Although the patterns of canonical loadings on the perfectionism

variates appear to support the distinction between maladaptive and adaptive profiles of perfectionism (see Lo & Abbott, 2013), it is the associations between the perfectionism

variates and the social-loafing

variates that are of particular interest.

Prior to testing our hypotheses, we examined relationships among the variables that compose each

variate for multi-collinearity (defined as r > .90; Meyers, Gamst, & Guarino, 2006).

where variable [Z.sub.j] represents a weight for the probability of changes in each pixel to identify a greater chi-square value, [M.sub.kj] is the MAD

variate of the kth band for pixel j, and [mathematical expression not reproducible]i is the variance of the no-change distribution.

(1995) and Stevens (2009) suggest the use of the correlation between individual observable variables and the associated canonical

variates for interpretation.

After accounting for the relationships between statistics anxiety and motivational beliefs in the first canonical

variates, the second pair of canonical

variates indicates that all motivational beliefs components are still related to test anxiety, interpretation anxiety, and worth of statistics.

It can be seen from (5) that envelope and phase are independent

variates. This is coherent with the complex Nakagami-m model [4, 5] in which the independence condition arose naturally out of the derivation of the model.

Basic Control Antithetic Hybrid K M algorithm

variates variates algorithm 80 1000 0.6548 0.3167 0.4248 0.1047 10000 0.2079 0.1012 0.1334 0.0342 100000 0.0657 0.0312 0.0428 0.0114 100 1000 0.4671 0.2317 0.3323 0.0112 10000 0.1502 0.0689 0.1098 0.0248 100000 0.0478 0.0219 0.0355 0.0077 120 1000 0.2843 0.1418 0.2454 0.0456 10000 0.0929 0.0437 0.0850 0.0152 100000 0.0298 0.0136 0.0276 0.0049

From the definition, it is clear that if [summation] = 0, then for Re(a) > (m-1)/2, the extended matrix

variate gamma function reduces to the multivariate gamma function [[GAMMA].sub.m](a).

For [OMEGA] = [I.sub.m], the above density reduces to a standard matrix

variate gamma density and in this case we write X ~ Ga(m, v, [theta]).

To determine if the observed variations differ between sexes, Canonical

Variate Analysis (CVA) was conducted (Tables 4 and 5).

These structure correlations are calculated by multiplying the vector and canonical weights by the matrix of the within set of correlations for each

variate according to the following equations:

As shown in Table 2, the first pair of canonical

variates was positively correlated with the ADMS.