[Multiple-Sample Testing of Variance Matrix]

It is beyond the scope of the current work to clearly underpin the statistical motivation of Roy '5- test. An elegant description of the Roy's test can be found in Section 6.1.4 of Rencher (2002). We now give a watered-down version of Roy's test. Let 1, denote the largest eigenvalue of the matrix E 'H. The Roy's largest root test is given by 0 = 1 + M (14.21) The test procedure is then to reject the hypothesis H if 0 > a,s.my, where s = min{UH, p), m = (10H - P| - 1), N = (VE - P - 1). For the rootstock dataset, the one-line R code below gives the result based on the Roy's test. > summary (root . manova, test = "Roy") Df Roy approx F num Df den Df Pr (> F) rs 5 1. 88 15 .8 5 42 1e-08 * * * Residuals 42 Signif. codes: 0 ' ***' 0.001 ' * *' 0.01 ' *' 0.05 ' .' 0.1 ' ' 1 The Roy's test also rejects the hypothesis H that the mean vector for the six strata are equal.Problem 14.8 Using base matrix tools of R, create a function which returns the value of Roy's test statistic given in Equation 14.21