The Factor Analysis undertaken involved an established approach consisting of Principal Axis Factoring (PAF), with the established Kaiser criterion (involving the extraction of factors whose eigenvalues exceed one, thus each factor identified offers a greater explanatory value of the data variance than an individual original variable) put in place to establish the number of factors, with Oblique rotation (based on the Direct Oblimin
process) used to develop a group of factors that are statistically correlated (Bryman and Cramer, 1994; Field, 2000).
This study has met the required sample size of 197 in terms of being sufficiently adequate for a Factor Analysis to be undertaken (Tabachnick and Fidell, 2007; Hair et al., 2010). This study applied the minimum required level of loading greater than 0.40, based on the suggestion of Hair et al (2010) for retention of the factors’ subsequent contribution to interpretation. The factor loadings can be identified for each variables (i.e.
item) loaded onto a factor. The output of the factor loadings can identify one or more variables loading on several factors in which all are significant. These are termed as cross-loadings and can complicate the interpretation of a factor. The objective is to have each variable only loaded to one factor. To eliminate cross-loadings a different rotation method can offer a solution to eliminate cross-loadings and define a simpler factor structure. However, if cross-loadings still remain after alternative rotation methods are applied, then the offending variable should be deleted (Hair et al., 2010).
When the significant loadings have been identified, it is necessary to examine any variables that are not adequately accounted for in the overall factor solution. The researcher can examine the communality of each variable as part of the assessment.
The communalities represent the amount of variance accounted for by the factor solution for each variable (Hair et al., 2010). The individual variables are required to meet acceptable levels of explanation. Variables with low communalities can be deleted since they are not giving sufficient explanation to the factor being extracted. However, the researcher may consider deletion or retainment of an individual variable primarily based on the definition that has been given to the factor under consideration.
Once the Factor Analysis is examined and accepted with the requirements of KMO, Bartlett, significance of loadings, identification of cross-loadings and assessment of communalities, the factors can be labelled and defined (Tabachnick and Fidell, 2007;
Hair et al., 2010). To analyse how consistent a variable or set of variables is to the intended measurements with the intended measurements, reliability measurement is performed as a post-hoc assessment. In the context of this study, reliability analysis measurement with Cronbach’s alpha is used. The reliability analysis is performed to decide which items should be eliminated in order to improve the overall internal consistency of the factor and the corresponding Alpha value. Cronbach’s alpha requires a 0.7 or higher as an indicator of internal reliability (Tabachnick and Fidell, 2007; Hair et al., 2010). “Alpha if item deleted” is used as a guideline whether to delete or to retain individual statements or items with the application of SPSS. Although improvements can
be made with deletions, these can be ignored if the extracted factor meets an acceptable level of internal reliability and it is used to assess the factorability of the data.
4.4.1 Assessment of the EFA
Some degree of correlation among the variables is desirable because the objective is to identify interrelated sets of variables. To assume factorability, the KMO should exceed the acceptable level of 0.5 with statistically significant correlation (Bartlett’s test significance of value < 0.05). In addition, a factor with less than three items is indicated as weak (Tabachnick and Fidell, 2007).
4.4.2 Results of the EFA
The scale items are detailed in Appendix D.1 of the thesis. The Factor Analysis considered the items measured in sections A to E of the survey and the acculturation variables (sections B to D). It therefore considered Acculturation life domains, Ethnic Identity, Ethnic Friendship, and Media Use (Appendix D.2). A second, separate factor analysis contained the culture variables i.e. Value Priorities (E), and a third analysis assessed various consumer behaviour variables, i.e. food and entertainment (A) (Appendix D.3).
4.4.3 Factorability of the Data
The preliminary analysis shows that the Bartlett test of Sphericity is significant (p = 0.000) and the Kaiser-Meyer-Olkin measure of sampling adequacy is good and greater than the acceptable level of 0.50 (Kaiser, 1974) for the acculturation data. The proportion of each variable’s variance, which can be explained by the retained factor, i.e.
communalities, are all above the accepted level of 0.50. Hence, factorability is assumed.
The acculturation variables (Analysis A) loaded onto eight factors. These eight factors explain a total of 74.80% of the variance. However, one item, “How often do you speak the Dutch language with your parents and family?” did not meet the minimum level requirement of factor loadings of being at least 0.40. The extraction in Table 9 identified a low extraction value (0.234) for this item. This item was eliminated from further analysis and accordingly adapted in the final questionnaire for Stage Two.
The Value Priorities (Analysis B) loaded onto two factors. The Bartlett test of Sphericity is significant (p = 0.000) and the Kaiser-Meyer-Olkin measure of sampling adequacy is good and greater than the acceptable level of 0.50 (Kaiser, 1974), therefore factorability is assumed. The two factors explain a total of 54.94% of the variance. All items are retained for further analysis.
The preliminary analysis of the consumer behaviour items (food and entertainment) showed that the Bartlett test of Sphericity was significant (p = 0.000) and the Kaiser-Meyer-Olkin measure of sampling adequacy (0.763) is greater than the acceptable level of 0.50 (Kaiser, 1974). Hence, factorability can be assumed. The consumer behaviour items (Analysis C) loaded onto two factors with four items on factor I and four items on factor II. The two factors explain a total of 64.13% of the variance. The rotated solution of the three separate analyses and the overall statistics for each factor are shown below in in section 4.5.
Table 9. Factor analysis
Factors KMO Significance % Variance Independent Variables
Acculturation 8 0.926 0.000 74.799
Independent Variables
Value Priorities 2 0.918 0.000 54.941
Dependent Variables
Food and Entertainment 2 0.763 0.000 64.129