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The most common test for heterogeneity of variance is Bartlett’s. It can be found

in almost all statistical texts. Recent work has shown, however, that it is too sensi-

tive. Analysis of variance is an immensely robust test that performs well even when

the assumptions of the analysis are not met in full. It copes well with minor het-

erogeneity of variance and with deviations from normality. About the only thing that

throws it out badly is bimodality of the response variable. A better test is Cochran’s

C, whose test statistic is simply the largest variance in a cell divided by the sum of

all cell variances. For the two-factor ANOVAgiven in Box 16.2 the largest cell variance

is returned by the replicate counts of gray kangaroos on day 2. It is s^2 =2566. The

sum of all six variances is ∑s^2 =6796.6, and so Cochran’s C=2566/6796.6 =0.378.

Looking up a table of the critical values of Cochran’s C(Appendix 2) reveals that

the test statistic would have to exceed C=0.398 (d.f. =7 per variance and there are

six variances) to represent a significant departure from homogeneity of variance. We

can thus choose to analyze without transformation.

284 Chapter 16

A sig

B sig

AB ns

A sig

Bns

AB ns

Ans

B sig

AB ns

A sig

B sig

AB sig

Ans

B sig

AB ns

Ans

Bns

AB sig

A 1 A 2 A 3 A 1 A 2 A 3

A 1 A 2 A 3 A 1 A 2 A 3

A 1 A 2 A 3 A 1 A 2 A 3

B 1

B 2

B 2

B 1

B 2

B 1

B 2

B 2

B 1

B 2

B 1

Response

Response

Response

B 1

Fig. 16.5Common

forms of interaction in

two-factor ANOVAs. ns,

Not significant; sig,

significant.

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