I have data on control and test groups of mice at several time points. I want to test the significance in a change in index of control over test groups at the different time points. What test should I use?
The problem is the following. If I calculate the ratios of the means from test and control groups at each time point (assuming each of the groups has similar variance), there will be a series of ratios (or indices). How can I test if these indices are significant?
1. How large is your sample size? If your sample size is smaller than n=30, it is highly recommended to test the normality of each sample (both control and test) before comparing the means. This is commonly done with the Shapiro-Wilkins test.
2. If you can assume normality in both samples at every time point, you can perform two-way "repeated measures" ANOVA with post-hoc test of your interest (or Tukey). If the normality is rejected in any of your samples (control or test) at any time point, you should perform the nonparametric test (Friedman's test or Scheirer-Ray-Hare test) with nonparametric post-hoc test.
3. If any significance is observed in these analyses, you can denote significance in your mean ratio plot.