Dear everyone,
I have a question regarding qPCR data I obtained, the data is obtained from 2 genotypes, over a series of 8 timepoints. The aim is to see a difference between the 2 genotypes, in a time-dependent manner.
- I could either analyse each timepoints with 2-way ANOVA followed with pairwise tests.
- Or pool the timepoints corresponding to "day" and "night" together, as there seems to be a difference between these two "4 timepoints" blocks.
My question is, can I carry out test statistics on the single timepoints, and on the pooled timepoints, without correcting the p-values for the 2 sets of tests, as the biological questions here are separate, even if close ? Meaning that I would only correct for the pairwise comparisons within each set of tests, but not between ?
I hope my question is clear enough.
Thank you in advance and have a nice day.
Best.
If you are testing two separate hypotheses (one for the single timepoints and another for the pooled timepoints), you should correct the p-values for multiple comparisons within each set of tests (e.g., using Bonferroni or false discovery rate correction). However, you would not need to correct for multiple comparisons between the two sets of tests, as they are independent hypotheses. Therefore, you can report the corrected p-values separately for each set of tests, but do not need to correct for multiple comparisons between the sets.
It's important to note that the decision to pool timepoints together should be based on biological reasoning, not just statistical significance. If you are pooling timepoints based on a difference between "day" and "night", you should make sure this difference is biologically meaningful and not just due to random variation. Additionally, pooling timepoints may reduce the power to detect differences between the genotypes if there are time-dependent differences that are being averaged out by pooling.
Ahmad Al Khraisat Thank you for your very clear answer.
Here, what confuses me is that notion of separate hypotheses. Could we consider these 2 hypotheses independent considering that they consist of the same dataset, just arranged in a different manner (pooled and unpooled ) ?
Also, the interest of checking the pooled times to compare day and night came after exploring my data and seeing quite a difference between those, yet it was not planned at first, it just occured upon seeing the raw data.
Would you think it is acceptable in such a case to do 2 tests, one on unpooled and then one on pooled data while only correcting the p-values within each tests, and not between each tests ?
Thierry Cottineau The decision of whether to consider the two hypotheses as independent or not depends on the research question and the scientific context. If the research question pertains to two distinct hypotheses (e.g., testing the effect of a treatment on two different outcomes), then the hypotheses are considered independent. However, if the research question pertains to one overall hypothesis (e.g., testing the effect of a treatment on a single outcome), but the data are analyzed in two different ways, the hypotheses may be considered dependent.
In your case, since the interest in comparing day and night came after exploring the data and was not planned in advance, it is reasonable to consider the two hypotheses as exploratory and not pre-specified. However, it is important to acknowledge that performing multiple tests on the same data increases the overall probability of making a type I error (false positive). Therefore, correcting the p-values within each test is appropriate, but it may also be necessary to correct for multiple comparisons across the two tests to control for the family-wise error rate. This can be done, for example, using Bonferroni or false discovery rate (FDR) correction.
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