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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 ]
A 2011 study concludes that Shapiro–Wilk has the best power for a given significance, followed closely by Anderson–Darling when comparing the Shapiro–Wilk, Kolmogorov–Smirnov, Lilliefors, and Anderson–Darling tests. [1] Some published works recommend the Jarque–Bera test, [2] [3] but the test has weakness.
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 ...
The test is conducted for a given sample size and level of significance or α. To perform the test a number n statistically independent runs of the model are conducted and an average or expected value, E(Y), for the variable of interest is produced.
The Bonferroni correction can also be applied as a p-value adjustment: Using that approach, instead of adjusting the alpha level, each p-value is multiplied by the number of tests (with adjusted p-values that exceed 1 then being reduced to 1), and the alpha level is left unchanged.
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".
Partial autocorrelation function of Lake Huron's depth with confidence interval (in blue, plotted around 0). In time series analysis, the partial autocorrelation function (PACF) gives the partial correlation of a stationary time series with its own lagged values, regressed the values of the time series at all shorter lags.
Mark and recapture is a method commonly used in ecology to estimate an animal population's size where it is impractical to count every individual. [1] A portion of the population is captured, marked, and released.