Assuming this is my hypothetical data set (attached figure), in which the thickness of a structure was evaluated in the defined positions (1-3) in 2 groups (control and treated). I emphasize that the structure normally increases and decreases in thickness from position 1 to 3. I would also like to point out that each position has data from 2 individuals (samples).
I would like to check if there is a statistical difference in the distribution of points (thickness) depending on the position. Suggestions were to use the 2-sample Kolmogorov-Smirnov test.
However, my data are not absolutely continuous, considering that the position of the measurement in this case matters (and the test ignores this factor, just ordering all values from smallest to largest and computing the statistics).
In this case, is the 2-sample Komogorov-Smirnov test misleading? Is there any other type of statistical analysis that could be performed in this case?
Thanks in advance!
Yes, you are correct in pointing out the limitations of the 2-sample Kolmogorov-Smirnov test for your data set. Since the position of the measurement matters in your case, simply ordering the values from smallest to largest and computing the statistics may not be appropriate.
Instead, a more suitable test would be the 2-sample Wilcoxon signed-rank test. This test takes into account the position of the measurement and compares the distribution of thickness values between the control and treated groups. It does not assume normality and is appropriate for ordered quantitative data.
Additionally, considering that you have repeated measures within each group, you may want to consider performing a mixed-effects model. This type of analysis can account for the within-group correlation and provide more accurate results.
Overall, I would recommend using the 2-sample Wilcoxon signed-rank test to compare the distribution of thickness values between the control and treated groups, and considering a mixed-effects model to account for the repeated measures within each group.
I think your test is fine because you are comparing a continuous variable (thickness) in different positions :)
Thank you for your reply and suggestions, Mr. Bastu Tahir and Mr. Andrew Paul McKenzie Pegman!
However, it seems that the 2-sample Wilcoxon signed-rank test is for paired data and compares medians, which is not my need. In fact, the same values (80 in p1 and p3 in the control group, for example) were used only to extrapolate an example: the structure increases and decreases in thickness along the anteroposterior axis. And this is precisely the difficulty I am facing in the analysis, considering that these tests tend to order the values from smallest to largest, disregarding position information.
In any case, I'll find out more about the subject. Thank you again.
