As soon as you talk about a "trend" you do consider the data as significant (that's precisely what the statemen "(statistically) significant": that you think your data is clear enough to allow the interpretation of a trend!) . So it depends on if you can live with a level of significance that high and that you can defend it against other scientists (e.g. reviewers). If you elswhere state, for instance, that p 0.05. If you did so, you would break your own rules.

Have you made a paired analysis to get rid of the between-subject variance?

I commend you for asking a question that more researchers should ask.

Your data provide no evidence for an treatment. The p-values mean that your results are consistent with results you might get with no treatment at all.

Furthermore you do not have a trend with just two points. You never can extrapolate beyond the points provided by the data. Now, it is possible that with more data you would have a chance of finding a significant effect. Your data is sparse which is precisely why your standard deviations are so large. They mask any underlying effect that might affect the larger population of mice not sampled. But with a larger sample you are equally likely find no effect at all.

Researchers sometimes say that they see a trend but failed to reach significance. But that is bad science. The reality is that the data are too sparse to suggest any effect or trend at all.

Get more data (rats) if you can to reduce the standard deviations and then you can hope to find an effect but your data at present tells you nothing about what you may find.

Please let me know if you need help understanding the problem.

If you can't reach significant with so high changes (going from 71 % to 350 %), that means that either you are not doing the right analysis or your data are awfully noisy, and you should first think about it, to understand its origin and eventually be able to do a better experiment with lower variability.

However, with only a few rats, you can't either expect miracles...

That biological data are "awfully noisy" is quite common, and more often than not there is no "better experiment with lower variability" one can imagine. Just because of this, there should be a study plan for animal experimens to ensure a sufficiently high power, given these unfortunate conditions. This should be stated in the proposal for the animal experiments that has to be approved by an ethical committee (almost everywhere in the world). It does not make much sense to let animals suffer and die with a high probability of ending up with inconclusive data. In this proposal, the rational of using just 3 rats for this experiment should be given, so that the "non-significant" data can be interpreted as no relevant treatment effects. If the choice of minimally relevant effect size (what seems to be extremely huge here) and the power were resonable may still be debatable -- but this debate should actually be done when the proposal is written and submitted.

@ Jochen: I definitely agree, and should have more clearly stated that "nothing is to be seen" is also an option... But thinking about how to reduce noise should also be included, even if there is often no practical solution. Sadly, I'm afraid that several animal ethical committees do not focus on the justification of the number of animals based on such grounds.

For this particular example, since the very very low amount of information we have about the experimental plan, the data and the processing steps, it remains a purely hypothetical discussion anyway... For instance, I'm quite sure that using % is not the correct way to deal with the data, because these are probably expressing changes from « controls » or « baseline ». But that's just a guess.

Klara Sundsvik The if p

Emmanuel Curis, I absolutely agree.

It would really change the game when manuscripts with animal experiments would be accepted from journals only when reviewers confirmed that the analyses were performed as described in the proposal ;)

May I ask exactly what the mean consumption levels and SD's were for time one (baseline) treatment, time one (baseline) control, time two (treatment), time two (control) as well as the sample size for both conditions? (I like to unpack each piece [mean/SD/sample size] and then think through the results - it helps me better understand what may be happening with these data in order to share ideas regarding possible interpretations.) Thank you-

In addition, were the assumptions for conducting a two-way repeated measures ANOVA met? Might be helpful to think through this as well -- (or it may be a moot point - not sure)

I'm pretty sure it's moot. The sample sizes are very small the means very different but the SDs very large (lots of disparity among the few samples. So the SDs are swamping out the means. Seems pretty straight forward. The conclusion is likely to be "These data provide no evidence to reject the null hypothesis that the treatments have no effect on alcoholism."

If the data are truly sparse then no amount of sophisticated modeling will help.

I would either gather more data. To say that there is any effect or trend would be wrong. To say that tDCS has no effect on alcoholism would be erroneous as well. You simply don't know with the data you have collected.

I was a neuroscience researcher in my "past life" and I know it can sometimes be hard to gather more data, despite the relevancy of doing so. I also agree that sophisticated modeling is not going to remedy the problem -

Having said that, if you are unable to raise the sample size (for whatever reason) then I would suggest it does not make sense to perform hypothesis testing - but if you can let us know what the results are, then maybe we can think about ways to represent these data (at least preliminarily).