5.6 DATA ANALYSIS
5.6.2 INFERENTIAL STATISTICS
Inferential statistics consist of statistical approaches that are used to test hypotheses that relate to relationships between variables. Inferential statistics strive to reach conclusions that extend beyond the immediate data alone and is utilised to make inferences to more general conditions (Cooper & Schindler, 2008).
127
Pearson’s Chi-square Correlation
The Pearson correlation matrix indicates the direction, intensity and significance of the bivariate relationships of all the variables in the study and is appropriate for interval and ratio-scaled variables (Sekaran & Bougie, 2010). Pearson’s correlation coefficient (r) is used to reveal whether two variables are related or correlated to one another and the chi-square test statistic allows researchers to assess whether or not a relationship exists between two categorical variables, and further determine whether the relationship between the two variables is systematic or due to chance. Correlation always fluctuates between -1 and +1 and if the correlation is greater than zero, then the variables are termed positively or directly related, meaning that as the one variable increases, so too does the other and vice versa. A correlation coefficient of less than zero means that there is a negative correlation or relationship between two variables where the one variable increases as the other variable decreases and vice versa.
Pearson's chi-squared test is ordinarily employed to evaluate two types of comparison, namely, tests of goodness of fit and tests of independence. A test of goodness of fit is relied upon to establish whether or not an observed frequency distribution diverges from a theoretical distribution. As the name suggests, the test of independence assesses whether paired observations on two variables are independent of each other. It is imperative when determining correlation coefficients to be aware of whether the correlation is in fact significant or not at the 1% and 5% levels of significance.
For this study, chi-square correlation analysis will be undertaken in order to determine the relationships and intercorrelations amongst the key dimensions (branding, savings potential/ability to pay off debt, price/affordability, quality, appearance/acceptability, adaptability of existing products, functionality/performance, packaging/quantity, advertising/awareness, accessibility/availability and partnering with MNCs) of the study.
Further to this, correlation analysis will be used to determine any relationships between the BOP consumers’ ability to pay off debt and the biographical variables of the respondents.
Spearman’s Rank-order correlation
Spearman's rank correlation coefficient (Spearman's rho), which is named after Charles Spearman, is a nonparametric measure of statistical dependence between two variables.
128
Spearman’s rank correlation coefficient is used to identify and examine the strength of a relationship between two sets of data and is often used as a statistical method to assist with either proving or disproving a hypothesis. According to Blumberg, Cooper and Schindler (2008), the Spearman’s rho correlation is a popular ordinal measure that correlates ranks between two ordered variables.
In terms of this study, Spearman’s rank-order correlation will be used to examine the relationship between the categories of consumer spending and each of the biographical variables (age, highest educational qualification, monthly income and number of people living in a household, gender and race), respectively. Additionally, Spearman’s rank-order correlation will be used to examine the relationship between the evaluative criterion (price/affordability, quality, appearance/acceptability, packaging/quantity, accessibility/
availability, brand preference, adaptability of existing products, functionality/performance and advertising/ awareness) that is relied upon to make purchase decisions and each of the biographical variables (age, highest educational qualification, monthly income and number of people living in a household, gender and race), respectively.
Kruskal-Wallis t-Test
There are certain instances when a researcher would be keen on knowing if two groups are different from each other on a particular interval-scaled or ratio-scaled variable of interest. A t-test is conducted in order to ascertain if there are any significant differences in the means for two groups in the variable of interest. A nominal variable that is split into two subgroups is then tested to determine whether or not there is a significant difference in the means between the two split groups on a dependent variable which is measured on an interval or ratio scale (Sekaran & Bougie, 2010).
In this study, the Kruskal-Wallis t-test will be used to determine whether or not the means of the two split groups (male and female) are significantly different from one another with regard to the key dimensions (branding, savings potential/ability to pay off debt, price/affordability, quality, appearance/acceptability, adaptability of existing products, functionality/performance, packaging/quantity, advertising/awareness, accessibility/
availability and partnering with MNCs) of the study and the evaluative criterion (price/affordability, quality, appearance/acceptability, packaging/quantity, accessibility/
129
availability, brand preference, adaptability of existing products, functionality/performance and advertising/awareness) that influences BOP consumers’ purchase decisions, respectively.
Kruskal-Wallis One-way ANOVA
The one-way analysis of variance (ANOVA) is used to ascertain whether there are any significant disparities between the means of two or more independent (unrelated) groups.
The one-way ANOVA is used in instances where there is just one categorical independent or predictor variable. According to Cooper and Schindler (2008), it is a parametric test that uses a single-factor, fixed-effects model to evaluate the effects of one factor on a continuous dependent variable. Researchers need to take cognisance of the fact that the one-way ANOVA is regarded as an omnibus test statistic which shows that there are at least two groups that are different but does not divulge which specific groups were significantly different from each other.
The result of ANOVA for this study will determine whether or not the means of the BOP consumers (varying in age, highest educational qualification, monthly income and number of people living in a household) are significantly different from one another with respect to the key dimensions (branding, savings potential/ability to pay off debt, price/affordability, quality, appearance/acceptability, adaptability of existing products, functionality/
performance, packaging/quantity, advertising/awareness, accessibility/ availability and partnering with MNCs) of the study, respectively. The result of ANOVA will also show whether or not the means of the BOP consumers (varying in age, highest educational qualification, monthly income and number of people living in a household) are significantly different from one another with respect to the evaluative criterion (price/affordability, quality, appearance/acceptability, packaging/quantity, accessibility/ availability, brand preference, adaptability of existing products, functionality/performance and advertising/awareness) that influences BOP consumers’ purchase decisions, respectively.
Mann-Whitney U-Test
The Mann-Whitney U-test is used to contrast divergences between two independent groups when the dependent variable is either continuous or ordinal, but not normally distributed.
The Mann-Whitney U-test is often considered the nonparametric substitute to the
130
independent t-test but unlike the independent-samples t-test, the Mann-Whitney U-test allows the researcher to draw different inferences about the data depending on the assumptions made by the researcher about the data's distribution.
For the purposes of this study, the Mann-Whitney U-test will be used to analyse the differences in the perceptions of male and female BOP consumers regarding the evaluative criterion (price/affordability, quality, appearance/acceptability, packaging/quantity, accessibility/availability, brand preference, adaptability of existing products, functionality/
performance and advertising/ awareness) that influence purchase decisions, respectively.
Further to this, differences in the perceptions of African and Coloured BOP consumers regarding the evaluative criterion will also be analysed using the Mann-Whitney U-test. The Mann-Whitney U-test will also be utilised in analysing the differences in the perceptions of male and female BOP consumers regarding the key dimensions (branding, savings potential/ability to pay off debt, price/affordability, quality, appearance/acceptability, adaptability of existing products, functionality/performance, packaging/quantity, advertising/awareness, accessibility/availability and partnering with MNCs) of the study, respectively.