50. Factorial experiments and conceptions of the interaction of variables in experimental psychology

I. A general conception of the factorial experiment.

A factorial experiment (FE) is an experiment whose experimental design takes into account changes in more than one independent variable.

The FE design: a specification of the conditions in which the levels of two or more variables are combined.

n × m, where n is the number of levels of the first factor, and m is that of the second.

Control: the functional control of each independent variable occurs independently of the others (the principle of isolated conditions); all combinations of the levels of each factor are possible.

A simple design for a bivalent 2x2 experiment: Factor A (2 levels) and factor B (two levels)

Thus, a 2x3 design means that the second independent variable was represented by three levels; accordingly, 6 experimental conditions differing in these two variables were used.

Why is an FE needed? Why introduce a second and so on independent variable?

1. To control changes connected with the same basic process that is influenced by the first independent variable.

2. To refine the psychological mechanisms standing behind the change in the dependent variable.

3. To refine hypotheses and, as a consequence, to choose a specific basic process (dependent variable).

4. To control accompanying confounds.

5. To conduct a multilevel experiment.

6. To separate different basic processes.

7. To test combined hypotheses.

Hypotheses in an FE:

1. 1. Hypotheses with a single relation. The introduction of a second independent variable serves the purpose of increasing internal validity or expanding the scope of generalization.

   2. Combined hypotheses. Their formulations present the directional influences of each of the independent variables on the dependent variable and the possible interactions between the experimental factors.

Other kinds of refinement used in factorial schemes are the control of accompanying confounds and the conduct of multilevel experiments.

Here there are no multiple changes in the independent variable and the dependent variable.

Combined hypotheses concern the manner in which the independent variables, combining with one another, influence the dependent variable. If there are several independent variables, then it is factorial, since the independent variable is a factor for controlling (changing) behavior.

Designs with three independent variables

When testing hypotheses involving the complex influence of more than 2 factors on the basic process, the realization of multilevel experiments becomes difficult (the full set of combinations requires a great many conditions).

One of the ways to reduce the dimensionality of the design is the Graeco-Latin square: with a full set of two varied variables, the levels of the third variable are distributed in such a way as to ensure their presence for each pair of combinations.

Evaluation of the results of such an experiment usually presupposes the use of analysis-of-variance schemes, which make it possible to quantitatively assess different sources of variability in the dependent variable, including first- and second-order interactions.

Factorial experiments planned for testing combined hypotheses presuppose not only the basic experimental effect of the individual variables, but also the determination of the type of interaction between the experimental factors.

An interaction is the difference between two differences.

An example cited by Gottsdanker: Gaffan's experiment with monkeys and a severed fornix.

Hypothesis: severing the brain leads to a deterioration of memory: in this case recognition, rather than association, is impaired.

The experimental group – monkeys with a severing of the fornix in the brain; the control group – the fornix intact.

In order to exclude the influence of an accompanying variable on the differences – namely, the influence of the very trepanation of the brain during the operation to sever the fornix on the deterioration of the animal's memory – trepanation was performed on all the monkeys. That is, the accompanying variable is set in all conditions, and in the end the differences should be conditioned only by the influence of the independent variable.

In the experiment the monkeys solved two different tasks, each of which included a series of familiarization trials. In this, in 5 trials an object was presented under which sweet corn lay, and the 5 subsequent ones were empty.

Next, before the monkey there were two cells – one closed with a copper disk, and in the other the same objects were presented one after another in the same order. And if the object was the one under which the bait had lain in the familiarization trial, then the bait also lay under it; if it was a different one – then the bait was placed under the disk. The dependent variable in this case was characterized by the number of attempts in which the bait was taken without error. Here a task of association was posed.

2) Next, in another task, the capacity for recognition was tested. In the familiarization trials

there were no empty ones, and during the test five new objects were given, behind which there was no bait. That is, the monkey had to recognize the old ones, and in the case of new ones to find the bait under the copper disk.

The control group solved both tasks equally successfully (approximately 80%), whereas the experimental group solved the first at 80% and the second at 60%.

And here we return to the definition of interaction.

88-62=26; 83-82=1; Interaction = 26-1=25

The magnitude of the interaction shows to what extent the result of severing the fornix depends on the tasks presented.

The number of experimental factors determines how many types of interactions can be established according to the data obtained. If there are two independent variables – then a first-order interaction between them is established. If there are three – then there may be both a first-order and a second-order interaction (how all the variables act). Third-order (see the lecture).

Types of interaction.

1) Zero / absence of interaction. The line segments of the results of both groups are parallel.

(The action of the second independent variable exerts an influence of equal magnitude on the dependent variable under all conditions of the first independent variable).

2) Divergent interaction (as in the case of the monkeys). (The second independent variable makes it possible to separate, in the values of the dependent variable, the contribution of the basic variable from that of the accompanying variables.

3) Crossing interaction. The differences in the results are equal but opposite in sign. This is the strongest interaction. Example: The monkeys with a severed fornix might not only solve recognition tasks worse than monkeys with a normal fornix, but also solve association tasks better.