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Lilliefors test is a normality test based on the Kolmogorov–Smirnov test. It is used to test the null hypothesis that data come from a normally distributed population, when the null hypothesis does not specify which normal distribution; i.e., it does not specify the expected value and variance of the distribution. [ 1 ]
Another remedy for data dredging is to record the number of all significance tests conducted during the study and simply divide one's criterion for significance (alpha) by this number; this is the Bonferroni correction. However, this is a very conservative metric.
However, in practice, most implementations of non-parametric test software use asymptotical algorithms to obtain the significance value, which renders the test non-exact. Hence, when a result of statistical analysis is termed an “exact test” or specifies an “exact p-value ”, this implies that the test is defined without parametric ...
Although the 30 samples were all simulated under the null, one of the resulting p-values is small enough to produce a false rejection at the typical level 0.05 in the absence of correction. Multiple comparisons arise when a statistical analysis involves multiple simultaneous statistical tests, each of which has a potential to produce a "discovery".
Hubert Whitman Lilliefors (June 14, 1928 – February 23, 2008 in Bethesda, Maryland) was an American statistician, noted for his introduction of the Lilliefors test. Lilliefors received a BA in mathematics from George Washington University in 1952 [ 1 ] and his PhD at the George Washington University in 1964 under the supervision of Solomon ...
Correction factor versus sample size n.. When the random variable is normally distributed, a minor correction exists to eliminate the bias.To derive the correction, note that for normally distributed X, Cochran's theorem implies that () / has a chi square distribution with degrees of freedom and thus its square root, / has a chi distribution with degrees of freedom.
The F statistic is the same as in the Standard Univariate ANOVA F test, but is associated with a more accurate p-value. This correction is done by adjusting the degrees of freedom downward for determining the critical F value. Two corrections are commonly used: the Greenhouse–Geisser correction and the Huynh–Feldt
This created a need within many scientific communities to abandon FWER and unadjusted multiple hypothesis testing for other ways to highlight and rank in publications those variables showing marked effects across individuals or treatments that would otherwise be dismissed as non-significant after standard correction for multiple tests.