I have asked a similar question here: stackoverflow I am puzzled by the interpretation for an interaction term. In my data my Y is an interval variable with the health outcome of an experiment. I have used an interaction term in which I have interacted the condition with the predisposition of the subject considering health status at base level. They are both categorical variables (factor variables in R).
Now it gets complicated because the Condition was two treatments: in treatment A subjects got the placebo first and then the real medicine whereas in treatment B they go the real medicine first and the placebo second. All it changes is the order.
Health outcome = a + Condition * Health.Base
I have the worst state of health at the base level as my reference category I find that interaction with the Condition is statistically significant but I am not sure how to interpret this.
I use the
lm() function of R (although my design looks more like an ANOVA) and in the output I get the b coefficient in an output that looks like this:
ConditionB:Health.Base.So.and.So (Beta and p-value) ConditionB:Health.Base.Excellent (Beta and p-value)
A statistically significant interaction term for those in Excellent health at baseline would mean that they are affected by the Condition B more than Condition A compared to the reference category people (Poor health at baseline). Is this right? What does the beta-coefficient represent?
If I would like to examine for each Health category at the base line separately without comparing to a reference category I would have to code each category as a dummy variable. However, in this case I would compare whether membership to a specific health status at the base line significantly changes between conditions compared to those who belong to the other health statuses at the base line. Is this right? Again, what does the beta-coefficient represent?
Would it be right to assume that the choice of the interaction between the Condition and the dummy variables is easier to interpret?
--- EDIT --- R output:
Call: lm(formula = HealthOutcome ~ Condition * HealthStatus, data = datA) Residuals: Min 1Q Median 3Q Max -1.5957 -0.5942 -0.2640 0.4423 2.4423 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 2.595652 0.053044 48.934 < 2e-16 *** ConditionCondB -0.001449 0.077071 -0.019 0.985 HealthStatusSo.and.So -0.331693 0.078094 -4.247 2.35e-05 *** HealthStatusExcellent -0.836724 0.092692 -9.027 < 2e-16 *** ConditionCondB:HealthStatusSo.and.So 0.137490 0.110612 1.243 0.214 ConditionCondB:HealthStatusExcellent -0.199787 0.133943 -1.492 0.136 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.8045 on 1059 degrees of freedom (68 observations deleted due to missingness) Multiple R-squared: 0.16, Adjusted R-squared: 0.156 F-statistic: 40.33 on 5 and 1059 DF, p-value: < 2.2e-16