1. Section #1 Quiz 1 Stem and Leaf Plot (N=29) X|8 2|2255667899999 3|0011222456668 4|00 Mean=29.9; M=30; Mode= 29; s=6.38;

2. Section #2 Quiz 1 Stem and Leaf Plot (N=36) X| 7 1|147889 2|244689 3|11122223333444567799 4|002 Mean=29.36; M=32; Mode= 32, 33; s=8.68;

3. Part II  igma Freud & Descriptive Statistics Chapter 5 Ice Cream and Crime: Computing Correlation Coefficients

4. What you will learn in Chapter 5 What correlations are and how they work All about correlations...  How to compute them  How to interpret them Other types of correlations that exist

5. Chapter 65 What they are not Correlations only tell us about the relationship and the strength of the relationship. Correlations do NOT tell us about cause and effect.

6. Chapter 66 What they are not Correlations do not imply causation Examples  Marijuana use and heroin  Milk use and cancer  Church attendance and drug use  Lead levels and behavior  Cigarette smoking and Alzheimer’s  Education and sexual activity  Sex life and longevity  Coffee and suicide risk

7. What Correlations are about… Examines the relationship between variables How the value of one variable changes in relation to changes in another variable  Range between -1 and 1  Bivariate correlation (2 variables)  Pearson product-moment correlation Karl Pearson

8. Types of Correlation Coefficients Positive Correlation  Direction Correlation When variables change in the same direction Negative Correlation  Indirect Correlation When variables change in opposite directions r XY = correlation between X and Y

9. Relationships Between Variables

10. Things to Remember Correlations…  Range in value from -1 to +1  Absolute value indicates strength  Reflect situation where there are at least two data points  May want to use “indirect” and “direct” instead of “positive” and “negative” to keep from assigning value to the relationship

11. Computing Simple Correlations Pearson product-moment… What do these symbols represent?

12. Steps in Computation List the two values for each participant Compute the sum of X values, and compute the sum of Y values Find square of sum for x and y Find sum of squares for x and y Find the sum of the XY products Now “plug” these values into the formula

13. Chapter 613 Pearson’s product-moment Steps in the process Step 1:  Calculate Σx Σx 2 (Σx) 2 Σy Σy 2 (Σy) 2

14. Chapter 614 Pearson’s product-moment Steps in the process Step 2:  Calculate Σxy  Sometimes referred to as the sum of the cross-products Step 3:  Substitute the values derived above into the formula Note that N = number of pairs of scores

15. The Visual Picture Scatterplot

16. Strong Positive Relationship

17. Strong Negative Relationship

18. Correlation Matrix IncomeEducationAttitudeVote Income1.000.574-0.08-0.291 Education1.00-0.149-0.199 Attitude1.00-0.169 Vote1.00

19. Interpreting Correlation Coefficients

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22. Chapter 622 Now You Try!! ParticipantHours/Week Video GamesCollege GPA 133.8 2152.1 3222.5 4300.6 5113.1 6251.9 763.9 8123.8 9171.7

23. Computing Simple Correlations Pearson product-moment… What do these symbols represent?

24. Variance Explained Coefficient of Determination  r xy =.70 .70 2 =.49 or 49% Coefficient of Alienation  r xy =.70 .70 2 =.49  1.00 -.49 =.51 or 51%

25. How Variables Share Variance Remember: Association NOT Causation

26. Different Types of Correlations

27. Using the Computer Computing Correlation Coefficients using SPSS

28. SPSS Output

29. SPSS Scatterplot Selecting Variables

30. SPSS Scatterplot Entering variables

31. SPSS Scatterplot Simple Scatterplot

32. Glossary Terms to Know Pearson-product moment correlation Direct correlation  Positive correlation Indirect correlation  Negative correlation Scatterplot