Getting back to the review by Hemilä that Lonely Moa cited in his OP: Hemilä reanalyzed two clinical trials to make his case that vitamin C reduces the duration of colds. As I discussed here
, in his reanalysis of Karlowski (1975), he disregarded the observed difference in treatment effect between blinded and unblinded subjects—a decision that is questionable at best. In his reanalysis of the other trial, Anderson (1974), Hemilä's p-hacking is so blatant that it's comical.
The Anderson (1974) trial had eight treatment arms, which differed in timing and dose of vitamin C and placebo. I pulled the results from the original paper and made the plot, below, of average cold duration vs dose of vitamin C. Each dot represents the result of one of the eight original treatment groups. The black line is the result of a linear regression using all the data—all eight arms. It's slope is not statistically significant, meaning that there is no good evidence that the dose of vitamin C affects the duration of subjects' colds.
In his re-analysis, however, Hemilä included only the three arms represented by the red dots in the plot, which gave him the regression line depicted in red. Naturally, his regression shows a significant relationship between dose of vitamin C and cold duration, because the three arms he chose all lie on a straight line. It's amazing what you can achieve when you simply ignore the majority of the data, and select precisely those few data points that give you the result you want.