Data Analysis

Data analysis in this study was separated into two stages. The first stage involved testing the reliability (inter-item consistency reliability) and validity of the measurement (convergent validity). Here, descriptive statistics such as: minimum; maximum; frequency; percent; mean; standard deviation; skewness; and kurtosis were also employed via SPSS. The descriptive analysis was also

employed for the demographic data. This analysis is presented in Chapter 6. The second stage involved testing the hypothesis proposed in the study by using the structural equation modelling (SEM) method using AMOS. This hypothesis testing is presented in Chapters 7 and 8. The justification of using the SEM approach is presented in Sub-section 5.11.1 below.

5.11.1 Structural Equation Modelling (SEM)

The main objective of this research is to investigate the effect of fairness perception of measures, and the process of development of the measures on managerial performance in a BSC environment. The argument underlying the objective was presented in the framework model that was developed in the study. In order to test the model, SEM is considered appropriate. It is expected that the model is both substantively meaningful and statistically well-fitting with the data (Jöreskog, 1993).

Structural equation modelling is a multi-variate technique that combines multi- variate regression and factor analysis to explain the relationship among multiple variables (Hair et al., 2006). Structural equation modelling is also known as path analysis with latent variables and has been used to represent dependency (arguable “causal”) relations in multi-variate data analysis in behavioural and social science (McDonald and Ho, 2002). It takes a confirmatory (i.e., hypothesis testing) approach to analysis of a structural theory underlying some phenomenon (Byrne, 2001). In addition, it conveys two important aspects of the procedures which are: 1) that the causal processes under study are represented by a series of structural equations; and 2) that these structural relations can be modelled pictorially to enable a clearer conceptualisation of the theory under study (Byrne, 2001).

Compared with other multi-variate analyses, SEM extends analysis in at least two important ways. First, SEM allows researchers to model the relationship among variables after accounting for the measurement error. Second, SEM provides tests for goodness-of-fit which is a very important aspect to test whether the sample data supports the hypothesis tested in the model (Cunningham, 2008).

Therefore, by using SEM, the hypothesised model can be tested statistically in a simultaneous analysis of the entire system of variables to determine the extent to which it is consistent with the data. If the goodness-of-fit is adequate, it means that the relationships among variables in the hypothesised model are supported by the data. In contrast, if the goodness-of-fit is inadequate, the tenability of such relations is rejected (Byrne, 2001).

5.11.2 Bootstrapping Procedures and Bollen-Stine Bootstrap Method

One of the critically important assumptions associated with SEM is the requirement that the data have a multi-variate normal distribution. As discussed in sub-section 6.9.4, it was found that the data in the present study do not have a multi-variate normal distribution, since the Mardia’s multi-variate coefficient is relatively high. This means that the assumption of multi-variate normal distribution is violated. One approach to handling the presence of multi-variate non-normal data is to use a bootstrap procedure (West et al., 1995; Yung and Bentler, 1996; Zhu, 1997). Bootstrapping serves as a re-sampling procedure by which the original sample is considered to represent the population. From here, multiple sub-samples of the same size as the parent sample are drawn randomly, with replacement from this population, to provide the data for empirical investigation of the variability of parameter estimates and indices of fit (Byrne, 2001).

In the present study, the Bollen-Stine bootstrap method was used to test the hypothesised model under non-normal data, since this approach tests the adequacy of the hypothesised model based on a transformation of the sample data, such that the model is made to fit the data perfectly (Byrne, 2001). The bootstrapping procedure calculates a new critical chi-square value (adjusted chi- square) that represents a modified chi-square (χ2) goodness-of-fit statistic. A new critical chi-square value is generated against which the original chi-square value is compared. Then the adjusted p-value is computed. If the Bollen-Stine p-value

samples is typically in the range of 250 to 2000 (Bollen and Stine, 1992). Therefore, it is necessary to use the Bollen-Stine bootstrap in the current research due to the situation of non-normality.

5.11.3 Sample Size Requirements

In general, SEM requires larger samples relative to other multi-variate analysis. However, there are no statistical theories that provide a guideline as to just how large a “large” sample needs to be. In the issue of sample size requirements for SEM, Hair et al. (2006) found that sample sizes as small as 50 provide valid results, but they recommended a minimum sample size of 100-150 to ensure stable Maximum Likelihood Estimation (MLE) solutions. They suggest a sample size in the range of 150-400. In the present research, the sample size of 164 was considered sufficient to run SEM.