# Is this a 2-ways repeated measures ANOVA?

Imagine a long, horizontal, transparent acrylic tube which is marked with duct tape every 50 cm in such a way that you can distinguish 10 "sections" of the tube.

I want to study the movements of ants in these plastic tubes, which are under four combinations of two different conditions, namely each tube has different texture of the inner wall and used a different (transparent) paint as repellent.

Therefore I consider TEXTURE and PAINT my two factors, each one with two levels: Texture1-Texture2 and Paint1-Paint2. We choose 100 random ants and put them in each tube, evenly distributed along the tube. We wait 5 hours and count how many ants we find in each one of the 10 sections of the tube.

So we have 4 tubes: Texture1 + Paint1 Texture1 + Paint2 Texture2 + Paint1 Texture2 + Paint1

In each tube we have 10 values (one number of ants per section). Eg. in a given tube I have Section1 with 10 ants, Section2 with 34 ants, etc. until Section10. In total, all 10 sections of a tube sum 100 ants.

In this way we can see if the horizontal distribution of the ants (eg. where is the maximum number of ants located inside the tube? in which section?) is related to the texture and/or paint used.

So my initial thought was a 3-ways ANOVA with Texture, Paint and Section as factors. My dependent variable is simply ANTS: the number of ants in a given section of a given tube.

But after thinking for a while I realize that the number of ants in each section is actually related, because the initial number of ants is fixed and therefore if I have 50 ants in one section then I have 50 less ants for the rest of the sections, right? Then I thought maybe this would be for a 2-Ways ANOVA, but with repeated measures. In this case the factors are Texture and Paint, and the repeated measures are Ants in each Section. So for each combination of Texture and Paint I would have 10 repeated measures.

However I am not sure because repeated measures is almost always related to time in the textbooks and examples (eg. measure something "before" and "after").. Is my reasoning correct? Can I use repeated measurements with the justification that the measurements are not independent even when time is not a factor or variable here?

• Sounds like an ANTOVA to me. – Marc Claesen Nov 19 '13 at 17:00
• Sorry, do you mean ANCOVA? – terauser Nov 20 '13 at 0:17