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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".
Chi-squared distribution, showing χ 2 on the x-axis and p-value (right tail probability) on the y-axis.. A chi-squared test (also chi-square or χ 2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large.
This is because () is the smallest in each one of the intersection sub-families and the size of the sub-families is at most , such that the Bonferroni threshold larger than /. The same rationale applies for H ( 2 ) {\displaystyle H_{(2)}} .
In Petrophysics a Klinkenberg correction is a procedure for calibration of permeability data obtained from a minipermeameter device. A more accurate correction factor can be obtained using Knudsen correction .
The simplest version of the test statistic from this auxiliary regression is TR 2, where T is the sample size and R 2 is the coefficient of determination. Under the null hypothesis of no autocorrelation, this statistic is asymptotically distributed as χ 2 {\displaystyle \chi ^{2}} with k degrees of freedom.
The bias-corrected and accelerated ... but with a different formula (note the inversion of the left and right quantiles): ... for a sample size n; this ...
Conversely, a “large" R 2 (scaled by the sample size so that it follows the chi-squared distribution) counts against the hypothesis of homoskedasticity. An alternative to the White test is the Breusch–Pagan test, where the Breusch-Pagan test is designed to detect only linear forms of heteroskedasticity. Under certain conditions and a ...
In equations, the typical symbol for degrees of freedom is ν (lowercase Greek letter nu).In text and tables, the abbreviation "d.f." is commonly used. R. A. Fisher used n to symbolize degrees of freedom but modern usage typically reserves n for sample size.