Interaction analyses — Interpreting effect sizes (part 2)

A simple example — binary moderator

First I started with a simple analysis, where the moderator is binary, coded as either 0 or 1, and there are exactly the same number of both values.

Extending to a continuous moderator

Simple-slopes is common approach to interpreting interaction analyses when the moderator is continuous. In essence, the slope of x on y is examined at different ranges of values of the moderator. Conventionally, three slopes are examined, and their range is defined by the mean and standard deviation of the moderator (usually 1.5xSD). If our moderator has values from 0 to 10, with an average of 5, and a standard deviation of 2, then the groups will be [0–2), [2–8], (8–10].

Quartiles Slope Correlation
2 1.63 0.99
3 2.21 1.00
4 2.57 1.00
5 2.83 1.00
6 3.03 1.00
7 3.19 1.00
8 3.32 1.00
9 3.44 0.99
10 3.54 0.99
11 3.63 0.99
12 3.71 0.99
13 3.78 0.99
14 3.85 0.99
15 3.91 0.99
Call:
lm(formula = Slope~ log(Quartiles), data = quart_comparison)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.00341 0.05489 18.28 3.97e-10 ***
log(Quartiles) 1.09602 0.02641 41.49 2.49e-14 ***
Multiple R-squared: 0.9931, Adjusted R-squared: 0.9925
F-statistic: 1722 on 1 and 12 DF, p-value: 2.488e-14

Final thoughts and next steps

If we return to my initial question: If a main-effect is bX = 0.3, with an interaction of bXM = 0.1, what does the data look like? We can now say for three quartiles, the difference in slope between the bottom and top quartiles is ~0.1 * 2, or 0.2, So the slope of the bottom quartile is ~0.2, and the slope of the top quartile is ~0.4.

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