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High Quality Content by WIKIPEDIA articles! In statistics, hypotheses suggested by the data must be tested differently from hypotheses formed independently of the data. For example, suppose fifty different researchers, unaware of each other's work, run clinical trials to test whether Vitamin X is efficacious in treating cancer. Forty-nine of them find no significant differences between measurements done on patients who have taken Vitamin X and those who have taken a placebo. The fiftieth study finds a big difference, but the difference is of a size that one would expect to see in about one of every fifty studies even if vitamin X has no effect at all, just due to chance. When all fifty studies are pooled, one would say no effect of Vitamin X was found, because the positive result was not more frequent than chance, i.e. it was not statistically significant.