Table 1.

Mixing probabilities and critical values of the previously stated asymptotic null distributions for k-trait multivariate tests according to the binomial mixture formula (2.2)

	χ02	χ12	χ22	χ32	χ42	χ52	Critical value (α = 0.01)	Critical value (α = 0.05)
k = 2	0.2500	0.5000	0.2500				7.289	4.231
k = 3	0.1250	0.3750	0.3750	0.1250			8.746	5.435
k = 4	0.0625	0.2500	0.3750	0.2500	0.0625		10.019	6.498
k = 5	0.0313	0.1563	0.3125	0.3125	0.1563	0.0313	11.183	7.480