Semester 2: Lecture 4 Quantitative Data Analysis: Bivariate Analysis I – Identifying Associations/Relationships
Prepared by: Dr. Lloyd Waller ©
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 exist3. 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.
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?
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.
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:
Bivariate Analysis 1
Conceptualization
Dependent VariableHair type preference: Whether or not persons prefer to wear wigs, braids, or any form of artificial hair extensions
Independent VariableVoting behavior: Whether or not persons are more likely vote for a party lead by Portia Simpson Miller rather than one lead by Bruce Golding
Bivariate Analysis 1
Operationalization
Dependent VariableHair 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’.
Bivariate Analysis 1
DATA ANALYSIS AND FINDINGSWe 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
Frequency Percent Valid Percent Cumulative Percent
Valid Yes1157 66.8 67.0
67.0
No571 33.0 33.0
100.0
Total 1728 99.8 100.0
Missing System 3 .2
Total 1731 100.0
Bivariate Analysis 1
Who will you vote for in the next election
Frequency Percent Valid PercentCumulative
Percent
Valid Bruce Golding367 21.2 21.2 21.2
Portia Simpson-Miller 1361 78.6 78.8 100.0
Total 1728 99.8 100.0
Missing System 3 .2
Total 1731 100.0
Bivariate Analysis 1
Case Processing Summary
1728 99.8% 3 .2% 1731 100.0%
Do you like to wearWigs, or extentions *Who will you vote forin the next election
N Percent N Percent N Percent
Valid Missing Total
Cases
Do you like to wear Wigs, or extentions * Who will you vote for in the next electionCrosstabulation
75 1082 1157
4.3% 62.6% 67.0%
292 279 571
16.9% 16.1% 33.0%
367 1361 1728
21.2% 78.8% 100.0%
Count
% of Total
Count
% of Total
Count
% of Total
Yes
No
Do you like to wear Wigs,or extentions
Total
Bruce Golding
PortiaSimpson-
Miller
Who will you vote for in the nextelection
Total
x
Bivariate Analysis 1
Bivariate Analysis 1
Do you like to wear Wigs, or extentions * Who will you vote for in the next election Crosstabulation
75 1082 1157
20.4% 79.5% 67.0%
292 279 571
79.6% 20.5% 33.0%
367 1361 1728
100.0% 100.0% 100.0%
Count
% within Who will you votefor in the next election
Count
% within Who will you votefor in the next election
Count
% within Who will you votefor in the next election
Yes
No
Do you like to wear Wigs,or extentions
Total
Bruce Golding
PortiaSimpson-
Miller
Who will you vote for in the nextelection
Total
Bivariate Analysis 1
Do you like to wear Wigs, or extentions * Who will you vote for in the next election Crosstabulation
75 1082 1157
6.5% 93.5% 100.0%
292 279 571
51.1% 48.9% 100.0%
367 1361 1728
21.2% 78.8% 100.0%
Count
% within Do you like towear Wigs, or extentions
Count
% within Do you like towear Wigs, or extentions
Count
% within Do you like towear Wigs, or extentions
Yes
No
Do you like to wear Wigs,or extentions
Total
Bruce Golding
PortiaSimpson-
Miller
Who will you vote for in the nextelection
Total
Bivariate Analysis 1
Do you like to wear Wigs, or extentions * Who will you vote for in the next election Crosstabulation
75 1082 1157
6.5% 93.5% 100.0%
20.4% 79.5% 67.0%
4.3% 62.6% 67.0%
292 279 571
51.1% 48.9% 100.0%
79.6% 20.5% 33.0%
16.9% 16.1% 33.0%
367 1361 1728
21.2% 78.8% 100.0%
100.0% 100.0% 100.0%
21.2% 78.8% 100.0%
Count
% within Do you like towear Wigs, or extentions
% within Who will you votefor in the next election
% of Total
Count
% within Do you like towear Wigs, or extentions
% within Who will you votefor in the next election
% of Total
Count
% within Do you like towear Wigs, or extentions
% within Who will you votefor in the next election
% of Total
Yes
No
Do you like to wear Wigs,or extentions
Total
Bruce Golding
PortiaSimpson-
Miller
Who will you vote for in the nextelection
Total
Bivariate Analysis 1
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
Bivariate Analysis 1
CONCLUSION AND RECOMMENDATIONS
What are the implications of the findings
• Implications for Theory
• Implications for Policy
• Policy Makers
• People
Bivariate Analysis 1
Place an example here – Page 94 from the blakie
The Strength/Direction of the Relationship
Bivariate Analysis 1
The Significance of the Relationship
Bivariate Analysis 1
The Significance of the Relationship
Bivariate Analysis 1
The Significance of the Relationship
Bivariate Analysis 1
The Significance of the Relationship
Chi-Square Tests
455.775b 1 .000
453.109 1 .000
440.370 1 .000
.000 .000
455.511 1 .000
1728
Pearson Chi-Square
Continuity Correctiona
Likelihood Ratio
Fisher's Exact Test
Linear-by-LinearAssociation
N of Valid Cases
Value dfAsymp. Sig.
(2-sided)Exact Sig.(2-sided)
Exact Sig.(1-sided)
Computed only for a 2x2 tablea.
0 cells (.0%) have expected count less than 5. The minimum expected count is 121.27.
b.
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
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.
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
What Faculty are you in?
360 20.8 20.8 20.8
768 44.4 44.4 65.3
144 8.3 8.3 73.6
144 8.3 8.3 81.9
312 18.0 18.1 100.0
1728 99.8 100.0
3 .2
1731 100.0
1=Social Sciences
2=Humanities andEducation
3=Pure andApplied Sciences
4=Faculty of Law
5=Faculty ofMedical Sciences
Total
Valid
SystemMissing
Total
Frequency Percent Valid PercentCumulative
Percent
E-Voting
1552 89.7 89.8 89.8
168 9.7 9.7 99.5
8 .5 .5 100.0
1728 99.8 100.0
3 .2
1731 100.0
1=Yes
2=No
8
Total
Valid
SystemMissing
Total
Frequency Percent Valid PercentCumulative
Percent
E-Voting * What Faculty are you in? Crosstabulation
248 760 144 144 256 1552
14.4% 44.0% 8.3% 8.3% 14.8% 89.8%
104 8 0 0 56 168
6.0% .5% .0% .0% 3.2% 9.7%
8 0 0 0 0 8
.5% .0% .0% .0% .0% .5%
360 768 144 144 312 1728
20.8% 44.4% 8.3% 8.3% 18.1% 100.0%
Count
% of Total
Count
% of Total
Count
% of Total
Count
% of Total
1=Yes
2=No
8
E-Voting
Total
1=SocialSciences
2=Humanitiesand Education
3=Pure andApplied
Sciences4=Faculty
of Law
5=Facultyof MedicalSciences
What Faculty are you in?
Total
E-Voting * What Faculty are you in? Crosstabulation
248 760 144 144 256 1552
68.9% 99.0% 100.0% 100.0% 82.1% 89.8%
14.4% 44.0% 8.3% 8.3% 14.8% 89.8%
104 8 0 0 56 168
28.9% 1.0% .0% .0% 17.9% 9.7%
6.0% .5% .0% .0% 3.2% 9.7%
8 0 0 0 0 8
2.2% .0% .0% .0% .0% .5%
.5% .0% .0% .0% .0% .5%
360 768 144 144 312 1728
100.0% 100.0% 100.0% 100.0% 100.0% 100.0%
20.8% 44.4% 8.3% 8.3% 18.1% 100.0%
Count
% within WhatFaculty are you in?
% of Total
Count
% within WhatFaculty are you in?
% of Total
Count
% within WhatFaculty are you in?
% of Total
Count
% within WhatFaculty are you in?
% of Total
1=Yes
2=No
8
E-Voting
Total
1=SocialSciences
2=Humanitiesand Education
3=Pure andApplied
Sciences4=Faculty
of Law
5=Facultyof MedicalSciences
What Faculty are you in?
Total
Chi-Square Tests
305.791a 8 .000
315.931 8 .000
14.831 1 .000
1728
Pearson Chi-Square
Likelihood Ratio
Linear-by-LinearAssociation
N of Valid Cases
Value dfAsymp. Sig.
(2-sided)
5 cells (33.3%) have expected count less than 5. Theminimum expected count is .67.
a.
Chi-Square Tests
305.791a 8 .000
315.931 8 .000
14.831 1 .000
1728
Pearson Chi-Square
Likelihood Ratio
Linear-by-LinearAssociation
N of Valid Cases
Value dfAsymp. Sig.
(2-sided)
5 cells (33.3%) have expected count less than 5. Theminimum expected count is .67.
a.
1.256
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
Bivariate Analysis 1
Incivility * Social Status Crosstabulation
296 8 96 400
37.0% 1.0% 100.0% 23.1%
17.1% .5% 5.6% 23.1%
472 120 0 592
59.0% 14.4% .0% 34.3%
27.3% 6.9% .0% 34.3%
32 688 0 720
4.0% 82.7% .0% 41.7%
1.9% 39.8% .0% 41.7%
0 8 0 8
.0% 1.0% .0% .5%
.0% .5% .0% .5%
0 8 0 8
.0% 1.0% .0% .5%
.0% .5% .0% .5%
800 832 96 1728
100.0% 100.0% 100.0% 100.0%
46.3% 48.1% 5.6% 100.0%
Count
% within Social Status
% of Total
Count
% within Social Status
% of Total
Count
% within Social Status
% of Total
Count
% within Social Status
% of Total
Count
% within Social Status
% of Total
Count
% within Social Status
% of Total
1=Strongly agree
2=Agree
3=Disagree
4=Strongly disagree
8
Incivility
Total
1=Lower(Working)
Class2=Middle
Class3=UpperMiddle
Social Status
Total
Incivility * Social Status Crosstabulation
296 8 96 400
17.1% .5% 5.6% 23.1%
472 120 0 592
27.3% 6.9% .0% 34.3%
32 688 0 720
1.9% 39.8% .0% 41.7%
0 8 0 8
.0% .5% .0% .5%
0 8 0 8
.0% .5% .0% .5%
800 832 96 1728
46.3% 48.1% 5.6% 100.0%
Count
% of Total
Count
% of Total
Count
% of Total
Count
% of Total
Count
% of Total
Count
% of Total
1=Strongly agree
2=Agree
3=Disagree
4=Strongly disagree
8
Incivility
Total
1=Lower(Working)
Class2=Middle
Class3=UpperMiddle
Social Status
Total
Bivariate Analysis 1
Chi-Square Tests
1425.277a 8 .000
1629.762 8 .000
220.288 1 .000
1728
Pearson Chi-Square
Likelihood Ratio
Linear-by-LinearAssociation
N of Valid Cases
Value dfAsymp. Sig.
(2-sided)
6 cells (40.0%) have expected count less than 5. Theminimum expected count is .44.
a.