all null hypotheses are true. If the observed number of positives is substantially greater than what should be expected, this suggests that there are likely to be some true positives among the significant results. For example, if 1000 independent tests are performed, each at level α = 0.05, we expect 0.05 × 1000 = 50 significant tests to occur when all null hypotheses are true. Based on the Poisson distribution with mean 50, the probability of observing more than 61 significant tests is less than 0.05, so if more than 61 significant results are observed, it is very likely that some of them correspond to situations where the alternative hypothesis holds. A drawback of this approach is that it overstates the evidence that some of the alternative hypotheses are true when the test statistics are positively correlated, which commonly occurs in practice. . On the other hand, the approach remains valid even in the presence of correlation among the test statistics, as long as the Poisson distribution can be shown to provide a good approximation for the number of significant results. This scenario arises, for instance, when mining significant frequent itemsets from transactional datasets. Furthermore, a careful two stage analysis can bound the FDR at a pre-specified level. Another common approach that can be used in situations where the test statistics can be standardized to Z-scores is to make a normal quantile plot of the test statistics. If the observed quantiles are markedly more dispersed than the normal quantiles, this suggests that some of the significant results may be true positives. See also q-value Key concepts Family-wise error rate False positive rate False discovery rate (FDR) False coverage rate (FCR) Interval estimation Post-hoc analysis Experimentwise error rate Statistical hypothesis testing General methods of alpha adjustment for multiple comparisons Closed testing procedure Bonferroni correction Boole–Bonferroni bound Duncan's new multiple range test Holm–Bonferroni method Harmonic mean p-value procedure Benjamini–Hochberg procedure Related concepts Testing hypotheses suggested by the data Texas sharpshooter fallacy Model selection Look-elsewhere effect Data dredging References Further reading F. Betz, T. Hothorn, P. Westfall (2010), Multiple Comparisons Using R, CRC Press S. Dudoit and M. J. van der Laan (2008), Multiple Testing Procedures with Application to Genomics, Springer P. H. Westfall and S. S. Young (1993), Resampling-based Multiple Testing: Examples and Methods for p-Value Adjustment, Wiley P. Westfall, R. Tobias, R. Wolfinger (2011) Multiple comparisons and multiple testing using SAS,