# Fold changes (ratio) vs differences in experimental design and t tests

I'm designing an experiment to test whether a drug blocks metastasis in a mouse model system. I will have a control group that receives the metastasis activating mutation without drug and a treatment group that receives metastasis activating mutation and drug. I plan to assess the difference in luciferase intensity between the control and experimental arms. I'm now designing the experiment and doing a power analysis.

I originally planned to use the two sample t-test to assess the difference in mean intensity between the two groups. In other biological settings (RNAseq count data), I've used log fold change (estimated with a negative binomial GLM) to measure change in mean expression between two groups. This makes me wonder, when is it appropriate to use a difference in means (absolute measure) vs a fold change of means (relative measure)?

I chose difference in means because the experiment seemed well suited to a t-test: 2 samples and continuous variable. But I don't seem to have a sufficient understanding of the differences between difference in means and fold change in means to understand when to use which measure.

When is it appropriate to use difference in means vs fold change in means to measure an outcome of a continuous variable between two groups?

## 1 Answer

This is a really good question. There probably isn't a clear answer.

It comes down to: Which is more consistent, the set of differences or the set of ratios. If one experiment goes from a mean of 5 to a mean of 10, and another goes from a mean of 20 to a mean of 40, do you think those are consistent (becuase they both are doublings) or do you think those are very distinct ( because the mean change of 5 is very different than a mean change of 20)?

In biology, I think fold changes are really common and too many people focus on differences rather than ratios.

An easy way to deal with ratios is to take the log of the ratios, and run the t test on the logs. The t test looks at differences, but the difference between two logarithms is the logarithm of the ratio. So a t test on logarithms esentially tests the null hypothesis that the ratio is 1.0.

• Would there be a difference in power if I decide to test difference in means vs fold change of means? Jan 30, 2020 at 23:15
• @TomasBencomo. Sure. You need to pick the method that makes most sense for the data, for which the assumptions of Gaussian distributions of the values analyzed (log or not) is likely to be closer to true. Jan 31, 2020 at 4:46