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.