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I have a question concerning the statistical analyses to conduct in the context of a psychology experiment.

There are two groups of students (experimental and control) who are exposed to either the treatment or the control condition. Each student is measured at three points in time : T0, T1 and T2. In T0, we evaluate the baseline state, in T1 the state after one month of treatment and in T2 the follow-up. We measure several things :

  • attentional biases (computed from difference scores in reaction times in ms)
  • the PASAT (a cognition test which gives values from 0 to 60)
  • the Beck Depression Inventory II (gives values from 0 to 63)
  • the Ruminative Response Scale (gives values from 0 to 88)

The groups are very small :

  • 7 in the experimental condition at T0 and T1. A few dropped out so there are only 4 at T2.
  • 6 in the control condition at T0 and T1. Also only 4 remained at T2.

Due to the sample size, we cannot say for sure if the data of the population behaves normally and is homoscedastic (homogeneity of variance). Hence I would like to use non-parametric tests. However, I am uncertain which non-parametric test to use in this case. The Friedman test would be suited at first glance, but as far as I know, it is only applicable for perfectly balanced designs, which is not the case here. I would tend to use the Skillings-Mack test, which can be used for incomplete data. I also read here an advice to use a non-parametric ANOVA following Brunner-Langer : Question link.

Do you have any recommendation or suggestion on which test to use in this case ?

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    $\begingroup$ Welcome to the site. What did you measure? $\endgroup$
    – Frans Rodenburg
    Commented Oct 23, 2019 at 8:23
  • $\begingroup$ @FransRodenburg Thank you. I edited the question to show what is measured. $\endgroup$
    – Makishima
    Commented Oct 23, 2019 at 8:34

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After speaking with a statistician, he advised me to :

  • Conduct two Friedman tests, one for the experimental and another for the control group. These two different tests are needed because a single Friedman test cannot be used on two independent groups. The test can be applied to only one independent group. However, it is possible to compare the results of two different tests on different groups. These Friedman tests should encompass the times T0 and T1 only.
  • Conduct a single Wilcoxon or Kruskal-Wallis test on the groups for the time T2. This is due to the fact that some participants dropped out of the study, so I cannot simply apply Friedman tests on all the three times of measurement.
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  • $\begingroup$ Usually it's better to put everything into one model instead of using multiple tests. But given the very small sample size, and the fact that subjects dropped out, there might not be a better option. $\endgroup$
    – Sal Mangiafico
    Commented Oct 25, 2019 at 12:57

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