Testing the Significance of the Moderator Effect
The method of determining the statistical significance of the
moderator effect depends to some degree on the characteristics of
the predictor and moderator variables. That is, when a moderator
effect is composed of predictor and moderator variables that both
are measured on a continuous scale, one continuous variable and
one categorical variable with two levels, or two categorical variables
each with two levels, the single degree of freedom F test,
representing stepwise change in variance explained as a result of
the addition of the product term, provides the information needed
(Aiken & West, 1991; Jaccard et al., 1990; West et al., 1996). This
process is somewhat different, however, when categorical variables
have more than two levels. As discussed most clearly by
West et al. (1996; see also Aiken & West, 1991; Cohen et al.,
2003; Jaccard et al., 1990), at least two code variables are needed
to fully represent the categorical variable in this situation. Consequently,
the moderator effect is tested with the multiple degree of
freedom omnibus F test representing stepwise change for the step
in which the multiple product terms are entered. If the omnibus F
test is statistically significant, the single degree of freedom t tests
related to specific product terms are inspected to determine the
form of the moderator effect. The importance of specific comparisons
also can be conceptualized in terms of the amount of variance
accounted for (i.e., by their squared semipartial correlations;
see Cohen et al., 2003). In other words, when there is more than
one coded variable, the amount of variance in the outcome variable
accounted for by each comparison is indexed by the squared
semipartial correlation associated with that comparison. Cohen et
al. described how to calculate semipartial correlations, which are
not always provided by statistical programs in their standard
output, and provided tables to calculate the power associated with
tests of their significance.
If the interaction term is not significant, the researcher must
decide whether to remove the term from the model so that the
first-order effects are not conditional effects. Aiken and West
(1991, pp. 103–105) reviewed the issues associated with this
decision and ultimately recommended keeping the nonsignificant
interaction term in the model if there are strong theoretical reasons
for expecting an interaction and removing the interaction if there is
not a strong theoretical rationale for the moderator effect (see also
Cohen et al., 2003). al. described how to calculate semipartial correlations, which are
not always provided by statistical programs in their standard
output, and provided tables to calculate the power associated with
tests of their significance.
If the interaction term is not significant, the researcher must
decide whether to remove the term from the model so that the
first-order effects are not conditional effects. Aiken and West
(1991, pp. 103–105) reviewed the issues associated with this
decision and ultimately recommended keeping the nonsignificant
interaction term in the model if there are strong theoretical reasons
for expecting an interaction and removing the interaction if there is
not a strong theoretical rationale for the moderator effect (see also
Cohen et al., 2003).
Verstehe ich das so richtig:
Habe ich nur zweistufige kategoriale Variablen muss ich nur ansehen, ob das zweite Modell (enthält UV, Moderator und Interaktionsterm) einen signifikanten Zuwachs an Varianzaufklärung ergibt ggü. dem ersten Modell (welchs nur UV und Moderator enthält)?
Habe ich jedoch 2+x Kategorien, muss ich mir auch erstmal ansehen ob der Zuwachs an Varianzaufklärung signifikant ist. Ist das der Fall, muss ich mir noch im Regressionsmodell die Koeffizienten ansehen. Ich gehe jetzt mal von Dummy-Codierung aus. Bei den signifikanten Koeff. gibt es zwischen den mit 1 codierten und den mit 0 codierten einen Unterschied in der AV (=Interaktion). Bei den nicht signifikanten gibt es keinen Unterschied zw. 1 und 0 in der AV.
