Types of non-parametric statistical techniques being applicable to this study

The two non-parametrical statistical techniques that were applicable for this study are the Kruskal-Wallis and the Mann-Whitney U tests, as the nature of the secondary data is ordinal and it could be ranked. The Kruskal-Wallis tests were performed to determine whether there are statistically significant differences over the three retirement phases, but in the cases where statistically significant differences were identified, it did not identify the applicable phase to which the statistical difference relates, in which cases the Mann-Whitney U test had to be performed. Details relating to both the Kruskal- Wallis test and the Mann-Whitney U test will be discussed below and the results will be discussed in Chapter 4 (section 4.3).

Kruskal-Wallis test

This test is also referred to as the Kruskal-Wallis H Test or a "one-way ANOVA on ranks", which is categorised as a rank based non-parametric test. This test could be used as an alternative to a one-way between groups’ analysis of variance (ANOVA) and as an extension of the Mann-Whitney U test (Pallant, 2013). This would allow for comparisons between the three retirement phases. This test is very similar in nature to the Mann-Whitney U test, with the only exception that the Mann-Whitney U test allows for comparisons between two groups only. The Kruskal-Wallis test converts scores into

analyses between the three retirement phases. Two variables, one categorical independent variable with three or more categories, being the three phases of retirement in this study, and one continuous dependent variable, being each of the selected questions as per Table 3.4, were needed to perform this test (Laerd Statistics, 2015a, 2015b; Pallant, 2013).

The most important information needed from the output to interpret the Kruskal-Wallis test is the Chi-Square value, the degrees of freedom (df), and the significance level (presented as Asymp. Sig). Significance levels less than 0.05 indicated that there was a statistically significant difference at a five percent level in the selected questions (continuous variable) as per Table 3.4 across the three retirement phases. In terms of the Kruskal-Wallis test, this also means that the null hypothesis of no significant differences has been rejected.

In the case where the result of the Kruskal-Wallis test indicates statistical significance, the precise statistically significant difference amongst the three retirement phases is still unknown. This would require the performance of the Mann-Whitney U test in order to identify the retirement phase to which the statistically significant difference applies. The post-hoc tests for the Kruskal-Wallis test available in SPSS were performed in this study prior to performing the Mann-Whitney U tests in an attempt to identify the existence of statistical differences across the three retirement phases.

Mann-Whitney U test

On a continuous measure, the Mann-Whitney U test is used to test for differences between two independent groups, which are two of the retirement phases that are used interchangeably. This test is also used as a non-parametric alternative to the t-test for independent samples. In the case of the t-test, the means of two retirement phases would have been compared, whereas with the Mann-Whitney U test median ranks are compared. Across the two retirement phases the scores on the selected questions as per Table 3.4 are converted into ranks. The ranks for the two retirement phases are then evaluated for significant statistical differences. The actual distribution of scores does not matter, with the scores being converted into ranks. Two variables, one

categorical variable (age group with two of the retirement phases) and the selected question as per Table 3.4 (one continuous variable), are needed to perform this test. The general assumptions related to non-parametric techniques (as mentioned above) would also be applicable to the Mann-Whitney U test (Pallant, 2013).

In order to reveal the retirement phase that relates to the statistically significant difference as identified by the Kruskal-Wallis test and as highlighted by the Kruskal- Wallis post-hoc test, the Mann-Whitney U test was performed interchangeably between the pre-retirement, close-to-retirement and post-retirement phases (pre-retirement with close-to-retirement, pre-retirement with post-retirement and close-to-retirement with post-retirement), as it provided additional assurance of possible statistically significant differences within the three retirement phases.

The most important information needed from the output to interpret from the Mann- Whitney U test is the Z value and the significance level, which is presented as Asymp. Sig (2-tailed). The significance is then interpreted in a similar manner to that of the significance levels in the Kruskal-Wallis test.

Effect size

Both the Kruskal-Wallis post-hoc tests and the Mann-Whitney U tests may reveal the existence of the statistically significant differences within the three retirement phases, but they do not indicate the extent of these differences. In such cases the effect size of each of the alternate phases, in the instances where the null-hypotheses were rejected, need to be calculated. Effect size estimates for the Mann-Whitney U test are used to measure the size of the statistically significant differences. In SPSS when running the Mann-Whitney U tests, the report also includes both the U-value and the standardised

Z-score, which could be used to calculate the correlation coefficient, r. The effect sizes

for each of the Mann-Whitney U tests were therefore calculated by hand according to the following formula (Tomczak & Momczak, 2014):

where r = correlation coefficient where r assumes the value ranging from -1.00 to 1.00 Z = standardised value for the U-value

n = the total number of observations on which Z is based

As the correlation coefficient includes the whole range of relationship strengths, these relationships range anything from no relationship, being zero, to what they refer to as a perfect relationship, being either 1 or -1. The effect size therefore indicates the extent of the relationship that exists between the different variables, being the three retirement phases in this study, and is therefore independent from the number of individuals that were tested. Cohen provided certain guidelines when interpreting these effect sizes, and he suggested that an r of 0.1 represents a small effect size, 0.3 represents a medium effect size and 0.5 represents a large effect size (Coolican, 2009).

3.4. ETHICAL CONSIDERATIONS

The South African FSB and their service providers adhered to the necessary ethical standards and code of conduct during the initial data collection (Roberts et al., 2012). Although the data is in the public domain, specific permission was obtained from the South African FSB to utilise the data for purposes of this study. The Research Ethics Review Committee of the College of Accounting Sciences granted ethical clearance for this study and the analysis that would be done by utilising the secondary data from the South African FSB’s survey. Password protected computers were used by the University to protect the data obtained from the South African FSB. The University did not receive the personal information of the respondents who formed part of the South African FSB’s survey and therefore protecting the privacy of the related respondents is not an issue. Other parties would not be sharing the data.

3.5. CONCLUSION

Comparative research was found to be the best research approach for this study with the aim of identifying and comparing possible differences that exist over the three retirement phases within the three core areas of the practical retirement planning process. As the results for each of the selected questions had to be interpreted over the

three retirement phases, it was found that the interpretive research paradigm would be appropriate for this study.

In order to address the research problem, the research process followed a step-by-step approach as discussed in section 3.3. This section addressed the heuristic model that was constructed for this study through a thorough literature review as discussed in Chapter 2; the assessment of the applicability of the South African FSB’s questionnaire as well as the process that was followed to prepare the data for the purposes of this study; the questions that were selected for the purposes of this study; and the methods involved in the data analysis that was performed. The data was analysed by using descriptive and inferential statistics. Because the data was ordinal and could be ranked, non-parametric statistical techniques, in the form of the Kruskal-Wallis test and the Mann-Whitney U test, were used to analyse the questions relating to the three core areas of the practical retirement planning process as addressed in Table 3.4 in order to identify in which retirement phases there are statistically significant differences in relation to the related question. The Kruskal-Wallis test was used to assess whether there are any statistically significant differences between the three retirement phases; however, because it did not identify which phase/s is significantly different from the other, the Mann-Whitney U test was used to test for differences between two of the retirement phases to determine which phase is statistically significantly different from the other. Although both the Kruskal-Wallis post-hoc tests and the Mann-Whitney U tests may have revealed the existence of the statistically significant differences within the three retirement phases, they did not indicate the extent of these differences. In these cases, the effect size of each of the alternate phases, which measures the size of the statistically significant differences, in the instances where the null-hypotheses were rejected, needed to be calculated. The results for both the Kruskal-Wallis and Mann- Whitney U tests as well as the results of the effect size calculations will be provided and discussed in Chapter 4 (sections 4.3).

CHAPTER 4