Traits- 12.71%
Situations- 10.17%
Interaction- 20.77%
Bowers used this type of analysis to argue for the interactionist position. (By the way the main effects for traits were smaller in “normal” populations than “abnormal” populations.)
Olweus argues that THIS TYPE OF REASONING IS FAULTY, and he provides some examples of this poor reasoning.
Imagine a study that would involve 3 levels of a Personality variable (e.g., low, medium, and high need for aggression; P1,P2, and P3, respectively) factorially combined with three levels of a Situational variable (e.g., low, medium, and high provocation; S1, S2, S3, respectively). Imagine that the dependent measure is the amount of force of each person’s fist hitting a wall. The scores are:
P1, S1 = 1
P2, S1 = 2
P3, S1 = 3
P1, S2 = 4
P2, S2 = 5
P3, S2 = 6
P1, S3 = 7
P2, S3 = 8
P3, S3 = 9
Means: S1 = 2, S2 = 5, S3 = 8----P1 = 4, P2 = 5, P3 = 6.
An analysis of variance of these data would show that 90% of the variance is accounted for by the situation main effect, and 10% of the variance is accounted for by the Personality trait. There is 0% of the variance in the interaction (trust me). Although a Situationist could interpret these data as supporting the Situationist position because the amount of situational variance 9 times larger than the personality variance, such a conclusion would be illogical and faulty. Why? Because the data also perfectly support the Trait position. The correlation of personality measures across situations is perfect, r = 1.0. P3 always hits harder than P2, who always hits harder than P1; given the same situation.
Example 2. Trust me that the following formula is TRUE. The correlation for personality across situations (rP) is equal to the variance for personality (vP) divided by the sum of vP plus the variance for the personality by situation interaction (vPS).
rP = vP/(vP + vPS). Thus when rP is approximately r = .45 (a magnitude of correlation that most would accept as showing an acceptable degree of transituational consistency according to the trait position), the percentage of variance for the interaction is larger than the percentage of variance for personality.
If rP = .5, then vP = vPS
if rP <.5, then vP < vPS
if rP >.5, then vP > vPS.
So data truly supporting the trait position could conceivable be of less magnitude than the interaction term data. So a statistical interaction larger than either main effect does not necessarily argue for an interactionist position to the exclusion of others. OLWEUS CONCLUDES THAT IT IS IMPOSSIBLE TO EVALUATE THE “CORRECTNESS’ OF THE THREE POSITIONS USING THE ANALYSIS OF VARIANCE COMPONENTS TECHNIQUE.
Olweus also presents a fruitful distinction among 4 possible meaning of the term INTERACTION.
1. TO COMBINE OR CONNECT. How do situations and personality variables interact in evoking behavior? This is a unidirectional effect of situations and personality upon behavior. How are 2 independent variables combined or connected to effect a dependent variable?
2. THE INTERDEPENDENCE AND INSEPARABILITY OF THE PERSON AND THE SITUATION (ALSO KNOWN AS INTERACTIONISM). This is a bi-directional effect and very different in meaning from #1 above.
3. RECIPROCAL ACTION. How the individual and environment sequentially affect each other.
4. INTERACTION IN A STATISTICAL ANALYSIS OF VARIANCE. (ANOVA)
#4 can be used to answer the how question posed in meaning #! Do persons and situations combine linearly if they are significant? Can they be summed? (i.e., no interaction); or do you need to consider an interaction of the personality variable with the situational variable.
ANOVAs have little use relevant to meanings #2 and #3. ANOVAs assume that the two main effects are independent (i.e., have independent variance) while #2 assumed that the person and situation are always DEPENDENT. For research investigating #3, there are more appropriate statistical analyses (e.g., conditional probabilities)