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Simple slopes analysis

Author: Dr Simon Moss

Introduction

Researchers often need to examine whether one variable moderates the association between two variables (James & Brett, 1984). They might, for instance, want to examine whether feelings of engagement moderate the relationship between workload and dishonesty.

To illustrate, workload might be positively related to dishonesty when individuals do not feel engaged in their tasks. However, workload might not be related to dishonesty when individuals feel engaged in their tasks. Engagement, thus, moderates or changes the relationship between workload and dishonesty.

This pattern of observations appears in the following figure. In this figure, two lines appear in a graph. One line slopes upwards, and represents the relationship between workload and dishonesty when engagement is below average-specifically, when the z value of engagement is -1 or 1 standard deviation below average. The other line is almost horizontal, and represents the relationship between workload and dishonesty when engagement is above average-specifically, when the z value of engagement is +1 or 1 standard deviation above average.

Usually, a technique called moderated regression is applied to ascertain whether or not one variable moderates the association between two other variables. Another procedure, called simple slopes analysis, can then be conducted to determine whether the gradient of one or both these lines differs from 0-that is, departs from the horizontal plane. This article will briefly reiterate moderated regression but will focus on simple slopes analysis.

Overview of moderated regression

To conduct moderated regression, researchers need to:

You will utilize these variables during the remainder of this analysis. Note that some researchers do not create standardized variables when they conduct moderated regression. Standardized variables-or at least centered variables, in which the mean is deducted-is necessary if you later want to undertake simple slopes analysis. Then, the researcher should:

The researcher can now interpret the output. A table, called coefficients, should appear, which resembles the following:

Unstandardized coefficients

Standardized coefficients

B

SE

Beta

t

sig

Constant

2.209

2.007

1.101

0.303

z_workload

1.071

0.103

0.830

-2.686

0.020

z_engagement

0.162

0.464

0.119

0.350

0.736

work_x_engage

-0.930

0.467

-0.838

2.102

0.004

According to this table, the significance or p value associated with work_x_engage is less than .05. This finding implies the interaction is significant (Aiken & West, 1991). In other words, engagement moderates the relationship between workload and dishonesty.

Overview of the construction of simple slopes

The next step is to construct the lines that appear on the previous figure. Specifically, the researcher needs to develop two equations, one representing each of these lines. First, they need to construct an equation that represents the relationship between workload and dishonesty when engagement is below average-specifically, when the z value of engagement is -1 or 1 standard deviation below average. Next, they need to construct an equation that represents the relationship between workload and dishonesty when engagement is above average-specifically, when the z value of engagement is +1 or 1 standard deviation above average. To achieve these goals, the researcher should:

Although not specified, these labels actually correspond to standardized variables. Next:

Simple slopes analysis

In the previous section, we developed two equations:

Simple slopes analysis can be conducted to answer the question as to whether these gradients-in this instance 2.001 or .141-differ from zero. That is, is workload positively related to dishonesty for both low and high levels of engagement.

Compute standard error of the slope

To answer this question, the researcher merely needs to calculate the standard error of this gradient. To compute this standard error, the researcher simply needs to apply the following formula:

work_x_engage

z_engagement

z_workload

work_x_engage

.218

.005

-.043

z_engagement

.005

.011

-.008

z_workload

-.043

-.008

.215

Compute the t values of the slope

Finally, to ascertain whether the simple slope--that is, the slope of each line--differs from zero, researchers need to:

Hence, in this contrived example, one of the two slopes or lines differs significantly from 0 or horizontal.

Simple slopes analysis in practice

Researchers do not have to construct the equations at Z=1 or Z=-1, but can incorporate other z values as well. Indeed, many researchers do not even ascertain whether these simple slopes differ significantly from zero. That is, the overall pattern, uncovered by the moderated regression, is often more important. Whether or not two arbitrary lines differ from the horizontal plane might not be as important.

References

Aiken, L. S., & West, S. G. (1991). Multiple regression: Testing and interpreting interactions. Thousand Oaks, CA: Sage.



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Last Update: 6/22/2016