1. Dr. G. Johnson, www.ResearchDemystified.org1 Exploring Relationships: Measures of Association Research Methods for Public Administrators Dr. Gail Johnson

2. Dr. G. Johnson, www.ResearchDemystified.org2 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

3. Dr. G. Johnson, www.ResearchDemystified.org3 Direction of Relationship Revisited Plus sign: direct relationship Both variables change in the same direction Example: as driving speed increases, death rate goes up

4. Dr. G. Johnson, www.ResearchDemystified.org4 Direction of Relationship Revisited Minus sign: inverse relationship Both variable change but in the opposite direction Example:as age increases, health status decreases

5. Dr. G. Johnson, www.ResearchDemystified.org5 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

6. Dr. G. Johnson, www.ResearchDemystified.org6 How To Interpret Measures of Association Measures of Association get interpreted in a similar way: Perfect Relationship = 1 Closer to 1: strong relationship.5 moderate/strong Closer to 0: no relationship.2 some/slight

7. Dr. G. Johnson, www.ResearchDemystified.org7 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

8. Dr. G. Johnson, www.ResearchDemystified.org8 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

9. Dr. G. Johnson, www.ResearchDemystified.org9 Gender and Attitude About Death Penalty: Revisited

10. Dr. G. Johnson, www.ResearchDemystified.org10 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” Value Phi.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).

11. Dr. G. Johnson, www.ResearchDemystified.org11 Gender differences in employment status? MenWomen Full time64%40% Part-time713 Not working (school, unemployed, retired) 2622 Keeping House123 Other22 Total100% n=641 100% n=859

12. Dr. G. Johnson, www.ResearchDemystified.org12 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 men Measure of Association: Cramer’s V =.354 Interpretation: It is a moderate or moderately strong relationship between gender and employment status

13. Dr. G. Johnson, www.ResearchDemystified.org13 Views on Spanking: Related to Education Level? STRONGLY AGREE AGREEDISAGREESTRONGLY DISAGREE Less than HS25%55%15%5%100% High school26%49%19%6%100% Junior college26%48%16%10%100% Bachelor12%52%29%7%100% Graduate15%49%23%12%100% Total23%51%20%7%N=997

14. Dr. G. Johnson, www.ResearchDemystified.org14 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?

15. Dr. G. Johnson, www.ResearchDemystified.org15 Do People With Higher Degrees Earn More ? Highest DegreeMeanN Less than HS$18,021249 High school diploma33,188704 Associate degree41,12987 Bachelor degree49,034216 Graduate degree62,275108 Total$35,7381364

16. Dr. G. Johnson, www.ResearchDemystified.org16 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

17. Dr. G. Johnson, www.ResearchDemystified.org17 Do People With Higher Degrees Earn More ? The computer crunches the numbers and states that Spearman’s Rho is.480 Interpretation?

18. Dr. G. Johnson, www.ResearchDemystified.org18 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

19. Dr. G. Johnson, www.ResearchDemystified.org19 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.

20. Dr. G. Johnson, www.ResearchDemystified.org20 Left Side of Scale: Disapproval Rates Right Side of Scale: Unemployment Rates

21. Dr. G. Johnson, www.ResearchDemystified.org21 PEW Explains Correlation Coefficients The 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

22. Dr. G. Johnson, www.ResearchDemystified.org22 Correlation Coefficients PresidentDisapproval Reagan 1 st term.86 Reagan-2 nd term-.57 GHW Bush.77 Clinton 1 st term-.34 Clinton 2 nd term-.26 GW Bush 1 st term.09 GW Bush 2 nd term.40 Obama.95

23. Dr. G. Johnson, www.ResearchDemystified.org23 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?

24. Dr. G. Johnson, www.ResearchDemystified.org24 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.

25. Dr. G. Johnson, www.ResearchDemystified.org25 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.

26. Dr. G. Johnson, www.ResearchDemystified.org26 Creative Commons This powerpoint is meant to be used and shared with attribution Please provide feedback If you make changes, please share freely and send me a copy of changes: Johnsong62@gmail.com Visit www.creativecommons.org for more informationwww.creativecommons.org