F-probability plot and its application to multivariate normality
We introduce the squared jackknife distance of a multivariate observation and derive its finite sampling distribution when a random sample is taken from a multivariate normal distribution. Based on the finite sampling distribution of the squared jackknife distance we recommend the use of an F-probability plot for checking multivariate normality and the F-probability plot correlation coefficient and the F-probability plot intercept as numerical measures of detecting deviation from normality. We report empirical percentiles of the F-probability plot correlation coefficient and the F-probability plot intercept. We compare the powers of tests for multivariate normality based on the F-probability plot and based on the “usual” chi-square probability plot and conduct extensive power studies of the proposed numerical measures.