# ANOVA and post hoc test of log data

I want to compare the antiviral effect of different drug concentrations to the untreated control. The highest concentration of my drug reduces the infectious virus titer from 5.2 E6 to 3.3 E2. However, the effect is very suprisingly not significant after performing an ANOVA and a Dunnet´s post hoc test. I assume that the large standard deviation of my control (2.5 E6, mean: 5.2 E6) is skewing the statistics for me even though normal distribution was positive.

I had the idea of using the log of my data. The statistics is now more sensitive and makes sense with the graphical representation. Now my question is whether I can use ANOVA again + Dunnet's post hoc test (normal and lognormal distribution is positive) or whether I have to somehow take the log transformation into account in the result.

In the following you find the summary results of the test.

https://i.sstatic.net/j2epW.png

https://i.sstatic.net/dMBUV.png

• Greetings! Could you provide more information? Some information about your data or at minimum the summary results from your test would be helpful. Mar 3, 2023 at 12:45

## 1 Answer

It's somewhat easy to present results when using a log transformation and traditional tests of the mean like anova, because the results are essentially on the geometric means of the data. That is, results could be presented as "The geometric means of Group A and Group B were statistically different.". And then back-transform the means and present the back-transformed results (so that they are on the same scale as the original data).

This is common in some fields.

However, some results for this kind of procedure can be different if the analysis were performed with appropriate methods on the original data. For example, the back-transformed confidence intervals for the means would be different than confidence intervals for the means on the original scale.

Another approach is to use a generalized linear model, analogous to anova.

Usually in cases where one might use log transformation, Gamma regression is appropriate. Getting the expected values for groups and post-hoc tests is relatively easy with good modern software.