Chapter 7 : Mediation Analysis and Hypotheses Testing

Transcription

1 Chapter 7 : Mediation Analysis and Hypotheses ing 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 (χ 2 ) 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). 144

2 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 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 Anderson and Gerbing s (1988) Chi-square Difference Further Chi-square Difference was conducted. Chi-square Difference 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) Sobel s (1982), the Aroian s (1944), and the Goodman s (1960) 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 145

3 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 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 (S ab ) is S ab b 2 S 2 a a 2 S 2 b S 2 a S 2 b Where, a = unstandardized regression coefficient of path a; b = unstandardized regression coefficient of path b; S a = standard error of a; S b = standard error of b. Aroian s Formulae for the tests provided here were drawn from MacKinnon & Dwyer (1994) and from MacKinnon, Warsi, & Dwyer (1995): z value a * b b * Sa a * Sb Sa * Sb 146

4 Goodman s z value a * b b * Sa a * Sb Sa * Sb 7.5. Mediating Hypotheses ing 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) 147

5 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) Teachers Organizational Commitment Teachers Job Contribution Standardized Regression Estimate S.E. C.R. P *** Teachers Job Contribution regresses significantly on Teachers Organizational Commitment hence the first condition of Baron and Kenny s Mediating Analysis is satisfied. 148

6 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) Teachers Organizational Commitment Teacher s Engagement Standardized Regression Estimate S.E. C.R. P *** 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 : 149

7 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 As the p > (p = 0.098), there exists full mediation by the mediating variable, hence the independent variable exerts its total influence through the mediating variable. 150

8 Chi-square Difference : Anderson and Gerbing s (1988) approach Chi-square Difference 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 for Mediating Hypothesis MedH1 Model Chi-square Df p-value Reject / Not Reject the Null Hypothesis Non-Mediating Model Mediating Model The chi-square Difference 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, Aroian s and Goodman s 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. 151

9 Table 7.5 Sobel s, Aroian s and Goodman s for Mediating Hypothesis for Mediating Hypothesis MedH1 Sobel s Aroian s Goodman s P Remarks Teachers Organizational Commitment Teachers Job Contribution Teacher s Engagement *** MedH1 accepted 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) 152

10 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 *** Teachers Job Contribution regresses significantly on Teachers Perceived Organizational Support hence the first condition of Baron and Kenny s Mediating Analysis is satisfied. 153

11 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) Teachers Perceived Organizational Support Teacher s Engagement Standardized Regression Estimate S.E. C.R. P *** Teacher s Engagement regresses significantly on Teachers Perceived Organizational Support hence the second condition of Baron and Kenny s Mediating Analysis is satisfied. 154

12 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 *** As the p < (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 155

13 variable, and it also exerts some of its influence directly on the dependent variable and not through mediating variable. Chi-square Difference : Anderson and Gerbing s (1988) Approach Chi-square Difference 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 for Mediating Hypothesis MedH2 Model Chi-square Df p-value Reject / Not Reject the Null Hypothesis Non-Mediating Model Mediating Model The chi-square Difference 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, Aroian s and Goodman s 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. 156

14 Table 7.10 Sobel s, Aroian s and Goodman s for Mediating Hypothesis for Mediating Hypothesis MedH2 Sobel s Aroian s Goodman s P Remarks Teachers Perceived Organizational Support Teachers Job Contribution Teacher s Engagement *** MedH2 accepted 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 Independent Mediating Dependent Result of Explanation Hypotheses Variable Variable Variable Hypothesis MedH1 Teachers Teachers Job Teacher s MedH1 Teachers Job Contribution Organizational Contribution Engagement Accepted significantly mediates the Commitment relationship between Teachers Organizational Commitment and Teacher s Engagement. MedH2 Teachers Teachers Job Teacher s MedH2 Teachers Job Contribution Perceived Contribution Engagement Accepted significantly mediates the Organizational relationship between Teachers Support Perceived Organizational Support and Teacher s Engagement. 157