# Can I use one way ANOVA for my normalized data?

I have trouble knowing the right statistical test that i need to use for my data. I have a group of animals subjected to a task, where each animal is exposed to three or four conditions. The data does not follow a gaussian distribution, so i know that I have to use a non-parametric repeated measure test, that is Friedman test and Dunn's to compare between conditions. Then, i have independent groups of animals tested in the same task. To avoid groups variability I normalized the conditions, setting the control condition (first condition) from each group as 100%. Then, the problem is that if want to compare the change in just one condition between independent groups using the percentages obtained from the normalized data, can I use an one-way anova?

I hope that I can be clear this time. I’m doing a behavioral task, in which each animal is tested to find a piece of chocolate (I measure the latency to find it (latency of detection) in a 10 min trial). This is repeated four times, meaning 4 trials. For the control group, the animals were injected with saline between trial 1 and 2. Then the animals were injected with the X drug between trials 2 and 3, and finally were injected with the Y drug between trials 3 and 4.

Example: Control group (n=10 rats) Each rat: Trial 1, ip injection (saline), Trial 2, ip injection (X drug), Trial 3, ip injection (Y drug), Trial 4, End of the task.

I have two other groups that were injected with two different drugs (Z and A drugs) between trials 1 and 2, but the same X drug and Y drug given between trials 2 and 3, and 3 and 4.

Example: Experimental groups (n=10 rats) Each rat: Trial 1, ip injection (Z or A drug), Trial 2, ip injection (X drug), Trial 3, ip injection (Y drug), Trial 4, End of the task.

So the objective is to evaluate the effect of the X and Y drugs on the latency of detection in the control group, and later, if the Z or A drug change those effects observed in the control group. To evaluate the effect of X and Y drugs on the control group I have to use an repeated measure test. But first, I did a normality test for the data obtained in the control group, and it showed me that the data does not follow a gaussian distribution. So, i figured that I have to use the Friedman test.

Then, to compare the change in the latency of detection induced by X and Y drugs between groups and evaluate if Z or A drugs modify it, I set the data obtained in the first trial for each group as 100% (this is to avoid group variability). Then I obtained a percentage of the change of the latency of detection for trials 2, 3 and 4 in control and experimental groups.

Example: Control group Trial 1 (latency 100%), ip injection (saline), Trial 2 (latency 99.5%) no change, ip injection (X drug), Trial 3 (latency 75%), ip injection (Y drug), Trial 4 (latency 43%), End of the task.

Example: Experimental group 1 Trial 1 (latency 100%), ip injection (Z drug), Trial 2 (latency 99.8%) no change, ip injection (X drug), Trial 3 (latency 95%), ip injection (Y drug), Trial 4 (latency 80%), End of the task.

Example: Experimental group 2 Trial 1 (latency 100%), ip injection (A drug), Trial 2 (latency 98.8%) no change, ip injection (X drug), Trial 3 (latency 105%), ip injection (Y drug), Trial 4 (latency 60%), End of the task.

Therefore, in control group the X drug reduce the latency of detection to a 75% but the injection of Z drug modify it to a 95% or 105% if it used the A drug. At this point, i want to know if the effect of the X drug in control group is statistically different from the effect of the X drug in the experimental groups. For that case, I don’t know what statistical test suits my data.

Sorry for my lack of clarity. Thank very much for your help.

• "The data does not follow a gaussian distribution, so i know that I have to use a non-parametric repeated measure test" -- this does not automatically follow (one might instead make a different parametric assumption, for example). When you say "to avoid groups variability..." it's a little unclear why it would be necessary to do this (or to be honest which 'groups' those are). If you could be more explicit about what you did and why that might help. (Note that it is not the marginal distribution of the response that is assumed to be Gaussian; what did you assess and how did you assess it?) Nov 16, 2015 at 7:22
• I added a detail explanation of my experiment design, I hope that it helps. thanks. Nov 16, 2015 at 21:36