Bivariate analysis involves the comparison of two variables (X, Y) simultaneously; it aims to determine relationships between pairs of variables under study through a correlation analysis between the constructs. Thus, it can be used to test hypotheses of association and/or to determine causal relationships among the variables (Babbie 2001; Hair, Black et al. 2010). There are many techniques available for making comparisons. Diamantopoulos and Schlegelmilch (1997) suggest that the decision of which technique to select depends upon: (a) what is being compared? (b) how many groups or how many measures do we have? (c) what is the level of measurement? (e.g. nominal, ordinal, interval, or ratio. Considering these criteria, the bivariate analyses carried out were: the chi-square for independence; the Friedman two-way analysis of variance (ANOVA); and one-way ANOVA. In the following paragraphs, a brief description of each technique is presented, as well as a justification for the selection.
Chi-Square for independence was selected for testing H2. The chi-square test is used when we want to compare two or more than two groups on a categorical variable. It tests whether there is a relationship between categorical variables (Diamantopoulos and Schlegelmilch 1997). In our hypothesis, we want to see whether there is a relationship between customer satisfaction and the variety of SB purchased. Depending on the variety of SB purchased, we have grouped respondents into four categories: non buyers are those that have indicated that they do not buy SB; light buyers are those that buy one product category; medium buyers are those that buy two or three product categories; and heavy buyers are those that buy from four product categories. Respondents could also fall into four categories of customer satisfaction (Table 4.12). Therefore, we are measuring only categorical variables. A combination of the two categories provides us with a contingency table with 16 categories (4x4). The contingency table provides us with the number of responses that fall into each combination of categories. The chi-square test compares the actual or observed frequencies to the frequencies expected by chance (Field 2009).
Table 4.12: Customer Satisfaction Categories
Customer satisfaction Category Average Level of satisfaction
Unsatisfied 1 – 2,3
Little satisfied 2,4 – 2,8
Satisfied 2,9 – 3,4
Very satisfied 3,5 – 4,0
Friedman’s ANOVA was selected for testing H6. This is a nonparametric
when the same participants have been used in all conditions. The Friedman’s
ANOVA ranks the data for each respondent, adds up the ranks for each
condition, and then calculates the test statistics
Fr
(Diamantopoulos and Schlegelmilch 1997; Field 2009). In our hypothesis, we test differences in the level of trust between the ten product categories of SB. Therefore, the sample of respondents (a single group) provides ten different measurements, which are then contrasted. The null hypothesis is that there are no differences in the level of trust among the product categories. The level of trust can range from a minimum of 1 (“do not trust at all”) to a maximum of 4 (“trust a lot”). Therefore,we have ten ordinal level measures, one per product category that needs to be compared to one another. The responses for each product category are ranked and the chi-square distribution with 9 degrees of freedom (number of variables –
1) as well as the significance was calculated.
The one-way ANOVA was selected to test H8. ANOVA is an extension of the t-test but it can be applied when more than two means are being compared to see if there are any significant differences among them. If we have two means to compare, then ANOVA provides the same results as the t-test for independent samples. When we have to compare more than two means and the level of measurement is interval, we use ANOVA rather than conducting multiple t-tests. To test H8, the one-way ANOVA was selected to compare the differences in mean values of the constructs among the groups because: (a) there are nine groups that are being compared (the nine grocery chains selected each one with a sample of 100 respondents), and (b) the level of adoption and penetration of
SBs (the construct of interest) is being measured on an interval scale (Diamantopoulos and Schlegelmilch 1997). Specifically, we have created a new variable, called “SB variety” that measures the level of SB purchase. Depending on the number of SB product categories that respondents have purchased “SB variety” can range from a minimum value of “0” to a maximum of “10”.
Respondents that they do not buy SBs are represented with the minimum value and respondents that buy SBs are represented based on the number of SB product categories that they buy (e.g. “1” for those that buy one product category, “2” for two categories, etc.). Thus, we have an interval scale since we establish
an ordered relationship between respondents with regard to the number of SB products that they buy (Diamantopoulos and Schlegelmilch 1997; Hair, Black et al. 2010).
The one-way ANOVA was also selected to test H9. In this case, we also have the nine grocery chains and the construct of interest is the level of trust with the SB. Therefore, we want to test whether there are differences in the mean values of the level of trust with the SBs among the nine grocery chains. Our data provide information for the level of trust for ten different product categories and it can range from a minimum of “1” (do not trust at all) to a maximum of “4” (trust a
lot). We measure level of trust as the average level of trust for the 10 product categories. Thus, the level of measurement is interval. Therefore, the one-way ANOVA is appropriate (Diamantopoulos and Schlegelmilch 1997).