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I have a set of 12 subjects: 6 administred with drug A and 6 with drug B. For each subject two time-points have been collected (before and after drug treatment) for each analyte (over 6000). I had a read around and it seems that mixed ANOVA suits my needs. Therefore I performed it using R as recommended on http://www.cookbook-r.com/Statistical_analysis/ANOVA/#mixed-design-anova Which is to say: 

funAV <- function(x) aov(x ~ Class*time+ Error(Subjects/time),data=X)

aovOb <- apply(X[,-(1:3)],2,funAV)

Once I get the results I have for each analyte a significant (or not significant) difference concerning Class (A or B), time (before or after) or a combination of both. On https://statistics.laerd.com/spss-tutorials/mixed-anova-using-spss-statistics.php it is reported that there is no need for a post hoc analysis with a 2 level factor between subjects. If this is true and I find a Class effect how can I know if the difference lies at time before or after? The same is true on the other way round i.e. if I find a time effect how can I know if the difference lies at drug A or B? I looked for post hoc analysis methods anywhere but all I could get was a bunch of methods for repeated measures ANOVA which is not exactly my case since I have an additional factor (the drug). Many thanks.

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The effect you're looking for is the Class:time interaction. That 2x2 interaction tells you that the effect of B-A differs across time. That's the critical thing to measure because it takes into account potential baseline variability in groups A and B at the first time. Given that it's the effect, B-A, across time that's being tested then there is no, "appears in time 2" etc. because it's very existence is measured in comparison to time 1.

Consider a situation where at time 1 group A tends to score higher than B. Then at time 2 group B scores higher. Each of those individual differences might not even be very large but the difference between the differences is going to be bigger and reveal what the effect of receiving the drug over time is. If you carry out that thought experiment a little more you realize that looking at the simple effects is a fools errand.

Going spelunking with post hoc tests with a 2x2 always ends up in logical fallacies of comparing significant v. not significant. Don't do it. Report your interaction and describe the pattern in the data.

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  • $\begingroup$ If we assume that an analyte undergoes a significant change after administration of both drug A and drug B we will not be able to record this change under the interaction effect but it will be reported by the main effect of "time". In this case I think it is necessary to explore the simple effects. $\endgroup$
    – RDGuida
    Commented Sep 18, 2014 at 13:31
  • $\begingroup$ Main effect of time is not a simple effect. The effect of time for drug A is an example of simple effect. (BTW, I wasn't sure if this was a two drug comparison or A was actually a placebo or special control) $\endgroup$
    – John
    Commented Sep 18, 2014 at 15:31

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