Inferential statistics

Inferential statistics were performed to enable the researcher to make inferences about the data. These included structural equation modelling (SEM), standard multiple regression analyses and tests for significant mean differences between gender, race and age groups.

Inferential statistics describe and illustrate the inferences that a researcher may draw about a population according to the specified indices, based on the equivalent indices acquired

from random samples of the population (Salkind, 2012). Inferential statistics test for differences between variables and are used to make predictions, based on the data collected in the study. Inferential statistics are also used to generalise findings from a sample to a population (Salkind, 2012). Statistical significance is also an important concept in inferential statistics. Statistical significance focuses on the possibility of rejecting a null hypothesis that is, in effect, true (Type I error), or accepting a null hypothesis when it is actually false (Type 2 error). The possibility of a Type II error decreases as the sample size increases (Salkind, 2012).

4.7.4.1 Structural Equation Modelling

SEM is a multivariate procedure which combines multiple regression and factor analysis and is used to examine the research hypotheses of causality within a system. SEM is divided into two different parts, including a measurement model and a structural model. The measurement model deals with the relationships between the measured and latent variables whereas the structural model deals with the relationships between the latent variables only (Garson, 2008; Hoyle, 1995; Hair, Black, Babin & Anderson, 2010). The ability of the SEM procedure to distinguish between direct and indirect relationships between variables and to analyse relationships between latent variables without random error differentiates SEM from other simpler, rational modelling processes such as multiple regression (Garson, 2008;

Hoyle, 1995). The SEM process focuses on the validation of the measurement model by obtaining estimates of the parameters of the model and by assessing whether the model itself provides a good fit to the data (Garson, 2008). The adequacy of the model is evaluated by means of goodness-of-fit measures which determine whether the model being tested should be accepted or rejected (Garson, 2008).

SEM with the maximum-likehood (ML) estimation method was used to investigate the structural model fit between self-directedness and employability attributes. The goodness-of-fit statistics w e r e evaluated by using the following absolute goodness-of-goodness-of-fit indices: the chi-square test, the root mean square error of approximation (RMSEA), and the standardised root mean square residual (SRMR). The following relative goodness-of-fit indices were also used to evaluate the model fit: the comparative fit index (CFI) and the Tucker-Lewis index (TLI). In line with guidelines provided by Garson (2008), it was assumed that an adequate fit of the structural model to the measurement data existed when CFI and TLI values of .90 or higher, a RMSEA of .08 or lower, and a SRMR of .05 or lower were obtained.

4.7.4.2 Standard multiple regression

Multiple regression analyses were used to forecast or predict performance of a dependent variable from various independent variables (Nisber et al., 2009). In statistics, regression analysis includes any techniques for modelling and analysing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps the researcher to understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable, given the independent variables (Field, 2009), that is, the average value of the dependent variable (e.g. employability attributes) when the independent variables (e.g. adult learner self-directedness) are held fixed. The levels of statistical significance of multiple regressions used in this study were F(p) ≤ .001; F(p) ≤ .01; and F(p) ≤ .05 as the cut-off for rejecting the null hypotheses.

In terms of practical significance, adjusted R² ≤ .12 (small practical effect size);

R² ≥ .13 ≤ .25 (moderate practical effect size) and R² ≥ 26 (large practical effect size) were considered for interpreting the magnitude of the practical significance of the results (Cohen, 1992). Since a number of independent (SEAS) variables had to be considered, the value of adjusted R² was used to interpret the results.

However, a high degree of correlation between independent variables raises multi-collinearity concerns and this may, in turn, lead to difficulties in interpreting the beta coefficients as meaningful (Nisber et al., 2009). Prior to conducting the various regression analyses, collinearity diagnostics were examined to ensure that zero-order correlations were below the level of concern ( r ≥ .80), that the variance inflation factors did not exceed 10, that the condition index was well below 15, and that the tolerance values were close to 1.0 (Field, 2009)

4.7.4.3 Tests of significant differences between mean scores

Based on the test for normality showing that the data from the sample in this study were not normally distributed, nonparametric tests were used to test for significant mean differences between the gender (Mann-Whitney U) and race and age (Kruskall-Wallis test) groups regarding their self-directedness and employability attributes.

Nonparametric analyses are usually conducted on data for which the assumption of normality could not be verified (Nisber et al., 2009). In view of the fact that it is not possible

to use the raw data in these analyses, ordered values are used (Nisber et al., 2009). The Mann-Whitney U test is used for the comparison of two independent groups (e.g. gender), while the Kruskal-Wallis test is used for the comparison of two or more independent groups (e.g. race and age). The Mann-Whitney analysis may be used instead of a two-sample t-test while the Kruskal-Wallis test may replace the one-way analysis of variance (Nisber et al., 2009). The Mann-Whitney U test focuses specifically on determining whether observed data in one population is ranked higher than observed data in another population (Nisber et al., 2009). Although the Mann-Whitney U and Kruskal-Wallis tests are indicated where sample sizes are small (< 100), these tests were used in this study because it was not possible to verify the assumption of normality.

4.8 SUMMARY

Chapter 4 discussed the population and composition of the sample used in this study.

Following this, the two measuring instruments, the data collection process, the administration of the measuring instruments and the data analysis process were described.

The formulation of the hypotheses related to the investigation concluded the chapter.

Chapter 5 will explore the data analysis as well as the interpretation and integration of the empirical findings.

CHAPTER 5