# How to compare multiple ratios to test for significant differences

Please forgive my ignorance. I have return rates of a molecule (quantity returned per hour, determined from 4 time points) from compound x from 3 separate microcosms (n=3) and return rates of compound y from an additional 3 separate microcosms (n=3). I calculate the average of the slopes for each compound tested and then divide them to get a ratio. I did this same procedure with 4 different sets of microcosms and have four different ratios; I'll call them a,b,c,d. I would like to determine which sets are different from each other for all possible comparisons. For example, is a significantly different from b,c,d and/or is c only different from d.

• You would need to adjust p-values for multiplicity. – Michael R. Chernick May 31 '18 at 2:50
• Thank you for your reply. I am open to any approach. Can you please add some details. Right now I just have propagated standard error attached to the individual ratios. Propagated from the standard error of n=3 compound x and n=3 compound y. I do not take into account the R2 value associated with the slopes. – SCT May 31 '18 at 22:37
• When running several tests simultaneously the probability of a type I error for any particular test increasing over what it would be for a single test alone. A conservative way to adjust for this is to apply the Bonferroni inequality. There are many other less conservative ways of doing this including resampling methods as described by Westfall and Young in their book. – Michael R. Chernick Jun 1 '18 at 0:07
• Thank you. I was trying to run an ANOVA but due to having ratios, I found this problematic. I have 6 samples total to make a ratio, but two different variances for each set. Is it still possible to run an ANOVA on my ratios (with a post-hoc Tukey's test)? – SCT Jun 1 '18 at 1:40