1. Semester 2: Lecture 4 Quantitative Data Analysis: Bivariate Analysis I – Identifying Associations/Relationships Prepared by: Dr. Lloyd Waller ©

2. Bivariate Analysis 1 In general, when examining the relationship between two variables, one asks the important questions: 1.Whether and to what extent changes or differences in the values of one variable – generally the independent variable – are associated with changes or differences in the values of the second, or dependent, variable. 2. What is the direction and form of any association that might exist 3. What is the likelihood that any association observed among cases sampled from a larger population is in fact a characteristic of that population and not merely an artifact of the smaller and more potentially unrepresentative sample.

3. Bivariate Analysis 1 In testing the hypothesis, five general questions must be addressed: Is there a relationship between the independent and dependent variables in the hypothesis What is the direction and shape/form of the relationship How strong is the relationship Is the relationship statistically significant? Is the relationship a causal one?

4. Bivariate Analysis 1 Generally speaking, a relationship or association between two variables exists if the values of the observations for one variable are associated with or connected to the values of the other. One methods of detecting this is with Crosstabulation A crosstabulation displays the joint distribution of values of the variable in a simple tables called the Contingency Table by listing the categories for on of the variables along one side of the table and the levels for the other variables across the top.

5. Bivariate Analysis 1 Suppose for example a researcher was interested in exploring the hypothesis that H1 : Persons who prefer to wear wigs, braids, or any form of artificial hair extensions (false hair) are more likely vote for a party lead by Portia Simpson Miller rather than one lead by Bruce Golding Restated this would be saying that H1: There Is a relationship between Hair type preference and Voting behavior: Ho: There is no relationship between Hair type preference and Voting behavior:

6. Bivariate Analysis 1 Conceptualization Dependent Variable Hair type preference: Whether or not persons prefer to wear wigs, braids, or any form of artificial hair extensions Independent Variable Voting behavior: Whether or not persons are more likely vote for a party lead by Portia Simpson Miller rather than one lead by Bruce Golding

7. Bivariate Analysis 1 Operationalization Dependent Variable Hair type status: This variable, a nominal variable, will be measured with an instrument designed to capture information regarding whether or not persons prefer to wear wigs, braids, or any form of artificial hair extensions or not. The respondents will be asked the question ’Do you like to wear Wigs, or extensions’ and two categories will be provided for them to select from. These options will be ‘Yes’ and ‘No’.

8. Bivariate Analysis 1 DATA ANALYSIS AND FINDINGS We would first collect the data, enter the data in the SPSS program and then generate the findings using the SPSS function –Analyze – Frequency – Cross tabulations Do you like to wear Wigs, or extensions FrequencyPercentValid PercentCumulative Percent ValidYes 115766.867.0 No 57133.0 100.0 Total 172899.8100.0 MissingSystem 3.2 Total 1731100.0

9. Bivariate Analysis 1 Who will you vote for in the next election FrequencyPercentValid Percent Cumulative Percent ValidBruce Golding 36721.2 Portia Simpson- Miller 136178.678.8100.0 Total 172899.8100.0 MissingSystem 3.2 Total 1731100.0

13. Bivariate Analysis 1 x

18. DISCUSSION OF FINDINGS What was found in general terms reflecting on the table numbers and page numbers Is the relationship a perfect one Why was this the case. What did the literature say or did not say. What may be used to explain the differences in the literature and your findings if there are differences

19. Bivariate Analysis 1 CONCLUSION AND RECOMMENDATIONS What are the implications of the findings Implications for Theory Implications for Policy Policy Makers People

20. Bivariate Analysis 1 Place an example here – Page 94 from the blakie The Strength/Direction of the Relationship

21. Bivariate Analysis 1 The Significance of the Relationship

22. Bivariate Analysis 1 The Significance of the Relationship

23. Bivariate Analysis 1 The Significance of the Relationship

24. Bivariate Analysis 1 The Significance of the Relationship From the data analyzed it was found that X 2 = 98.00, p < 0.05 Since P is less than the critical value we reject the null hypothesis that there is no relationship between hair type preference and voting behaviour. Thus you are 95% sure that the findings are correct and represent the true picture in the population. P = 0.01

25. Bivariate Analysis 1 It is important for researchers to know the following: 1. Chi square is not a string statistical in that it does not convey information about the actual strength of a relationship. 2. The combination of chi square and contingency table is most likely to occur when either both variables are nominal or when on is nominal and the other is ordinal. 3. When both variable are ordinal or interval/ratio, other approaches to ascertain the relationships between the variables are needed. Correlation is most favored in this instance which allows the researcher to detect relationship, strength and the nature of this relationship (positive/negative) more easily. In SPSS the programme however allows one to calculate the phi coefficient which can give some indication of the strength of the relationship. 4. Chi-square tests should be adopted for the use of a 2/2 table 5. Chi-square can be unreliable if expected cell frequencies are less than five.

26. There is no relationship between knowledge of the EVBIS and faculty This could be restated: Students from the Faculty of Social Sciences have the same amount of knowledge about the EVBIS as those in Law, Medicine, Pure and Applied Sciences and the Humanities

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33. Bivariate Analysis 1 There is a strong positive relationship between social class and the belief that incivility is a garrison phenomenon. Middle and upper class people believe that incivility is a garrison phenomenon more so than working class people

34. Bivariate Analysis 1