untitled

The three-factor ANOVAfollows the general lines of the two-factor except that seven

rather than three questions are now being addressed simultaneously. Table 16.3 gives

the sums of squares and degrees of freedom.

Box 16.3 gives an example, again kangaroos counted by aerial survey, but with

factor YEARSadded. YEARSis fixed because we wish to test specifically whether density

286 Chapter 16

Model Source Denominator of F

One-factor ANOVA

A fixed A MSe

A random A MSe

Two-factor ANOVA

A fixed, B fixed A MSe

BMSe

AB MSe

A fixed, B random A MSAB

BMSe

AB MSe

A random, B random A MSAB

BMSAB

AB MSe

Three-factor ANOVA

A fixed, B fixed, C fixed A MSe

BMSe

CMSe

AB MSe

AC MSe

BC MSe

ABC MSe

A fixed, B fixed, C random A MSAC

BMSBC

CMSABC

AB MSe

AC MSe

BC MSe

ABC MSe

A fixed, B random, C random A XXX

BMSBC

CMSBC

AB MSABC

AC MSABC

BC MSe

ABC MSe

A random, B random, C random A XXX

B XXX

C XXX

AB MSABC

AC MSABC

BC MSABC

ABC MSe

XXX, no explicit test is possible; MSe, mean square of the residual.

Table 16.2The mean

square providing

the denominator for

an F-ratio testing

significance of a factor

or interaction (i.e.

source of variation).

16.6.6Three-factor

ANOVA

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