I just skimmed the summary but in the results section it reports three significant results and two after “multiple-test correction”. I’m not sure how they did that correction; I would expect that measures of cognitive performance are correlated for each child and so the standard Bonferroni correction might be too harsh to apply here.

> Covariate-adjusted analyses of standardized scores (mean [SD], 0 [1]; higher values indicating better performance) showed positive associations of high-dose vitamin D3 with verbal memory (β = 0.17 SD; 95% CI, 0.03-0.32 SD; P = .02), visual memory (β = 0.24 SD; 95% CI, 0.06-0.42 SD; P = .01), and flexibility or set shift (β = 0.19 SD; 95% CI, 0.01-0.37 SD; P = .04); however, high-dose vitamin D3 was no longer associated with flexibility or set shift after multiple test correction.

My statistics isn't great but reading the study more it looks like they control the rate of false positives via the q values so my initial concern may be unwarranted. I'm surprised that it keeps so many barely significant results with so many hypotheses. I'll have to look it up when I get time.