# Which test to use? Independent data or not?

What I have is a cross section of a bone divided in 60 equal slices. These 60 slices form 4 groups of 15 slices each corresponding to the 4 anatomical orientations (anterior, lateral, posterior and medial). I measured bone compactness for each of these 60 slices. Bone compactness corresponds to the quantity of bone in a slice and varies between 0 and 1.

I would like to compare the mean bone compactness between these four groups. I first thought of doing a one-way ANOVA, but I realized that my measurements of compactness are interdependent and therefore prevent me from doing so. I looked at the repeated measures ANOVA but for me it does not suit my question.

Any idea?

• Maybe your density data are not normal. If you were comparing only Medial and Lateral, you could use a paired Wilcoxon test (one sample test on differences) looking at M - L differences for 15 specimens. Similar comparisons for A, L, P, M could be done using a Friedman test. If significant, use paired Wilxoxon for ad hoc comparisons, with Bonferroni P-values to avoid false discovery. (Friedman test often illustrated in terms of Brands and Tasters rating, wine, chocolate, etc. Tasters $\approx$ Specimens, A,L,P,M $\approx$ Brands.) – BruceET Jun 2 at 0:18
• Friedman is the non-parametric alternative to the repeated measures ANOVA and imo it does not suitable for my data either. Also, my data are normally distributed in each group. – JGonet Jun 2 at 9:42
• What about a permutational Anova? – JGonet Jun 2 at 11:23