Help requested for 2-way ANOVA results interpretation

#1
Hello, everyone,

I am a biologist by training, and I do not have a solid background in statistics. I must produce a statistical analysis for a research paper (asked by the reviewers) for an experiment we did in our laboratory. This experiment consisted in measuring the speed of tracked particles toward a target as a function of their distance from that target. We compared two different conditions: the control condition (Ctrl) and the disturbed condition (Exp). We performed 557 independent measurements for the "Ctrl" and 624 independent measurements for the "Exp". We then average our results per bin (5, 10, 15, 20, 25 and 30 µm) and wanted to know if the profile of speed according to distance were different in our two conditions. We first tested the statistical significance, bin per bin, using a Mann-Whitney test.

However, the reviewers asked us to perform a 2-way ANOVA with post-hoc tukey test instead. We did so and obtain the following result table (see below).

Question #1 :

What would tell me if the two profiles (Ctrl vs Exp) are statistically different? The interaction p-value?

Question #2 :

Do you think the 2-way ANOVA is the best test to address my question?

Thank you in advance,

Ben

P.S. if needed I can provide .csv file with the data.

FActMesh_PAKLT_StatTests2.png
 

Miner

TS Contributor
#2
Answer 1) The rows p-value compares the mean effect of the control vs experiment while the interaction compares the slopes.
Answer 2) It is better than the Mann-Whitney because it helps guard against the false positives of that many tests. You could also try a polynomial or nonlinear regression with control/experiment as an indicator variable.