When I was taking a course in marketing many years ago the instructor said something like this, " Make the plan look nice for the bank. It does not matter if it is totally right, but if it looks good, nobody will question the study."
Two things first, my mind is failing me, and the symbols used today in statics are not the same as they were. I do not know if it is an industry thing or time.
In the following study, look at the scanter of the data on the last graphs where the data is plotted (page 5). and note the statement. (49% cross-block covariance; P = .004) where P is the probability that hypothesis is wrong. Something does not compute there. Is the P value reported for the line or the data?
This type of study should be a cross over design with a wash out period between to mean anything.
Also not that this are a small groups but it does not say how the people were selected and assigned to the groups. Prescreening for favorable response? also it was funded by Danone Research.
It don't matter what they say, I sill am not gonna eat rotten dairy products.
In statistical significance testing, the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. A researcher will often "reject the null hypothesis" when the p-value turns out to be less than a certain significance level, often 0.05 or 0.01.
ref bad logic https://yourlogicalfallacyis.com/pdf/FallaciesPoster24x36.pdf