3 Multiplicidad: el problema de la naturaleza

This chapter examined the structure and context of three attitude dimensions of the New Zealand Superannuation Scheme (criterial referent domain). The context of the dimensions reinforced the nature of social attitudes and the tenets of social justice (equality, need and capacity). I attempted to link the results from each Factor Analysis for the structure of social attitudes to the theory of social justice and social attitudes. I did this by stating the relevant central tenet of social justice along with stating the attitude construct for each factor that emerged from the Factor Analysis. The attitude dimensions included the nature of the New Zealand Superannuation Scheme, the equity of dependents and the environment of reciprocity in the Scheme. These dimensions contribute in part to how attitudes towards the New Zealand Superannuation Scheme are structured. However, the structure provides little information as to why these attitudes are structured in a particular way and the direction of support or lack of support for the Superannuation Scheme.

Chapter Seven

The Correlates of Social Attitudes towards Superannuation

This chapter examines the nature of social attitudes towards support for the New Zealand Superannuation Scheme. It looks at the association between some demographic characteristics (attributes) and the three aspects of social attitudes and their underlying factors that emerged from the Factor Analyses. These criterial ‘referents’ are the nature of the New Zealand Superannuation Scheme, the equity of dependents and the environment of reciprocity for the Superannuation Scheme. Each factor (outcome variable Yij) underlying these criterial ‘referents’ is assessed using a two-way Analysis of Variance and a Ordinary Least Squares Regression model after assessing for correlations and the statistical assumptions.80 These factors are the dependent variables that contain a factor scale by means of which a set of dummy variables of two demographic characteristics are related to the factor scores. Generation and household income are used for the analysis. Each factor for an attitude dimension along with its relationship to attitude responses are examined with respect to demographic characteristics.

7.1 Statistical Background

A two-way Analysis of Variance (Univariate Analysis: parametric analysis) is a method for examining if there are differences in the attitude responses of each factor for different generations and household incomes.81 This analysis tests whether the means are different for the independent variables (generations and household income). The Levene Test checks for homogeneity across the independent variables for the factor. A significant result implies that the factor’s variance across the independent variables is not equal. This means that the independent variables have different distributions around the factor and

80

The statistical analyses from the Multiple Regression and the Pearson Correlations are not included in the appendix of this thesis. However, some of the results contributed to the interpretation of and the confirmation of statistical assumptions for the Ordinary Least Squares Regression.

81

To test all independent variables, a Multivariate Analysis of Variance can be performed. If the Mahalanobis Distance suggests outliers and normality is violated, then either there are outliers or issues of homogeneity.

are different from each other. Consequently, the two-way Analysis of Variance has errors in its output. Therefore, the Analysis of Variance was not assessed.82

A Games Howell GH test is used when there are unequal variances and unequal sample sizes of generations and household incomes. This test attempts to reduce the potential for making a Type One Error when interpreting whether or not the means for the independent variables are different. A Type One Error is where the researcher states that there is a generation or household income difference in the population when none exists. The Games Howell GH is the most powerful procedure and the most effective in controlling the potential for a Type One Error by using a liberal α value83 when a two-way Analysis of Variance has been performed. The results of this procedure may be confusing but it does provide information about where the significant differences lie between generations or household incomes. This difference can also be assessed by the numerical results of the independent variables (frequency tables).

Essentially, the tests are to find out if different generations have unequal variances and means for the questions of an underlying factor. This enables the researcher to comment that the attitude responses of one generation or household income may be different to another. Meanwhile, an insignificant result of the Levene Test implies that the variance of the factor is equal across the independent variables. Further statistical analysis can provide information about the differences for the means of different independent variables and to find out where the impacts of the attitude responses for different independent variables on the factor lies.

An Ordinary Least Squares Regression Analysis is a method for finding a minimum line of best fit (regression line) for the factor (outcome variable) on the basis of reducing the differences between variables. This means that the least amount of variance between the attitude responses with respect to age (X1i) and household income (X2j), and the factor

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A Bivariate Analysis can help to identify if both or one variable is causing the issue for violating normality. I found issues of homogeneity that was primarily associated with age. These statistical results are not included in the appendix.

score for the factor (Yij) from the attitude dimension is found. In other words, the Regression Analysis searches for linear relationships between the dependent variable (factor or latent variable) and the independent variables.84 The direction (positive or negative) and magnitude (predictor value) of these effects are revealed in the standardised Beta scores (βn).

A positive value indicates a positive effect between the predictor (independent variable) and the factor (outcome variable). In other words, the magnitude of the effect occurs when there is one unit change in the independent variable on the dependent variable. A value of zero reveals that there is no predictor value, while a value of 0.5 or greater indicates a strong unique contribution to the dependent variable (factor), when other independent variables are controlled for. A high negative value indicates a strong contribution by the predictor (independent variable) and the factor (outcome variable). This negative effect may occur where there is a low score (generation of 18 to 21) on one scale and a high score for the factor score on another scale or, conversely, a high score (generation of 62 plus) occurs when there is a low score for the factor score. Therefore, question scales are important when interpreting results of the factor.

The correlates of the independent variables do not imply that a variable predicts another. However, there are a number of cases where variables predict another and the correlates between them are high. In essence, the correlates are a measure of how variables effect each other and how these variables change relative to the factor score. The factor scores for each factor are placed into the Regression Analysis as a dependent variable. Meanwhile, two demographic characteristics, generations and household incomes, were used to represent the independent variables. These independent variables are transformed into dummy variables.

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The equation for the regression model is Yij = β0 + β1i X1i + β2j X2j + εij where i = 1..6 and j = 1..6. The

The dummy variables are binary for each assessed demographic characteristic.85 These characteristics are age and household income. The results of the model produce standardised Beta scores that are based upon effects between the independent variable and the dependent variable. For each standardised Beta score, all independent variables, including their dummy categories, are controlled apart from the one in which the Beta score is being calculated for its impact upon the dependent variable (factor or outcome variable).86 These Betas are the contributions (regression coefficient) to the prediction of the dependent variable (factor) that indicate the direction (positive or negative) and the magnitude (numeric value) of the effect from demographic characteristics to the factor score for the factor. In other words, regression coefficients (βn) provide information about how each dummy variable for any demographic characteristic impacts upon the factor score. This impact is a unit change in the independent variable.