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Chapter 7 : Mediation Analysis and Hypotheses Testing

7.1. Introduction

Data analysis of the mediating hypotheses testing will investigate the impact of mediator on the

relationship between independent variables and dependent variable. This study examines

mediating effect on the direct path between the independent variables and the dependent variable

using the Baron and Kenny’s (1986) three-step mediation analysis and chi-square (χ2) difference

test. The results of the mediating effect are further confirmed by Sobel’s (1982) test, the Aroian’s

(1944) test, and the Goodman’s (1960) test.

A variable may be considered a mediator to the extent to which it carries the influence of a given

independent variable to a given dependent variable. Mediation can be said to occur when...

(1) the independent variable significantly affects the mediator,

(2) the independent variable significantly affects the dependent variable in the absence of the

mediator,

(3) the mediator has a significant unique effect on the dependent variable, and

(4) the effect of the independent variable on the dependent variable shrinks upon the addition of

the mediator to the model.

These criteria can be used to informally judge whether or not mediation is occurring, but

MacKinnon & Dwyer (1993) and MacKinnon, Warsi, & Dwyer (1995) have popularized

statistically based methods by which mediation may be formally assessed by using the Sobel’s

(1982) test, the Aroian’s (1944) test, and the Goodman’s (1960) test. These tests consider the

unstandardized regression and standard error for the association between independent variable and

mediator, and also the unstandardized regression and standard error for the association between

mediator and the dependent variable.

We propose the following mediating hypothesis:

Mediating Hypothesis MedH1 : Teachers Job Contribution (Mediator) significantly mediates

the relationship between Teachers Organizational Commitment (Independent Variable) and

Teacher’s Engagement (Dependent Variable).

Mediating Hypothesis MedH2 : Teachers Job Contribution (Mediator) significantly mediates

the relationship between Teachers Perceived Organizational Support (Independent

Variable) and Teacher’s Engagement (Dependent Variable).

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7.2. Baron and Kenny’s (1986) Three-Step Mediating Analysis

A variable may be considered a mediator to the extent to which it carries the influence of a given

independent variable to a given dependent variable. Hence, a mediator accounts for the

relationship between an independent variable and the dependent variable. Mediation can be

said to occur when...

1. the independent variable significantly affects the mediator,

2. the independent variable significantly affects the dependent variable in the absence of the

mediator,

3. the effect of the independent variable on the dependent variable shrinks upon the addition of

the mediator to the model.

Perfect mediation holds if the independent variable has no effect on the dependent variable, when

the mediator is controlled. That is complete mediation or full mediation exists if the independent

variable exerts its total influence through the mediating variable.

Partial mediation is given if the independent variable exerts some of its influence on the

dependent variable through the mediating variable, and it also exerts some of its influence directly

on the dependent variable and not through mediating variable.

7.3. Anderson and Gerbing’s (1988) Chi-square Difference Test

Further Chi-square Difference Test was conducted. Chi-square Difference Test is Anderson and

Gerbing’s (1988) approach to testing nested models to ensure that the mediating models produced a

better fit than non-mediating models. In this process, mediating models and non-mediating models

of two indirect relationship models were tested and evaluated based on χ2 statistics. If the mediating

models are better suited to the data than non-mediating models, the change in χ2 statistic should be

statistically significant (Byrne, 1998).

7.4. Sobel’s (1982) Test, the Aroian’s (1944) Test, and the Goodman’s (1960)

Test

MacKinnon & Dwyer (1993) and MacKinnon, Warsi, & Dwyer (1995) have popularized

statistically based methods by which mediation may be formally assessed by using the Sobel’s

(1982) test, the Aroian’s (1944) test, and the Goodman’s (1960) test. These tests consider the

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unstandardized regression and standard error for the association between independent variable and

mediator, and also the unstandardized regression and standard error for the association between

mediator and the dependent variable.

Sobel’s Test

Researchers argue that it is not enough to report whether the size of the relation between the

predictor and the outcome variable becomes smaller (partial mediation) or insignificant (full

mediation) when the mediator is added to the equation (Frazier, Tix, & Barron, 2004). Thus, the

Sobel (1982) tests were also applied to more thoroughly confirm the significance of the mediated

effect.

The mediated, indirect effect of the predictors on outcome variables is defined as the product of the

predictor-moderator path (a) and the moderator-outcome variable path (b), or ab. The mediated

effect was tested for statistical significance by dividing the estimate of the mediating variable effect

by its standard error and comparing this value to a standard normal distribution (MacKinnon,

Lockwood, Hoffman, West, & Sheets 2002; Sobel, 1982). The standard error of the indirect effect

(Sab) is

222222

babaab SSSaSbS

Where,

a = unstandardized regression coefficient of path a;

b = unstandardized regression coefficient of path b;

Sa = standard error of a;

Sb = standard error of b.

Aroian’s Test

Formulae for the tests provided here were drawn from MacKinnon & Dwyer (1994) and from

MacKinnon, Warsi, & Dwyer (1995):

222222 **** baba SSSaSbbavaluez

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Goodman’s Test

222222 **** baba SSSaSbbavaluez

7.5. Mediating Hypotheses Testing

Mediating Hypothesis MedH1

Null Hypothesis : Teachers Job Contribution (Mediator) does not significantly mediates the

relationship between Teachers Organizational Commitment (Independent Variable) and Teacher’s

Engagement (Dependent Variable).

Alternate Hypothesis : Teachers Job Contribution (Mediator) significantly mediates the

relationship between Teachers Organizational Commitment (Independent Variable) and Teacher’s

Engagement (Dependent Variable).

Figure 7.1 : Independent Variable (Teachers Organizational Commitment), Mediator

(Teachers Job Contribution) and Dependent Variable (Teacher’s Engagement)

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Baron and Kenny’s Mediating Analysis

Condition 1: The independent variable should significantly affect the mediator.

Figure 7.2 : Baron and Kenny’s First Condition : Independent Variable Mediator

(Teachers Organizational Commitment Teachers Job Contribution)

Table 7.1

Standardized Regression Estimate : : Independent Variable Mediator (Teachers

Organizational Commitment Teachers Job Contribution)

Standardized

Regression

Estimate

S.E. C.R. P

Teachers Organizational Commitment

→ Teachers Job Contribution 0.763 0.055 7.949 ***

Teachers Job Contribution regresses significantly on Teachers Organizational Commitment hence

the first condition of Baron and Kenny’s Mediating Analysis is satisfied.

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Condition 2: The independent variable significantly affects the dependent variable in the absence

of the mediator.

Figure 7.3 : Baron and Kenny’s Second Condition : Independent Variable Dependent

Variable (Teachers Organizational Commitment Teacher’s Engagement)

Table 7.2

Standardized Regression Estimate : : Independent Variable Dependent Variable

(Teachers Organizational Commitment Teacher’s Engagement)

Standardized

Regression

Estimate

S.E. C.R. P

Teachers Organizational

Commitment → Teacher’s

Engagement

0.456 0.080 4.873 ***

Teacher’s Engagement regresses significantly on Teachers Organizational Commitment hence the

second condition of Baron and Kenny’s Mediating Analysis is satisfied.

The effect of the independent variable on the dependent variable with the moderator :

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Figure 7.4 : Effect of the Independent Variable on the Dependent Variable with the

Mediator for Mediating Hypothesis MedH1

Table 7.3

Standardized Regression Estimate : : Independent Variable Mediator Dependent

Variable for Mediating Hypothesis MedH1

Standardized

Regression

Estimate

S.E. C.R. P

Teachers Organizational

Commitment → Teachers Job

Contribution → Teacher’s

Engagement

0.187 0.083 1.653 0.098

As the p > 0.050 (p = 0.098), there exists full mediation by the mediating variable, hence the

independent variable exerts its total influence through the mediating variable.

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Chi-square Difference Test : Anderson and Gerbing’s (1988) approach

Chi-square Difference Test is Anderson and Gerbing’s (1988) approach to testing nested models to

ensure that the mediating models produced a better fit than non-mediating models. If the mediating

models are better suited to the data than non-mediating models, the change in χ2 statistic should be

statistically significant (Byrne, 1998). The following table shows the chi-square difference test for

mediating hypothesis MedH1.

Table 7.4

Chi-square Difference Test for Mediating Hypothesis MedH1

Model Chi-square Df p-value Reject / Not

Reject the Null

Hypothesis

Non-Mediating Model 42.451 30

Mediating Model 73.149 47

The chi-square

Difference Test

30.698 17 0.0217289 Reject

The chi-square difference test reveals a significant mediation, thus it can be concluded that the

null hypothesis (MedH1) is rejected, and hence the alternative hypothesis is accepted.

Sobel’s Test, Aroian’s Test and Goodman’s Test

Thus to confirm the above mediating hypothesis we conducted the Sobel’s (1982) test, the

Aroian’s (1944) test, and the Goodman’s (1960) test. These tests were conducted in line with the

z-prime method (MacKinnon, Lockwood, Hoffman, and West & Sheetes, 2002) to check for the

statistical power of our models and discount the possibility of Type I error while exploring the

strength of mediation.

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Table 7.5

Sobel’s Test, Aroian’s Test and Goodman’s Test for Mediating Hypothesis for Mediating

Hypothesis MedH1

Mediating Hypothesis MedH2

Null Hypothesis: Teachers Job Contribution (Mediator) does not significantly mediate the

relationship between Teachers Perceived Organizational Support (Independent Variable) and

Teacher’s Engagement (Dependent Variable).

Alternate Hypothesis: Teachers Job Contribution (Mediator) significantly mediates the

relationship between Teachers Perceived Organizational Support (Independent Variable) and

Teacher’s Engagement (Dependent Variable).

Figure 7.5: Independent Variable (Teachers Perceived Organizational Support), Mediator

(Teachers Job Contribution) and Dependent Variable (Teacher’s Engagement)

Sobel’s

Test

Aroian’s

Test

Goodman’s

Test P Remarks

Teachers Organizational Commitment →

Teachers Job Contribution →

Teacher’s Engagement

4.659 4.634 4.685 *** MedH1

accepted

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Baron and Kenny’s Mediating Analysis

Condition 1: The independent variable should significantly affect the mediator.

Figure 7.6 : Baron and Kenny’s First Condition : Independent Variable Mediator

(Teachers Perceived Organizational Support Teachers Job Contribution)

Table 7.6

Standardized Regression Estimate : : Independent Variable Mediator (Teachers

Perceived Organizational Support Teachers Job Contribution)

Standardized

Regression

Estimate

S.E. C.R. P

Teachers Perceived Organizational

Support → Teachers Job Contribution 0.739 0.088 10.916 ***

Teachers Job Contribution regresses significantly on Teachers Perceived Organizational Support

hence the first condition of Baron and Kenny’s Mediating Analysis is satisfied.

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Condition 2: The independent variable significantly affects the dependent variable in the absence

of the mediator.

Figure 7.7 : Baron and Kenny’s First Condition : Independent Variable Mediator

(Teachers Perceived Organizational Support Teachers Job Contribution)

Table 7.7

Standardized Regression Estimate : : Independent Variable Dependent Variable

(Teachers Perceived Organizational Support Teacher’s Engagement)

Standardized

Regression

Estimate

S.E. C.R. P

Teachers Perceived Organizational

Support → Teacher’s Engagement 0.583 0.063 9.632 ***

Teacher’s Engagement regresses significantly on Teachers Perceived Organizational Support

hence the second condition of Baron and Kenny’s Mediating Analysis is satisfied.

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The effect of the independent variable on the dependent variable with the moderator

Figure 7.8 : Effect of the Independent Variable on the Dependent Variable with the

Mediator for Mediating Hypothesis MedH2

Table 7.8

Standardized Regression Estimate : : Independent Variable Mediator Dependent

Variable for Mediating Hypothesis MedH2

Standardized

Regression

Estimate

S.E. C.R. P

Teachers Perceived Organizational

Support → Teachers Job Contribution →

Teacher’s Engagement

0.546 0.094 5.989 ***

As the p < 0.050 (p < 0.001), there exists partial mediation by the mediating variable, hence the

independent variable exerts some of its influence on the dependent variable through the mediating

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variable, and it also exerts some of its influence directly on the dependent variable and not through

mediating variable.

Chi-square Difference Test : Anderson and Gerbing’s (1988) Approach

Chi-square Difference Test is Anderson and Gerbing’s (1988) approach to testing nested models to

ensure that the mediating models produced a better fit than non-mediating models. If the mediating

models are better suited to the data than non-mediating models, the change in χ2 statistic should be

statistically significant (Byrne, 1998). The following table shows the chi-square difference test for

moderating hypothesis MedH1.

Table 7.9

Chi-square Difference Test for Mediating Hypothesis MedH2

Model Chi-square Df p-value Reject / Not Reject

the Null Hypothesis

Non-Mediating Model 43.754

30

Mediating Model 76.456 47

The chi-square Difference

Test

32.702 17 0.01229 Reject

The chi-square difference test reveals a significant mediation, thus it can be concluded that the

null hypothesis (MedH2) is rejected, and hence the alternative hypothesis of is accepted.

Sobel’s Test, Aroian’s Test and Goodman’s Test

Thus to confirm the above mediating hypothesis we conducted the Sobel’s (1982) test, the

Aroian’s (1944) test, and the Goodman’s (1960) test. These tests were conducted in line with the

z-prime method (MacKinnon, Lockwood, Hoffman, West and Sheetes, 2002) to check for the

statistical power of our models and discount the possibility of Type I error while exploring the

strength of mediation.

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Table 7.10

Sobel’s Test, Aroian’s Test and Goodman’s Test for Mediating Hypothesis for Mediating

Hypothesis MedH2

Thus, Teachers Job Contribution (Mediator) significantly mediates the relationship between

Teachers Perceived Organizational Support (Independent Variable) and Teacher’s Engagement

(Dependent Variable).

Table 7.11 : Summary of Mediating Hypotheses Results

Mediating

Hypotheses

Independent

Variable

Mediating

Variable

Dependent

Variable

Result of

Hypothesis

Explanation

MedH1 Teachers

Organizational

Commitment

Teachers Job

Contribution

Teacher’s

Engagement

MedH1

Accepted

Teachers Job Contribution

significantly mediates the

relationship between Teachers

Organizational Commitment and

Teacher’s Engagement.

MedH2 Teachers

Perceived

Organizational

Support

Teachers Job

Contribution

Teacher’s

Engagement

MedH2

Accepted

Teachers Job Contribution

significantly mediates the

relationship between Teachers

Perceived Organizational Support

and Teacher’s Engagement.

Sobel’s

Test

Aroian’s

Test

Goodman’s

Test P Remarks

Teachers Perceived Organizational Support →

Teachers Job Contribution →

Teacher’s Engagement

4.594 4.568 4.621 *** MedH2

accepted