W5: Meditation and Moderation

Question 1

In Meditation we are interested as: (3)

Answer 1

• Whether a direct effect of X on Y exists
• Whether a indirect effect of X on Y via Mediator M exists
• Whether an additional effect of X on Y having allowed Mediator M exists

Question 2

Meditation diagram

Answer 2

Question 3

If M helps us to explain why changes in X causes changes in Y then M is known as the

Answer 3

Meditator variable

Question 4

If particular values of M causes the effect to happen, or changes its strength then M is known as a

Answer 4

moderator variable

Question 5

Suppose we are interested in whether a covariate X causes changes in a continuous response variable Y

effect of X on Y can sometimes be affected by another
variable, M, related to X and Y

We do a

Answer 5

meditation or moderator analysis depending on M variable

Question 6

Steps in Meditation Analysis (4)

Answer 6

1. Assess sig of simple linear regression of Y on X
2. Assess sig of simple linear regression of M on X
3. Assess the signifiance of M in multiple regression of Y on X and M
4. Assess the signifiance of X in multiple regression of Y on X and M

Question 7

Steps in Meditation Analysis Equations (4)

Answer 7

1. Y = a + bx
2. m = a + bx
3. Y = a + bx + cm (is meditator sig? [ m])
4. Y = a + bx (is x sig?) + cm

Question 8

Assumptions of Meditation Analysis

We need to check the assumptions of linear regression for each of the

Answer 8

3 regressions

Question 9

Assumptions of linear regression (3)

Answer 9

• Errors are independent
• Normally disturbed
• Constant variance

Question 10

Step 2: Interpret assess sig of simple linear regression of Y on X - (4) Meditation - page on Spec 1

Answer 10

From the regression of Confidence on Introversion, we see that the
regression equation is

Confidence = 44.909 − 0.536 × Introversion.

The Introversion coefficient is significant at the 0.1% level.

Thus we have a relationship between Introversion and Confidence: increased
introversion decreases confidence.

Question 11

Step 3: Interpret assess sig of simple linear regression of M on X - (3) page on Spec 1

Answer 11

From the regression of Time on Introversion, we see that the regression equation is

Time = 54.442 + 0.580 × Introversion.

The Introversion coefficient is significant at the 0.1% level. Thus
we have a relationship between Introversion and Time: increased
introversion increases practice time

Question 12

Step 3 & 4: Interpret significance of M and X in multiple regression of Y on X and M - (6) page on Spec 1

Answer 12

From the multiple regression of Confidence on Introversion and Time,
we see that the regression equation is

Confidence = 88.323 − 0.797 × Time − 0.073 × Introversion.

The Time coefficient is significant at the 0.1% level. Thus we have a
direct relationship between Time and Confidence: those who practise most have least confidence.

The Introversion coefficient is not significant, however, even at the 5% level.

When adjusting for the meditator, time, there is no effect of introversion on confidence

Thus we see that time spent practising fully mediates the relationship between introversion and confidence

Question 13

Step 5 of Meditation is Sobel Test page on Spec 1

Answer 13

We see Sobel test is significant at 0.1% level, indicating the meditation is statisticaly significant.

Question 14

Moderation -> M is often

Answer 14

a factor with a small number of levels

Question 15

Moderation Diagram

Question 16

Whatever the forms of X and M are in moderation we can perform a

Answer 16

multiple linear regression

Question 17

If Moderator (M) and covariate X are factors then perform a

Answer 17

two factor ANOVA and assess significance of interaction

Question 18

Moderation:

We fit the multiple linear regression model:

Answer 18

Y = a + b1X + b2M + b3 XM + e

Question 19

Moderation

Multiple linear regression model what does XM and B3 are? - (2)

Answer 19

XM is an interaction term:
coefficient b3 tells us how changes in M affect relationship of X and Y

Question 20

Moderation

If b3 is significant in multiple linear regression model then conclude that

Answer 20

M is a moderator for the effect of X on Y

Question 21

Moderation results