3.4.1.2.2 Measures of Dispersion or Variability
3.4.2 Bivariate Data Analysis
Bivariate data is data that has two variables that can change and are compared to find relationships (Sekaran and Bougie, 2010: 307). Saunders et al. (2012:266) define statistical inference as “the process of coming up with conclusions about a population on the basis of data describing the sample.” Hence, inferential statistics infer something about the population from
which the sample was taken which is based on the characteristics (frequently expressed using descriptive statistics) relating to the sample.
Cross-tabulation
Cross tabulation is “a technique of comparing categorical data from demographic variables and the study’s target variables. It uses tables consisting of rows and columns that correspond to the coded values of each variable’s category” (Cooper and Schindler, 2008:459). The combination of the variables in rows and columns forms cells which illustrate the groupings of data in order to identify the relationship amongst variables and whether it is independent or not.
When tables are constructed for statistical testing, they are referred to as contingency tables. The purpose of cross-tabulation is to establish a relationship between two variables;
if so, the information can be represented in two-dimensional frequency distributions by cross-tabulating the variables. When variables take on different values and cannot be meaningfully cross-tabulated, graphic displays and summary statistics help to describe the extent of the association between the variables. The table below indicates the hypotheses generated in data analysis for cross tabulation:
Table 3.3: Hypotheses for Cross-Tabulation
HypothesisHo1: The association between SAmp3.com and digital music distribution does not inspire innovation to the musician.
HA1: The association between SAmp3.com and digital music distribution does inspire innovation to the musician.
Ho2: There is no association between the means and the medium of distribution in the music industry.
HA2: There is an association between the means and the medium of distribution in the music industry.
Source: Designed by researcher from research instrument.
Cross-tabulation is used to tabularise the data from Section A of the questionnaire which relates to biographical information, with other elements of the questionnaire in Sections B and C. The cross-tabulated results were then evaluated against the Chi-Square tests and hypotheses investigated.
Correlation
According to Saunders et al. (2012); and Sekaran and Bougie (2010) correlation is the extent to which two variables are related to each other. A correlation coefficient is a
“statistical measure of covariation, or association between two variables” (Zikmund et al., 2013:561). “Covariation is the extent to which a change in one variable corresponds systematically to a change in another” (Zikmund et al., 2013:561). A Pearson correlation mix will prove the above by indicating the direction, strength, and significance of the bivariate relationships among all the variables that are measured in the study. Correlation tests whether a relationship exists between the two variables and indicates the nature, strength, and direction of the relationship using Pearson product moment correlation coefficient (Sekaran and Bougie, 2010:321). The correlation coefficient enables the researcher to quantify the strength of the relationship between the two variables.
Pearson’s Correlation:
Pearson’s correlation is employed when a continuous independent and continuous dependent variables are analysed. Pearson’s correlation coefficient measures the magnitude and direction of linear association. The measure is represented by the r symbol and can take on a range between +1 and -1 (Cooper and Schindler, 2008:510). The magnitude indicates the degree of the relationship to which variables move in unison or opposition. The significance of the sign is only indicative of the direction of the relationship. The decision rule on Pearson’s correlation coefficient is that, when the probability associated with the T-statistics is 0.5 or less, the researcher can assume that there is a relationship between the dependent and independent variables. Table 3.4 below displays the range of values, strengths and the direction of the Pearson r values:Table 3.4: Pearson’s Correlation
Pearson (r) Strength and Direction
+1 Perfect positive
+0.7 Strong positive
+0.4 Moderate positive
0.0 No relationship
-0.4 Moderate negative
-0.7 Strong negative
-1 Perfect negative
Source: Cooper and Schindler. (2008) Business Research Methods. New York: McGraw Hill.
Pearson’s correlation coefficient is applied to the variables in Section C of the questionnaire which evaluates the dynamics of music distribution, supply and demand and supply chain competence and capability. Although the instrument does not indicate the predictive power of each variable over the other, the strength and direction of the relationship is used together with the multiple regression models that illustrate model predictors. In this case, Pearson r provides greater insight on the strength and direction of the predictor variable that influences the overall regression model.
T-test
The t-test is conducted to check if there are any significant mean differences between two groups on a variable of interest. The t-test can be used to examine the same group prior to and following a treatment. It indicates whether two groups comprising of nominal variables are significantly different from each other with regard to a particular variable (Sekaran and Bougie, 2010:339).
Analysis of Variance (ANOVA)
“An analysis of variance (ANOVA) helps examine the significant mean differences among more than two groups on an interval or ratio-scale dependent variable. The results of ANOVA show whether or not the means of the various groups are significantly different from one another” (Sekaran and Bougie, 2010: 347).
Inferential Statistics
Inference refers to drawing conclusions and testing hypotheses about a population based on the evidence collected in a sample (Walliman, 2001:257). It is important to ascertain if the variable in the sample deviates somewhat from the population; if it does, one needs to determine if the difference is statistically significant or insignificant. Cooper and Schindler (2008:468) state that, “a difference is statistically significant if there is a good reason to believe that the difference does not represent random sampling fluctuations.” One method of testing for statistical significance is the development of hypotheses.
Hypothesis testing:
When testing for significance, two types of hypotheses are used. The null hypothesis (H0) is a statement that no difference exists between the two variables under study or that there is no significant difference between the two groups. The alternate hypothesis (H1) is the exact opposite of the null hypothesis, stating that there is a relationship between two variables or significant differences between two groups (Cooper and Schindler, 2008:458). For this study, the confidence level used was 95% correspondingto a significance level of p = 0.05. If p is less than 0.05, the decision is to accept the alternate hypothesis, concluding that there is a significant difference or relationship between the variables. Hence, the variables reach statistical significance.
Chi-square
The Chi-square test was also be used as an analytical tool. Saunders et al. (2012: 666) describe the Chi-square test as a “statistical test to determine the probability (likelihood) that two categorical data variables are associated. A common use is to discover whether there are statistically significant associations between the observed frequencies and the expected frequencies of two variables presented in cross-tabulation.”