1. Unit 2: Bivariate Relationships Lesson 2: Covariance and Pearson r EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas Next Slide
2. Covariance Are The Variables Correlated??? “ The average cross-product of the deviation scores.” Answers 2 Questions: 1. Is there any relationship between X and Y? 2. If there is a relationship, is it positive or negative? Next Slide
3. “Rules” for Covariance <ul><li>Covariance will be 0 (zero) when the sum of the cross- </li></ul><ul><li>products is 0 (e.g., IQ and shoe size) </li></ul><ul><li>The “sign” of the covariance tells the “direction” of the </li></ul><ul><li>relationship </li></ul>Do they “Covary” Together??? 1. There are no “bounds” for values for the covariance Are The Variables Correlated??? Next Slide
4. Pearson r “ The average cross-product of the standardized deviation scores.” Answers 3 Questions: 1. Is there any relationship between X and Y? 2. If there is a relationship, is it positive or negative? 3. How well does one line describe the data? Next Slide
5. Pearson r “ How well does a single line represent my data?” r = .85 r = -.25 r = 1.0 Next Slide
6. Pearson r r = .00 Next Slide X 0 0 1 1 Y 0 1 0 1
7. “Guessing” Pearson r Height and weight Moderate Positive SES and Math Achievement High Negative Tobacco use and Life Expectancy High Positive GPA and SAT Near Zero Shoe size and IQ Moderate to High Positive Next Slide Parameters Pearson r
8. “Rules” for Pearson r <ul><li>A zero value for the Pearson r means that there is NO </li></ul><ul><li>relationship between the two variables of interest </li></ul><ul><li>Pearson r’s cannot be compared between two studies </li></ul>1. The “bounds” for Pearson r are between +1.0 and -1.0 4. The Covariance determines the sign of the Pearson r Next Slide
9. Square Before You Compare R 2 = .25 R 2 = .36 “ Study 2 explains 11% more variance than Study 1” Next Slide Study 1 Pearson r between GPA and GRE r = .50 Study 2 Pearson r between IQ and GRE r = .60
10. A Little Practice r = 1.0 r = .832 Next Slide X 5 6 7 8 9 Y 10 12 14 16 18 X 5 6 7 8 9 Y 10 12 14 16 14
11. Unit 2: Bivariate Relationships Lesson 2: Covariance and Pearson r EDER 6010: Statistics for Educational Research Dr. J. Kyle Roberts University of North Texas
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