed (or anywhere close). Given the repeated measures, I cannot therefore perform a Mann Whitney test on the 32 measurements I have. I could mean the 4 measures within each group & perform a Mann-Whitney on the means, but I have seen some suggestions of calculating ranks & performing multilevel modelling on those ranks.

Do you think that is appropriate?

If so, would:

MIXED rank_d BY Treatment Group 
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE) 
/FIXED=Treatment | SSTYPE(3) 
/METHOD=REML 
/RANDOM=Group | COVTYPE(VC).

be an appropriate analysis in SPSS?

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    $\begingroup$ Is your only problem that the data aren't normal? The Gauss-Markov theorem tells us that normality isn't necessary--you'd just have to bootstrap your standard errors. (Of course, I have no idea how you'd do that in SPSS.) On the other hand, if your samples are large enough, SE's based on asymptotics would probably be OK, but your samples might need to be awfully large depending on how non-normal your data is. $\endgroup$
    – gung - Reinstate Monica
    Commented Nov 14, 2011 at 6:19
  • $\begingroup$ No, I'm pretty sure that there's not a good way to analyse this using parametric tools. For one thing, the experiment is non normal by design. Essentially, the measurement is the deviation about a target value. I can expect the deviation around the target to be normal, but do not care whether that deviation is positive or negative, and am hence taking the absolute value of the deviation. Thus there is no way the resultant statistic is going to be normal. Essentially, my treatment is effective if it minimises the absolute values of the deviations. Secondly, my sample size is pretty small. $\endgroup$
    – argon1024
    Commented Nov 14, 2011 at 12:57

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GENLINMIXED with a Gamma distribution would be one way to look at this.

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