Deck 20: Mediation and Moderation

Question 1

A researcher conducts a simple mediated regression to determine the extent to which reading performance mediates the relationship between time spent on homework and science performance. The researcher finds the following results. Indicate what type of mediation it is (full or partial) and interpret the coefficients for X and M.

OUTCOME VARIABLE:
SCIENCE
$\begin{array}{l}\text { Model Summary }\\\begin{array}{rrrrrrr}R & \text { R-sq } & \text { MSE } & \text { F (HC4) } & \text { df1 } & \text { df2 } & \text { P } \\.6468 & .4184 & 78.5197 & 309.8067 & 2.0000 & 1207.0000 & .0000\end{array}\end{array}$ $\begin{array}{l}\text { Model }\\\begin{array}{lrrrrrr} & \text { coeff } & \text { se(HC4) } & t & p & \text { LLCI } & \text { ULCI } \\\text { constant } & 19.9463 & 2.9626 & 6.7327 & .0000 & 14.1339 & 25.7588 \\\text { HOMEWORK } & .0008 & .0248 & .0311 & .9752 & -.0479 & .0494 \\\text { READING } & .3849 & .0155 & 24.8780 & .0000 & .3545 & .4152\end{array}\end{array}$

$\begin{array}{ll}\text { Standardized coefficients } \\& \text { coeff } \\\text { HOMEWORK } & .0008 \\\text { READING } & .6468\end{array}$

Answer 1

Reading fully mediates the relationship between homework and science performance. This is shown as the observed probability for homework is not statistically significant (p = .9752) but is statistically significant for reading (p < .001).

The coefficient for homework (X) tells us that two students that differ by one unit on homework but are equal on reading performance are estimated to differ by .0008 units on science.

The coefficient for reading (M) tells us that two people who are equal on homework (X) but that differ by one unit on reading are estimated to differ by .3849 on science.

Question 2

A researcher conducts a simple mediated regression to determine the extent to which reading performance mediates the relationship between time spent on homework and science performance. The researcher finds the following results. Interpret the partially standardized total effect and partially standardized direct effect.

************** TOTAL, DIRECT, AND INDIRECT EFFECTS OF X ON Y **************

$\begin{array}{l}\text { Total effect of } \mathrm{X} \text { on } Y\\\begin{array}{rrrrrrrrr}\text { Effect } & \text { se }(\mathrm{HC} 4) & \mathrm{t} & \mathrm{p} & \text { LLCI } & \text { ULCI } & \text { c\_ps } & \text { c\_cs } \\.0212 & .0304 & .6971 & .4859 & -.0385 & .0809 & .0018&.0225\end{array}\end{array}$

$\begin{array}{l}\text { Total effect of } \mathrm{X} \text { on } Y\\\begin{array}{rrrrrrrrr}\text { Effect } & \text { se }(\mathrm{HC} 4) & t & p & \text { LLCI } & \text { ULCI } & c^{\prime} \text {\_ ps } & c^{\prime} \text { \_cs } \\.0008 & .0248 & .0311 & .9752 & -.0479 & .0494 & .0001&.0008\end{array}\end{array}$

Answer 2

The partially standardized total effect suggests that two cases that differ by one unit on homework (X) will differ by about .0018 standard deviation on science (Y) as a result of the combined direct and indirect effects by which homework affects science.

The partially standardized direct effect suggests that, independent of the mediating effect of reading, a student that is one unit higher on homework will be about .0001 standard deviations different on science.

Question 3

A researcher computes a moderated regression model and finds the following. Describe what the interaction term represents (e.g., which terms are interacting), and interpret the interaction.
**************************************************************************
Model : 1
Y : MATH
X : SCIENCE
W : READING
Sample
Size: 1210
**************************************************************************
OUTCOME VARIABLE:
MATH

$\begin{array}{l}\text { Model Summary }\\\begin{array}{rrrrrrrr}R & R-s q & \text { MSE } & \text { F (HC4) } & \text { df1 } & \text { df2 } &P \\.7050 & .4971 & 135.7397 & 323.8703 & 3.0000 & 1206.0000 & .0000\end{array}\end{array}$

$\text { Model }$

$\begin{array}{lrrrrrr} & \text { Coeff } & \text { Se (HC4) } & t & p & \text { LLCI } & \text { ULCI } \\& & & & & & \\\text { constant } & 31.1829 & 31.4492 & .9915 & .3216 & -30.5183 & 92.8840 \\\text { SCIENCE } & .9186 & .3579 & 2.5668 & .0104 & .2165 & 1.6207 \\\text { READING } & .2803 & .1730 & 1.6205 & .1054 & -.0591 & .6197 \\\text { Int\_1 } & -.0010 & .0019 & -.5006 & .6168 & -.0048 & .0028\end{array}$

Product terms key:
$\text { Int\_ } 1: \text { SCIENCE } \mathrm{x} \text { READING }$



$\text { Test (s) of highest order unconditional interaction (s): }$

$\begin{array}{rrrrr}&\mathrm{R} 2-\mathrm{chng} & \mathrm{F}(\mathrm{HC} 4) & \text { df1 } & \text { df2 } & p \\\mathrm{X} * \mathrm{~W}&.0003 & .2506 & 1.0000 & 1206.0000 & .6168\end{array}$

$\begin{array}{r}\text { Focal predict: SCIENCE }&(X) \\\text { Mod var: READING }&(W)\end{array}$

Answer 3

The interaction represents the product of science and reading and indicates how the effect of science (X) on the dependent variable, math, changes as reading (W, the moderator) changes by one unit. More specifically, as reading increases by one unit, the dependent variable decreases by .0010 as science increases by one unit.

Question 4

A researcher conducts a moderated regression with W as the moderator. Interpret the conditional effects presented here.

Conditional effects of the focal predictor at values of the moderator(s):
$\text { Conditional effects of the focal predictor at values of the moderator(s): }$

$\begin{array}{rrrrrrr}W&\text { Effect } & \text { se }(\mathrm{HC} 4) & t & p & \text { LLCI } & \text { ULCI } \\1.5000 & .5236 & .0342 & 15.3307 & .0000 & .4566 & .5906 \\2.0000 & .4373 & .0269 & 16.2711 & .0000 & .3846 & .4901 \\2.5000 & .3511 & .0381 & 9.2266 & .0000 & .2765 & .4258\end{array}$

Question 5

A researcher conducts a moderated regression with W as the moderator. Interpret the results from probing the interaction using the Johnson-Neyman technique.

Question 6

A researcher is examining the relationship between science and mathematics performance. The researcher believes that there may be an indirect effect of science on mathematics through literacy. Which of the following types of models would you recommend the researcher examine?

A) Mediation
B) Moderation
C) Neither
D) Both

Question 7

A researcher is examining the relationship between weight and blood pressure. The researcher believes that there may be an indirect effect of weight and blood pressure through stress. Which of the following types of models would you recommend the researcher examine?

A) Mediation
B) Moderation
C) Neither
D) Both

Question 8

A researcher is examining the relationship between science and mathematics performance. The researcher believes that science may interact with literacy. Which of the following types of models would you recommend the researcher examine?

A) Mediation
B) Moderation
C) Neither
D) Both

Question 9

A researcher is examining the relationship between time on task and academic performance. The researcher believes that time on task may interact with age. Which of the following types of models would you recommend the researcher examine?

A) Mediation
B) Moderation
C) Neither
D) Both

Question 10

A researcher has conducted a moderated multiple regression analysis and finds f² of .03. Based on Cohen's guidelines, what is the interpretation of the effect?

A) Small
B) Moderate
C) Large
D) None of the above

Question 11

A researcher has conducted a moderated multiple regression analysis and finds f² of .16. Based on Cohen's guidelines, what is the interpretation of the effect?

A) Small
B) Moderate
C) Large
D) None of the above

Question 12

Which of the following is NOT an assumption for moderated multiple regression?

A) Expected frequencies
B) Homoscedasticity
C) Linearity
D) Normality

Question 13

What is one of the challenges with the Johnson-Neyman approach for probing an interaction?

A) Interactions cannot be proved with this approach.
B) Regions of significance cannot be determined with this approach.
C) This approach can be used only with continuous moderating variables.
D) Violations of homogeneity of regression cannot be handled with this approach.

Question 14

In a mediation model, a positive sign for the direct effect indicates which of the following?

A) One unit higher on X is estimated to be higher on Y.
B) One unit higher on X is estimated to be lower on Y.
C) One unit higher on X is estimated to be the same as Y.
D) Impossible to determine with this information.

Question 15

In a mediation model, a negative sign for the direct effect indicates which of the following?

A) One unit higher on X is estimated to be higher on Y.
B) One unit higher on X is estimated to be lower on Y.
C) One unit higher on X is estimated to be the same as Y.
D) Impossible to determine with this information.

Question 16

Which of the following represents an indirect effect in a simple mediation model?

A) The dependent variable influences the mediating variable, which then influences the independent variable.
B) The independent variable influences the mediating variable, which then influences the dependent variable.
C) The independent variable influences the dependent variable, which then influences the mediating variable.
D) The mediating variable simultaneously influences the independent and dependent variable.

Question 17

Which of the following is an interpretation of the direct effect of the independent variable on the dependent variable?

A) How much two cases that differ by one unit on the dependent variable will differ on the independent variable.
B) How much two cases that differ by one unit on the independent variable will differ on the mediator.
C) How much two cases that differ by one unit on the independent variable will differ on the dependent variable.
D) Two cases that differ by one unit on the mediator but are equal on the independent variable will differ by b units on the dependent variable.

Question 18

In a moderation model where X is the independent variable and W is the moderating variable, the inclusion of the interaction term (XW) is testing the effect of X on the dependent variable is conditional on W.

Question 19

Which one of the following is not a way to examine an interaction?

A) Graphical methods
B) Johnson-Neyman technique
C) Pick-a-point approach
D) All of the above
E) None of the above

Question 20

Which of the following will be evident in a full mediation model?

A) The relationship between the independent and dependent variable will completely disappear
B) The relationship between the independent and dependent variable becomes stronger

Question 21

Which of the following may impact power in moderated multiple regression?

A) Measurement error
B) Sample size
C) The variance of the predictor is smaller in the population.
D) All of the above
E) None of the above

Question 22

The underlying framework for mediation is to understand which one of the following:

A) How the mediator relates to the moderator.
B) The way in which the independent variable relates to the dependent variable.
C) Which independent variable is related to the dependent variable.
D) Which dependent variable produces statistically significant results.

Question 23

The direct effect in a simple mediation model is denoted by which one of the following?

A) a
B) b
C) c'
D) e

Question 24

In a moderated regression model, the interaction term reflects which one of the following?

A) The dependent variable controlling for the moderating variable
B) The product of the dependent variable and independent variable
C) The product of the independent variable and moderating variable
D) The sum of the regression coefficients

Question 25

The conditional effect of the independent variable on the dependent variable when the moderating variable is zero is interpreted in which one of the following ways?

A) The difference in X for two cases that differ by one on W but differ by zero on
B) The difference in W for two cases that differ by one on X but differ by zero on
C) The difference in for two cases that differ by one on W but differ by zero on X
D) The difference in for two cases that differ by one on X but differ by zero on W

Question 26

Testing that the effect of the independent variable (X) on the dependent variable (Y) is dependent on the moderating variable (W) is conducted by including which term in the moderation model?

A) X
B) XY
C) W
D) WY
E) XW

Question 27

Which one of the following is needed to determine whether the relationship between the independent and dependent variables systematically varies as a function of the moderator?

A) Graph of the interaction
B) Probe for an interaction
C) Test for an interaction
D) Visualization of the XY relationship

Question 28

Which one of the following is NOT an effect size that is recommended to avoid in reporting mediation results?

A) Kappa squared
B) Partially standardized total effect
C) Ratio of the indirect effect to the direct effect
D) The proportion of variance in the dependent variable that is explained by the indirect effect

Question 29

The assumptions for moderation are the same as which of the following procedures?

A) Binary logistic regression
B) Multinomial logistic regression
C) Multiple linear regression
D) Simple linear regression

Question 30

The assumptions for mediation are the same as which of the following procedures?

A) Binary logistic regression
B) Multinomial logistic regression
C) Multiple linear regression
D) Simple linear regression

Question 31

Moderation occurs in which of the following situations?

A) The effect of the dependent variable on the moderating variable can be predicted by the independent variable.
B) The effect of the independent variable on the dependent variable can be predicted by the moderating variable.
C) The interaction of the independent and dependent variables can be predicted by the moderating variable.
D) The moderating variable can be predicted by the effect of the independent variable on the dependent variable.

Question 32

Which one of the following represents moderation?

A) Exponentiation of the regression coefficient
B) Interactions in factorial ANOVA
C) Random effects with a completely crossed design
D) Repeated measures within persons

Question 33

Which one of the following reflects partial mediation?

A) Some relationship between X and Y remains, and that relationship becomes stronger.
B) Some relationship between X and Y remains, but that relationship is smaller in magnitude.
C) The relationship between X and Y completely disappears.
D) The relationship between X and Y exponentiates.