Regions of Significance (RoS) with respect to Z (Moderator)
Lower threshold for RoS with respect to Z = -0.207
Upper threshold for RoS with respect to Z = 0.216
where values of Z outside this region are significant
These values represent the upper and lower bounds of values for Moderator (between -2 and + 2) at which the regression of Outcome on Predictor is statistically significant (alpha = .05). The regression of Outcome on Predictor is significant for all values of Moderator that fall outside the region [-0.207, 0.216]. In the figure, only regressions based on values of Moderator between -2 and + 2 are probed and graphed.
Simple slope at Z = 1 is 0.30, t(1000) = 6.40, p = 0.000
Simple slope at Z = -1 is -0.30, t(1000) = 7.07, p = 0.000
Regions of Significance (RoS) with respect to X (Predictor)
Lower threshold for RoS with respect to X = 0.433
Upper threshold for RoS with respect to X = 0.969
where values of X outside this region are significant
These values represent the upper and lower bounds of values for Predictor at which the regression of Outcome on Moderator is statistically significant (alpha = .05). The regression of Outcome on Moderator is significant for all values of Predictor that fall outside the region [0.433, 0.969].
Simple slope at X = 2 is 0.40, t(1000) = 5.44, p = 0.000
Simple slope at X = -2 is -0.80, t(1000) = 11.80, p = 0.000
Proportion of the Interaction (PoI) with respect to Predictor
PoI values provide a way to express the proportion of the total interaction that is represented on the left and right sides of the crossover point. If the crossover point for the two regression lines occurs on the far right side of Predictor (e.g., 1.5 SDs above the mean), then the interaction qualifies a narrow range of the effects in question. If the regression lines intersect in the middle of Predictor, then the interaction qualifies a maximum amount of the effects in question.
The PoI values are computed as the area of the triangle to the left of the crossover point and the area of the triangle to the right of the crossover point, bounded by -2 and 2 on Predictor by convention. These two PoI values should sum to 1.00. If there is no interaction--or if the crossover falls outside of the -2 to + 2 SD range, these values will be undefined or will be extreme (e.g., 1.00 and 0.00).
PoI right = 0.20
Proportion Affected (PA) with respect to Predictor
The PA index represents the proportion of people differentially affected by the crossover interaction. This is computed by finding the point on Predictor where the regression lines intersect and calculating the proportion of cases on Predictor that fall above that crossover point.
This particular index can be valuable because it quantifies the proportion of people who are differentially affected by the interaction. Below the crossover point, for example, people high on Moderator might score lower on Outcome than people low on Moderator. Above the crossover point, however, this relationship might be reversed such that people high on Moderator score higher on Outcome compared to people low on Moderator. The PA index essentially summarizes the proportion of people for whom the association between Moderator and Outcome is reversed or qualified.
In practice, the PA index should be computed with respect to the sorted empirical values of Predictor. Because this web application does not use raw empirical data as input (only summary statistics), the PA index is computed under the assumption that Predictor is normally distributed. To the extent to which the actual distribution of Predictor departs from a normal distribution, the PA index will be inaccurate. It is possible to compute PA in SPSS or Excel simply by creating a new variable using the following pseudo-code: NEWVAR = 1 if X > crossover value. A simple frequency analysis of NEWVAR will reveal how many cases fall above the crossover point.
Crossover point on Predictor = 0.667
PA index (normal distribution assumed) = 0.252
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