Dear Bioconductor Community,

I would like to ask a specific question regarding the interpretation of an "ANOVA" approach in limma and topTable function. In detail, in a previous post i have created ( C: Questions about complex design in limma regarding an agilent microarray dataset ) , Aaron helpfully mentioned the difference about dropping separately each coefficient in topTable about a statistical comparison (i.e. coef=1) and by dropping for instance coef=1:4, which essentially performs an ANOVA test checking for DE in any of my comparisons. Thus, my crucial (and might naive question) is the following: is it sensible  to get a significantly greater number of DE genes in my ANOVA implementation, than in the sum of dropping each coefficient separately ? And this could be probably due to the "nature" of the ANOVA testing ? In other words, what is the crucial difference in the computation of statistics and DE genes when moving from i.e. coef=2 (a specific comparison) to coef=1:4 ? For instance, the ANOVA approach also tests for difference in means in coef=1 versus coef=2 ? Or this is irrelevant  as all the mentioned comparisons have been specified in the makeContrasts function? (above link for code).

Please excuse me for this beginner question, but I'm a newbie in R/statistics and this specific part is very crucial !!

Best Regards,

Konstantinos Yeles

There's no secret difference between anova and t-tests, it's sort of commonsense.

You can think of the anova test as pooling the four separate t-tests into an F-test. If all four t-tests were borderline significant, then the anova F-test will naturally be more powerful than doing separate t-tests, because it will accumulate information from all the tests. Getting one borderline t-statistic may not be surprising, but getting four of them is less likely by chance and will lead to a small p-value. The F-test therefore can be more significant than any of the individual t-tests.

On the other hand, if only one of the t-tests is large and the other three are small, then the F-test will be less powerful than the t-tests because the small statistics will dilute the large one. So the F-test may be much less significant than the most significant of the t-tests.

In general, if all four contrasts are similar in size then the F-test will be more powerful than the t-tests. If only one of the contrasts tends to be DE, then individual t-tests will tend to be more powerful.