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strong test of the effect of the treatments themselves is possible unless those treat-

ments are replicated.

Replicates are not meant to be similar. They are meant to sample the natural range

of variability. Consequently, one does not look for six similar sites to provide three

treatments and three controls. One picks six sites at random. A common excuse offered

for a lack of replication in management experiments (and even in research experi-

ments) is that sites similar enough to act as replicates could not be located. Such an

excuse is not valid and points to a lack of understanding of the nature of evidence.

These principles carry over to all other forms of comparison. We cannot conclude

from two specimens that parrots of a given species have a higher hemoglobin count

near the tops of mountains than at lower altitudes. We get no further forward by

taking a number of blood samples (subsampling) from the two individuals. Instead,

we must test the blood of several parrots from each zone, look at the variation within

each group of parrots, and then calculate whether the average difference between groups

is greater than the difference within groups. Hence, we must replicate. The arith-

metic of such a comparison can be extracted from any book on statistical methods.

That is the easy part. The difficult part is getting the logic right.

Experimental design has its own vocabulary. The thing that we monitor, in this case

the density or rate of increase of the quail, is the response variable. That which affects

the response variable, in this case WHEAT, is a factor. In our imaginary experiment

the factor we examined had two levels: no supplementary feeding of wheat and some

supplementary feeding of wheat (Fig. 16.1). Equally, its levels could have been set

at 0, 30, 70, and 250 kg of grain per hectare per month as in Fig. 16.2. The levels

of a factor need not be numbers as in that example. The levels of factor HABITAT, for

example, might be pine, oak, and grassland. The levels of factor ORDERmight be first,

second, third, and fourth. The levels of factor SPECIESmight be mule deer, white-tailed

deer, and elk.

Suppose we wished to examine the effect of two management treatments simultan-

eously. Instead of looking at the effect of just wheat on density of quail we might

wish also to examine the effect of supplying extra salt. There are now two factors:

WHEATand SALT. The questions now become:

1 Does WHEATaffect density?

2 Does SALTaffect density?

3 Is the effect of WHEATon density influenced by the level of SALT, and vice versa?

In statistical language the last question deals with the interaction between the two

factors, whether their individual effects on density are additive (i.e. independent of

each other) or whether the effect of a level of one factor changes according to which

level of the other factor is combined with it. Section 16.6.3 considers interactions in

greater detail.

Figure 16.3 gives an appropriate experimental design for such a two-factor experi-

ment. Its main features are that each level of the first factor is combined with each

level of the second, that there are therefore 2 × 4 =8 cells or treatments, that each

treatment is replicated, and that the number of replicates per treatment is the same

for all treatments.

A control is that level of a factor subjected to zero treatment. That is not to say that

it is necessarily left undisturbed. Everything done to the other levels must also be

274 Chapter 16

16.5 Experimental and survey design

16.5.1Controls

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