Statistical Methods for Psychology

One of the convenient things about hierarchical designs is that they allow us to specify

models very clearly and simply. Assume that we have four variables (A, B, C, and D). The

notation ABCspecifies a model that includes the ABCinteraction, and, because we are

speaking about hierarchical models, also includes A, B, C, AB, AC, and BC. We do not have

to write out the latter to specify the model (well, you do in SPSS GENLOG)—ABCwill

suffice. Similarly, the label ABstands for a model that includes A, B, and AB, but not Cor

any interactions involving C. Finally, a model written as AB, ACDis really the model that

involves A, B, C, D, AB, AC, AD, CD, and ACD, but not BC, BD, ABC, ABD, or BCD. In

much of what follows we will characterize models by the interactions that define them

(sometimes called their defining set,or generating class). Because the program that we

will use for the following examples (SPSS GENLOG) is not restricted to hierarchical mod-

els, if we want to tell it to use a hierarchical model for AB,AC, we need to explicitly spec-

ify the model as A,B,C,AB,AC. With a program such as SPSS HILOGLINEAR, the same

model would be specified as AB, ACbecause the rest would be assumed. I chose GENLOG

because its printout most neatly fits the material that I want to present.

A Three-Way Example

In the previous section we examined the relationship between Fault and Verdict in the

study of rape by Pugh (1983). Pugh also attempted to manipulate a third variable

(Moral) by varying the trial transcript to present the victimas someone with “high moral

character,” “low moral character,” or “neutral” on this dimension. We now have three

variables by which to categorize the data: Fault (F), Moral (M), and Verdict (V). Fault

and Moral refer to characteristics attributed to the victim, whereas Verdict represents a

judgment on the defendant. Fault and Verdict each have two levels, whereas Moral has

three levels. Pugh’s data collapsed across a fourth variable (Gender of juror) are given

in Table 17.8.

Possible Models

Our task is to try to explain the pattern of obtained cell frequencies in Table 17.8. We could

ask a variety of possible questions in seeking an explanation, including the following:

1. Can the pattern of cell frequencies be explained (solely) by differences in the number of
   participants in the three Moral conditions?

Section 17.6 Three-Way Tables 645

defining set

generating class

Table 17.8 Pugh’s data collapsed across Gender

Moral

Verdict Fault High Neutral Low Total

Guilty Low^427932153

High 23 65 17 105

Total 65 144 49 258

Not Guilty Low^412824

High 11 41 24 76

Total 15 53 32 100

Column total 80 197 81 358