Correlations

1. Correlations 11/5/2013

2. BSS Career Fair • Wednesday 11/6/2013- Mabee A & B • 12:30-2:30P

3. Readings • Chapter 8 Correlation and Linear Regression (Pollock) (pp. 182-187) • Chapter 8 Correlation and Regression (Pollock Workbook)

4. Homework Due 11/7 • Chapter 7 Pollock Workbook • Question 1 • A, B, C, D, E, F   • Question 2 • A, B, C, D  • Question 3 (use the dataset from the homework page) • A, B, C, D • Question 5 • A, B, C D, E

5. Opportunities to discuss course content

6. Office Hours For the Week • When • Wednesday10-12 • Thursday 8-12 • And by appointment

7. Course Learning Objectives • Students will be able to interpret and explain empirical data. • Students will achieve competency in conducting statistical data analysis using the SPSS software program.

8. Measures of Association

9. Why Hypothesis Testing • To determine whether a relationship exists between two variablesand did not arise by chance. (Statistical Significance) • To measure the strength of the relationship between an independent and a dependent variable? (association)

10. Measures of Association for Nominal Variables

11. Measures of association For Cross-Tabs Nominal Ordinal Strength Significance Direction! • Strength • Significance

12. Ordinal Measures of Association

13. Adding a Third Variable How to Control for a Variable?

14. A Third Variable • the relationship between two variables may be spurious, weak or even too strong • "controlling" for a third variable is a method of removing or separating the effects of another variable. • This gets at the underlying relationship

15. Why Add the Third Variable • Is there an antecedent variable at play? • Is the observation different for different groups of people

16. Marijuana and a Third Variable • H1: People with children will have different views on legalization than others of the same ideology • Cross-tabs • Input Row Variable • Input Column Variable • To control for a variable place it in the area that says Layer 1 of 1.

19. Views on Homosexuality, Party ID and Race • DV- homosex2 • IV- partyid3 • Control- race 2

20. Finally Correlations You have been waiting to use this

21. What is correlation? • Any relationship between two variables • Correlation does not mean causation

22. What Could Be Happening? • Variable A influences variable B • Variable B influences variable A • It is a coincidence • Some other variable (C) influences both A and B

23. Correlation Coefficients Note the lower case r • Pearson’s Product Movement (Pearson’s r) • A way of measuring the goodness of fit between two continuous variables

24. Rules on Correlations • Variables must be continuous. • You cannot use ordinal or nominal variables here • Small samples >30 can give you odd results

25. Measuring Pearson’s r • Measure from -1 to 0 to 1. • -1 means a perfect negative relationship • 0 is the absence of any relationship • +1 is a perfect positive relationship • Like Somers’ D, Pearson's "r" scores tell us • Direction • Strength of Association • Statistical significance of the measure

26. PEARSON'S r's are PRE Measures! • Squaring the (r) value provides a measure of how much better we can do in predicting the value of the d.vby knowing the independent variable. • We call this a r2(r-square) value.

27. Significance and Strength • Significance Levels: We use the .05 level • Count your Stars(if available) • *=significant at .05 • **= significant at.01 • No Stars= No Significance • Relationship strengths of r-square values • .000 to .10 = none- • .11-.20 weak-moderate • .20-.35 moderate • .35-.50 moderate- strong • .50 there is a strong relationship

28. An Example from long ago

29. The Previous Example • We Square the correlation value .733 • This gives us a value of .537 (r-square) • From this we can say 53.7% (PRE) of the variation in the dependent variable can be explained by the independent variable • We cannot, however, say that being Baptist increases the syphilis rate.

30. American Cities • Violent Crime Rate, Teen Unemployment Rate, Roadway congestion, Heart Disease

31. World Health Indicators • Coal consumption , Adequate Sanitation, Child Mortality, Child Immunization

32. Correlations in SPSS • Analyze • Correlate • Bivariate • You can include multiple variables

33. Scatterplots

34. A Way of Visualizing a Correlation

35. More on Scatterplots • We can think of this line as a prediction line. • The closer the dots to the line, the stronger the relationship, the further the dots the weaker the line. • If all the data points are right on the regression line, then there is a perfect linear relationship between the two variables. • This only graphs a correlation...... this means that it does not mean causality nor should it be used for testing!

36. CO2 and Urban Population

37. Scatterplots in SPSS

38. How to do it • Graphs • Legacy Dialogs • Scatter/Dot...

39. A Window pops up Select simple Choose Define

40. Adding Case Labels • put your variable in the Label Cases by area • Click on Options, and this will open up a window • Click on display chart with case labels and continue • Click OK

41. Including a fit Line with your Scatterplot

43. Do not use scatterplots for testing! There are better measures, especially if you have more than 1 iv. (your paper should not include any scatterplots)