Hi
I'm currently working on a project in STATA, where I look at the effect of performance information on trust in government (two treatment groups and 1 control group in the performance information variable). Besides this, I have included a binary interaction variable (social democrat/not social democrat). I get the results shown in the screenshots.
I'm aware that the interaction variable is not significant, but I still want to interpret the results. The coefficient for the interaction variable is -0,045 and -0,140. Does this mean, that a social democrat that received treatment 1 will be 0,045 points lower in trust than the average receiver of treatment 1? I'm not entirely sure how to interpret the data. I hope you can help :-)
Suggest that you look at a book like D Montgomery, Design and Analysis of experiments. You want the part that discusses interaction effects in a factorial design. Best regards, D Booth
Hello Malte,
I'm not sure why you'd want to estimate the point estimates (coefficients) for the two interaction variates given that neither can be reliably distinguished from zero, based on your data set results.
The longer answer depends on how the 3-level IV was recoded into two comparison or dummy variates.
In ordinary anova, the model for two factors is: Y = mu + a[i] + b[j] + ab[i,j] + error
The ab term, in definitional form: MeanY[i,j] - MeanY[i] - MeanY[j] + MeanY,
where:
MeanY[i,j] is cell mean for combination i,j of the two factors (a, b)
MeanY[i] is mean for level i of factor a
MeanY]j] is mean for level j of factor b
MeanY is overall sample mean on the dependent variable.
Good luck with your work.
there's no average receiver here as all rhs variables are discrete. you can say the effect for the social democrat receiver of T1 is 0.427-0.045 higher w.r.to the non-social democrat receiver of T1 and 0.427-0.045-0.403 lower than the non-social democrat control.
Thank you Luca Mancini . Regarding T1 and what you wrote. The non social democrat receiver of T1 have a coefficient of -0.403 and the coeffient for the social democrat receiver is -0.405, so when a "respondent" goes from not being a social democrat o being a social democrat the result will be -0.403-0.405 = -0.808. Is that correctly interpreted?
the effect on the log-odds of trusting the government from being an SD receiver of T1 is 4.925 -0.403+0.427-0.045 =4.904
the same effect for a non-SD receiver of T1 is 4.925 -0.403=4.522
so, conditional on receiveing T1, going from not being an SD respondent to being one, the log-odds of trust in government increase by 4.904-4.522=0.382
"I'm aware that the interaction variable is not significant, but I still want to interpret the results."
The lack of statistical significance tells you that you should not interpret the sign of the coefficients. You can not clearly distinguish these estimates from noise. It would be rather stupid to interpret them anyway.
What you could do, though, is to have a look at the confidence intervals. You may conclude that the coefficient is not more extreme than the outer limits of these intervals. In your example, you may conclude that the absolute interaction is not greater than about 1 (what you can not conclude is whether the interaction is positive or negative!). If a relevant interaction would be grater than that, you could conclude that the interaction is irrelevant.
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