dr. g. johnson, exploring relationships: measures of association research methods for public...

Dr. G. Johnson, www.ResearchDemystified.org

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Exploring Relationships: Measures of Association

Research Methods for Public Administrators

Dr. Gail Johnson


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Exploring Linear Relationships

Researchers use crosstabs and comparison of means between two variables to see if there is a relationship

If we see some differences that suggest there is a relationship, the next steps is to determine how strong it is


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Direction of Relationship Revisited

Plus sign: direct relationshipBoth variables change in the same

directionExample: as driving speed increases,

death rate goes up


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Direction of Relationship Revisited

Minus sign: inverse relationshipBoth variable change but in the opposite

directionExample:as age increases, health status

decreases


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Measures of Association

How strong is the association? Several different measures of association

Some measures of association range from 0 to 1 Others range from minus1 to plus 1


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How To Interpret Measures of Association

Measures of Association get interpreted in a similar way:

Perfect Relationship = 1Closer to 1: strong relationship .5 moderate/strong

Closer to 0: no relationship .2 some/slight


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How To Interpret Measures of Association

Interpreting measures of association that have a minus sign: Minus sign indicates an inverse relationship

(meaning as one variable goes up, the other goes down)

As age increases, memory decreases For example, -.9 is a very strong relationship

(almost perfect relationship because it is close to 1), but it is an inverse relationship because it has a minus sign


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Level Of Data: Common Measures of Association: Nominal Data

Cramers V and Phi Ordinal Data

Kendall’s Tau b and Tau c Ordinal with interval/ratio data

Spearman’s Rho Interval/Ratio data

Person’s r


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Gender and Attitude About Death Penalty: Revisited

FAVOR OR OPPOSE DEATHPENALTY FOR MURDER

Total

FAVOR OPPOSE MALE Number 515 129 644 % 80.0% 20.0% 100.0%

FEMALE Number 506 241 747 % 67.7% 32.3% 100.0%


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Gender and Attitude About the Death Penalty The computer using SPSS provided these

Measures of Association for the data on gender and attitude on the death penalty—expressed as the “Value”

ValuePhi .191

Cramer's V .191

Interpretation: There is some difference in support of death penalty based on gender but it is a weak (fairly close to zero).


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Gender differences in employment status?

Men Women

Full time 64% 40%

Part-time 7 13

Not working (school, unemployed, retired)

26 22

Keeping House 1 23

Other 2 2

Total 100%n=641

100%n=859


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Gender Differences in Employment Status? Interpretation of Percent Distribution: Yes, there

are some differences based on gender. Sixty-four percent of the men reported working full time compared to 40% of the women. On the other hand, 23% of the women reported keeping house as compared to 1% of the menMeasure of Association: Cramer’s V = .354

Interpretation: It is a moderate or moderately strong relationship between gender and employment status


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Views on Spanking: Related to Education Level? STRONGLY

AGREEAGREE DISAGREE STRONGLY

DISAGREE

Less than HS 25% 55% 15% 5% 100%

High school 26% 49% 19% 6% 100%

Junior college 26% 48% 16% 10% 100%

Bachelor 12% 52% 29% 7% 100%

Graduate 15% 49% 23% 12% 100%

Total 23% 51% 20% 7% N=997


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Attitudes about Spanking: Does education make a difference?

Attitudes and Education are ordinal variables and the computer provides this measures of association:

Tau C=.095

Interpretation?


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Do People With Higher Degrees Earn More?

Highest Degree Mean N

Less than HS $18,021 249

High school diploma 33,188 704

Associate degree 41,129 87

Bachelor degree 49,034 216

Graduate degree 62,275 108

Total $35,738 1364


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Do People With Higher Degrees Earn More? Hypothesis: people with higher degrees will earn

more Education is the independent variable: we think it

explains differences in earnings. Earnings is the dependent variable Education level is an ordinal scale (even though it looks

nominal-there is an order to it) Earnings are ratio level data

Measure of Association: Spearman’s Rho


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Do People With Higher Degrees Earn More? The computer crunches the numbers and

states that Spearman’s Rho is .480 Interpretation?


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Pearson’s r

Also called Pearson product-moment correlation coefficient is a measure of the correlation between two interval/ratio-level variables

It gives a measure that is between plus 1 and minus one.

The closer to zero, the weaker the relationship


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Correlation In The News

PEW Report: What is the relationship between unemployment and

Presidential approval ratings? Using opinion data from the Gallup Polls and

unemployment rates from census, PEW tried to determine the extent to which changes in unemployment rates correlated with citizens’ approval ratings of Presidents between 1980 and 2009.


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Left Side of Scale: Disapproval RatesRight Side of Scale: Unemployment Rates


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PEW Explains Correlation CoefficientsThe correlation coefficients shown in the next table

measure the degree to which unemployment rates and presidential disapproval ratings “varied together over the past 30 years (coefficient of 1 or –1 indicating a totally positive or totally negative correspondence between two variables, a zero coefficient indicating no relationship at all).

PEW: “It’s All About the Jobs Except When It Is Not,” January 26, 2010.Pew Research Center for the People & the Press http://pewresearch.org/pubs/1476/unemployment-presidential-approval-ratings-1981-2009-

reagan-obama


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Correlation Coefficients

President DisapprovalReagan 1st term .86

Reagan-2nd term -.57

GHW Bush .77

Clinton 1st term -.34

Clinton 2nd term -.26

GW Bush 1st term .09

GW Bush 2nd term .40

Obama .95


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Discussion:

Reagan’s first term and Obama’s first year show a high correlation: as unemployment rates went up, so did their disapproval ratings

But the trend lines for both are not perfectly matched

What other factors besides unemployment might affect disapproval ratings of Clinton and Bush?


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Relationships

When looking at relationships, a central question is: how strong is the relationship?

When presenting relationship data, researchers should provide the measures of association so the readers can make their own decision about the strength of the relationship.

Remember: it is rare to get high correlations or measures of association—especially in the social sciences.


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Relationships

Correlation does not mean the variables are in a cause-effect relationship.

Yes, good researchers begin by exploring a possible relationship and then “control for stuff” to see if the relationship disappears or if a relationship gets stronger under different scenarios.

Statistical controls is an effective technique to eliminate rival explanations but is not as strong as the classic experimental design.


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dr. g. johnson, exploring relationships: measures of association research methods for public...

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