Stness against this source of variety I 
and variety II errors. 
We also establish that this robustness is lacking to all the several solutions for combining pvalues proposed to date for metaalytic research or for the exact same goal as the UKS test. The onesample KolmogorovSmirnov test assesses irrespective of whether a sample is most likely to become drawn from a theoretical distribution. It truly is based on the biggest difference between the empirical and theoretical cumulative distributions. We use it to assess irrespective of whether pvalues are uniformly distributed between and : the unilateral test enables rejecting the hypothesis that there is no individual impact by displaying that the distribution of individual pvalues is purchase Licochalcone-A abnormally biased towards modest pvalues. The UKS test statistic is TK max ( in { pi ) where pi is the ith pvalue in increasing order and n the population size. The UKS test is resistant because TK cannot reach the. threshold unless at least three or more pvalues are below a low limit that varies with population size. For example, with a sample of pvalues, the UKS test is not significant at the. threshold (TK ) unless there are individual pvalues below.. Based on the Kolmogorov distribution, we computed for different population sizes the minimum number of pvalues necessary for the set to be significant at the. PubMed ID:http://jpet.aspetjournals.org/content/189/2/327 and. threshold (Table ). This minimum number of pvalues asymptotically tends towards.!N for the. threshold, and towards.!N for the. threshold. The formula for computing TK makes the test robust also with respect to type II errors: it is clear that one, two or three high outlier pvalues cannot prevent the UKS test to yield a significant outcome if most individual tests result in low pvalues. This twosided robustness of the UKS test with respect to outlier pvalues is unique among numerous altertive methods for combining independent pvalues. Many methods have been proposed for combining independent pvalues in metaalytical studies (reviews in references ). The most popular ones were devised by Fisher and Stouffer and colleagues. These two methods deserve special Olmutinib chemical information attention because two independent groups have proposed them to be used in fMRI studies for the same purpose as UKS test here, i.e. as altertive to mixedeffects alyses. The Fisher’s statistic is TF log (P), where P is the product of n independent pvalues. TF follows a x distribution with n degrees of freedom. It is easy to see that a single arbitrary small pvalue can make TF arbitrary high and its probability arbitrary close to. The method proposed by Stouffer and colleagues is based on the n pffiffiffi P statisticTS W (pi ) n where F is the inverse normal cumulative distribution function. If the global null hypothesis holds, TS follows the standard normal distribution. The formula for computing TS shows the high sensibility of Stouffer’s to for both small and high outlier pvalues. On the one hand, a sufficiently low pvalue can make TS significant even if the other pvalues have uniform distribution between and. On the other hand, a piDealing with Interindividual Variations of EffectsFigure. Type II errors and reproducibility with heterogeneous experimental effects. Each panel displays the proportion of significant hypothetical experiments as a function of the difference d between the constant values of experimental effect in (panels A ) or subpopulations (panel F). The lines show the proportion of significant tests in hypothetical experiments for values of d from to by. steps for RM Anovas (continuous line).Stness against this source of kind I and kind II errors. We also establish that this robustness is lacking to all of the various methods for combining pvalues proposed to date for metaalytic research or for the exact same goal as the UKS test. The onesample KolmogorovSmirnov test assesses whether or not a sample is most likely to be drawn from a theoretical distribution. It can be primarily based around the biggest difference in between the empirical and theoretical cumulative distributions. We use it to assess no matter whether pvalues are uniformly distributed between and : the unilateral test allows rejecting the hypothesis that there’s no person effect by showing that the distribution of individual pvalues is abnormally biased towards compact pvalues. The UKS test statistic is TK max ( in { pi ) where pi is the ith pvalue in increasing order and n the population size. The UKS test is resistant because TK cannot reach the. threshold unless at least three or more pvalues are below a low limit that varies with population size. For example, with a sample of pvalues, the UKS test is not significant at the. threshold (TK ) unless there are individual pvalues below.. Based on the Kolmogorov distribution, we computed for different population sizes the minimum number of pvalues necessary for the set to be significant at the. PubMed ID:http://jpet.aspetjournals.org/content/189/2/327 and. threshold (Table ). This minimum number of pvalues asymptotically tends towards.!N for the. threshold, and towards.!N for the. threshold. The formula for computing TK makes the test robust also with respect to type II errors: it is clear that one, two or three high outlier pvalues cannot prevent the UKS test to yield a significant outcome if most individual tests result in low pvalues. This twosided robustness of the UKS test with respect to outlier pvalues is unique among numerous altertive methods for combining independent pvalues. Many methods have been proposed for combining independent pvalues in metaalytical studies (reviews in references ). The most popular ones were devised by Fisher and Stouffer and colleagues. These two methods deserve special attention because two independent groups have proposed them to be used in fMRI studies for the same purpose as UKS test here, i.e. as altertive to mixedeffects alyses. The Fisher’s statistic is TF log (P), where P is the product of n independent pvalues. TF follows a x distribution with n degrees of freedom. It is easy to see that a single arbitrary small pvalue can make TF arbitrary high and its probability arbitrary close to. The method proposed by Stouffer and colleagues is based on the n pffiffiffi P statisticTS W (pi ) n where F is the inverse normal cumulative distribution function. If the global null hypothesis holds, TS follows the standard normal distribution. The formula for computing TS shows the high sensibility of Stouffer’s to for both small and high outlier pvalues. On the one hand, a sufficiently low pvalue can make TS significant even if the other pvalues have uniform distribution between and. On the other hand, a piDealing with Interindividual Variations of EffectsFigure. Type II errors and reproducibility with heterogeneous experimental effects. Each panel displays the proportion of significant hypothetical experiments as a function of the difference d between the constant values of experimental effect in (panels A ) or subpopulations (panel F). The lines show the proportion of significant tests in hypothetical experiments for values of d from to by. steps for RM Anovas (continuous line).