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Understanding Correlation Coefficients: Meaning, Computation, and Interpretation

Learn about correlations, their computation, and interpretation, as well as different types of correlations. Discover how variables share variance and the importance of not assuming causation. Use SPSS to compute correlation coefficients and create scatterplots.

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Understanding Correlation Coefficients: Meaning, Computation, and Interpretation

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  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 IISigma 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. 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. 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 rXY = 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. Pearson’s product-momentSteps in the process • Step 1: • Calculate • Σx • Σx2 • (Σx)2 • Σy • Σy2 • (Σy)2

  14. Pearson’s product-momentSteps 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

  19. Interpreting Correlation Coefficients

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  22. Now You Try!!

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

  24. Variance Explained • Coefficient of Determination • rxy = .70 • .702 = .49 or 49% • Coefficient of Alienation • rxy = .70 • .702 = .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

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