untitled

changed between 1987 and 1988. We do not wish to test the more general question

of whether kangaroo populations remain stable with time. The ANOVAshows that of

the three main effects, the three first-order interactions, and the one second-order

interaction, only the main effect of kangaroo species is significant. We conclude there-

fore that the two species certainly differed in density but that there was insufficient

evidence to identify a day effect or a change in density between years. Neither did

any factor appear to interact with any other.

Testing of wildlife management treatments requires rigorous definition of the

expected outcome of the treatments. Once a verifiable outcome is posed as a hypo-

thesis, the data to test it can be collected by following the logic of experimental design.

Insufficient replication of treatments to sample the range of natural variability is a

common shortcut, but it nullifies the point of the exercise.

The principles illustrated in this chapter can be summarized as the basic rules of

experimental design. There are exceptions to several of them, but until the manager

or researcher learns how and in what circumstances they may safely be varied, these

should be followed in full.

1 To determine whether a factor affects the response variable under study, more than

one level of that factor should be examined. The levels may be zero (control) and

some non-zero amount, or they may be two or more categories (e.g. habitat types)

or non-zero quantities (e.g. altitudinal bands).

2 “Before” is a poor control for “after,” because subsequent trends can be caused by

other influences unrelated to the treatment under study.

3 Treatments must be replicated, not subsampled. (See Hurlbert (1984) for an excel-

lent exposition of the pitfalls of “pseudo-replication” in ecological research.)

4 The number of replications per treatment (including the control treatment)

should be as close as possible to equal across treatments.

5 Treatments must be interspersed in time and space. Do not run the replications

of treatment A and then the replications of treatment B. Mix up the order. Do not

site the replications of treatment A in the north of the study region and the replica-

tions of treatment B in the south. Mix them up.

6 If the influence of more than one factor is of interest, each level of each factor should

be examined in combination with each level of every other factor (factorial design).

7 If an extraneous influence (site in the quail example) is likely to be correlated with

one of the designated factors, either it should be declared a factor in its own right

and the design modified accordingly or its range should be covered at random by

EXPERIMENTAL MANAGEMENT 287

16.7 Summary

ROWeffect (1/ncl)∑Ti^2 −(1/nrcl)T^2 d.f. =r− 1

COLUMNeffect (1/nrl)∑Tj^2 −(1/nrcl)T^2 d.f. =c− 1

LAYEReffect (1/nrc)∑Tk^2 −(1/nrcl)T^2 d.f. =l− 1

RC interaction (1/nl)∑Tij^2 −(1/ncl)∑Ti^2 −(1/nrl)∑Tj^2 +(1/nrcl)T^2 d.f. =(r−1)(c−1)

CL interaction (1/nr)∑Tjk^2 −(1/nrl)∑Tj^2 −(1/nrc)∑Tk^2 +(1/nrcl)T^2 d.f. =(c−1)(l−1)

RL interaction (1/nc)∑Tik^2 −(1/ncl)∑Ti^2 −(1/nrc)∑Tk^2 +(1/nrcl)T^2 d.f. =(r−1)(l−1)

RCL interaction (1/n)∑Tijk^2 −(1/nl)∑Tij^2 −(1/nr)∑Tjk^2 −(1/nc)∑Tik^2

+(1/ncl)∑Ti^2 +(1/nrl)∑Tj^2 +(1/nrc)∑Tk^2 −(1/nrcl)T^2 d.f. =(r−1)(c−1)(l−1)

Residual ∑X^2 ijkm−(1/n)∑Tijk^2 d.f. =(n−1)rcl

Total ∑X^2 ijkm−(1/nrcl)T^2 d.f. =nrcl− 1

Table 16.3Calculation

of sums of squares and

degrees of freedom for

three-factor ANOVA.

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