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Production of a small p-value by multiple testing. 30 samples of 10 dots of random color (blue or red) are observed. On each sample, a two-tailed binomial test of the null hypothesis that blue and red are equally probable is performed. The first row shows the possible p-values as a function of the number of blue and red dots in the sample.
The value q s is the sample's test statistic. (The notation | x | means the absolute value of x ; the magnitude of x with the sign set to + , regardless of the original sign of x .) This q s test statistic can then be compared to a q value for the chosen significance level α from a table of the studentized range distribution .
In statistics, the coefficient of multiple correlation is a measure of how well a given variable can be predicted using a linear function of a set of other variables. It is the correlation between the variable's values and the best predictions that can be computed linearly from the predictive variables.
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
Computing the Pearson correlation coefficient between variables X and Y results in approximately 0.970, while computing the partial correlation between X and Y, using the formula given above, gives a partial correlation of 0.919. The computations were done using R with the following code.
The new multiple range test proposed by Duncan makes use of special protection levels based upon degrees of freedom. Let γ 2 , α = 1 − α {\displaystyle \gamma _{2,\alpha }={1-\alpha }} be the protection level for testing the significance of a difference between two means; that is, the probability that a significant difference between two ...
An approach used by the fisher.test function in R is to compute the p-value by summing the probabilities for all tables with probabilities less than or equal to that of the observed table. In the example here, the 2-sided p -value is twice the 1-sided value—but in general these can differ substantially for tables with small counts, unlike the ...
An f-test pdf with d1 and d2 = 10, at a significance level of 0.05. (Red shaded region indicates the critical region) An F-test is a statistical test that compares variances. It's used to determine if the variances of two samples, or if the ratios of variances among multiple samples, are significantly different.