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I have three treatments: control, treatment1, and treatment2. A total of four patients were examined after receiving each of these three treatments. The dependent variable is continuous. My dataset looks like this:

Patients   control  treatment1  treatment2
patient1    23.4    34.5         67.4
patient2    10.9    78.9         23.0
patient3    23.2    50.8        100.8
patient4    24.2    67.1         90.8

I first performed one-way ANOVA, and got a p-value of 0.45. Then, considering repeated measures data in my case (paired data for each patient), I was thinking that I should use repeated measures ANOVA, but I am having trouble in deciding which test to use for small-sample data.

I hope somebody could provide me not only with a good idea about this specific case, but also about important issues related to small-sample data analysis.

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    $\begingroup$ How can a single patient be in both a treatment and a control group? $\endgroup$ Dec 22 '16 at 15:44
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    $\begingroup$ @YuvalSp as long as it's reasonable to assume that measurement under one condition won't effect measurement on subsequent conditions, then it's completely reasonable to do a within-subjects condition manipulation. For example, measure participant's blood sugar on day 1 on an empty stomach (control), on day 2 30 minutes after a carb-heavy meal (treatment 1), and then on day 3 30 minutes after a protein-heavy meal (treatment 2). $\endgroup$ Dec 22 '16 at 17:45
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    $\begingroup$ It is actually a control group and both treatment groups. This is possible in a crossover design. I think it would help to know what the response is. I think it is clear that this sample size is too small to compare 2 treatments and a control. The crossover trial is very complicated. The patients may need to wait after one treatment so it won't confound the results with the next treatment. Also we would expect that there would be a fixed time after treatment for the response to be measured. $\endgroup$ Dec 22 '16 at 17:46
  • $\begingroup$ @MichaelChernick Normally how you analyze the data from crossover trial similar to my case? Can we just perform repeated measurement analysis to such data? But still the very small sample size is big headache. $\endgroup$
    – juanli
    Apr 6 '17 at 17:54
  • $\begingroup$ @Amy Have you already collected the data? If so the cross-over design is out of play. $\endgroup$ Apr 6 '17 at 18:06
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The Kruskall Wallis test is the most appropriate for analyzing sample sizes not large enough to assume normality. It is a non-parametric substitute for the ANOVA.

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    $\begingroup$ I am afraid this is not appropriate for the design here which has repeated measures whereas the K-W is for independent samples. $\endgroup$
    – mdewey
    Oct 1 '18 at 12:57

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