dr. g. johnson, exploring relationships: measures of association research methods for public...
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Dr. G. Johnson, www.ResearchDemystified.org
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Exploring Relationships: Measures of Association
Research Methods for Public Administrators
Dr. Gail Johnson
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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%
Dr. G. Johnson, www.ResearchDemystified.org
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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).
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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?
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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?
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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.
Dr. G. Johnson, www.ResearchDemystified.org
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Left Side of Scale: Disapproval RatesRight Side of Scale: Unemployment Rates
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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
Dr. G. Johnson, www.ResearchDemystified.org
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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?
Dr. G. Johnson, www.ResearchDemystified.org
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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.
Dr. G. Johnson, www.ResearchDemystified.org
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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.
Dr. G. Johnson, www.ResearchDemystified.org
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