Back to the thread, maybe? If you seriously wanted to know whether the quality, presence or absence of children's footwear had an impact on their educational achievement, you'd have to set up a properly controlled trial.

Let's say it is shoes vs slippers. Divide your cohort of children randomly into two groups, one wears shoes, the other slippers. When seated for lessons, their feet should be hidden from view (inside a pillowcase), so that no bias - conscious or unconscious - could come from the teacher. Their academic work is marked independently by someone who never sees the children - shod or otherwise - and the results collated. The code is then broken by a researcher who also never sees the children and the mean performance of each group is worked out. This gives you a first analysis.

Then you apply tests of statistical significance to the results to ensure that the result could not have arisen by chance. Then - and only then - could you say that slippers were better than shoes (or vice versa) with any confidence. Was all this done by the academics at the heart of this discussion? I don't know, but I suspect not.

In short, it is the classic "post hoc ergo propter hoc" fallacy. Since one thing follows another, it is assumed the first thing CAUSED the second thing. Not always the case, it seems.