> It's cheating, it's goes against experimental design analysis, and it does not differentiate between given data and data that was carefully collected. We have experimental design class for a reason. It helps us to be honest. Of course there are tons of pit falls many novice statisticians can do.

Explicit sequential testing runs into exactly the same problem. The problem is, the null hypothesis is not true. So no matter whether you use fixed (large) sample sizes or adaptive procedures which can terminate early while still preserving (the irrelevant) nominal false-positive error rates, you will at some sample size reject the null as your power approaches 100%.

This is mostly right, but you are still thinking of these rejections as "false positives" for some reason. They are real deviations from the null hypothesis ("true positives"). The problem is the user didn't test the null model they wanted, it is 100% user error.

Can you explain that last sentence? What is a valid null model if everything is correlated?

A model of whatever process you think generated the data.

EDIT:

I guess I should say that the concept of testing a "null model" without interpreting the fit relative to other models is wrong to begin with. You need to use Bayes' rule and determine:

  p(H[0]|D) = p(H[0])p(D|H[0])/sum(p(H[0:n])*p(D|H[0:n]))

Lots of stuff wrong with what has been standard stats for the last 70 years, it literally amounts to stringing together a bunch of fallacies and makes no sense at all.

Thanks for the response. Do you know of any you good blog posts or articles that dive into this a bit more? It looks very interesting.

This is the best description of the main problem (testing your own vs some default hypothesis) I have seen:

Paul E. Meehl, "Theory-Testing in Psychology and Physics: A Methodological Paradox," Philosophy of Science 34, no. 2 (Jun., 1967): 103-115. https://doi.org/10.1086/288135

Free download here: www.fisme.science.uu.nl/staff/christianb/downloads/meehl1967.pdf

Andrew Gelman (andrewgelman.com) has a great blog that often touches on this issue.

Thanks a bunch for sharing, I appreciate it. I'll add these resources to my reading list. I may also pass it along to my brother who getting a graduate degree in psych :)