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I am investigating the effect of an intervention treatment on a group of samples over 5 time points (a period of 2 months in total)

For example:

Subject 1 - Timepoint 1 (Dose 1), 2 (Dose 1), 3 (Dose 2), 4 (Dose 3), 5 (No dose)

Subject 2 - Timepoint 1 (Dose 1), 2 (Dose 1), 3 (Dose 2), 4 (Dose 3), 5 (No dose)

etc.

The dependent variable measured is a protein concentration, so it is a continuous variable. At timepoints 3 and 4, the dosage of the intervention was increased. To compare the protein concentration of the samples between all 5 timepoints, which test would be more suitable?

I am personally leaning towards Friedman's test over Kruskal-Wallis, but would like some confirmation.

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Because the measurements are blocked by Subject, you have paired or repeated measures data. In this particular case, the data arranged in unreplicated complete block design. Friedman's test can be applied in this case. Kruskal-Wallis would not be ideal for repeated measures data. I would encourage you to look at Quade test also, which is used for similar situations as Friedman's test.

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Given your structure (blocked by subject, paired or repeated data measures), you can use the Friedman's test.

Furthermore, if Friedman's test shows that there are significant differences among your treatments, then you will need to use a post-hoc test, such as the Nemenyi's test.

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