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Descriptive Statistics III REVIEW

Descriptive Statistics III REVIEW. Variability Range, variance, standard deviation Coefficient of variation (S/M): 2 data sets Value of standard scores?. Correlation and Prediction. HPER 3150 Dr. Ayers. Correlation (Pearson Product Moment or r). Are two variables related?

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Descriptive Statistics III REVIEW

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  1. Descriptive Statistics IIIREVIEW • Variability • Range, variance, standard deviation • Coefficient of variation (S/M): 2 data sets • Value of standard scores?

  2. Correlation and Prediction HPER 3150 Dr. Ayers

  3. Correlation(Pearson Product Moment or r) • Are two variables related? • Car speed & likelihood of getting a ticket • Skinfolds & percent body fat • What happens to one variable when the other one changes? • Linear relationship between two variables

  4. Attributes of r

  5. Scatterplot of correlation between pull-ups and chin-ups (direct relationship/+) Chin-ups (#completed) Pull-ups (#completed)

  6. Scatterplot of correlation betweenbody weight and pull-ups(indirect relationship/-) Pull-ups (#completed) Weight (lb)

  7. Scatterplot of zero correlation (r = 0) Figure 4.4 Y X

  8. Correlation Formula(page 54)

  9. Correlation issues • Causation • -1.00 < r < +1.00 • Coefficient of Determination (r2) (shared variance) • Linear or Curvilinear (≠ no relationship) • Range Restriction • Prediction (relationship allows prediction) • Error of Prediction (for r ≠ 1.0) • Standard Error of Estimate (prediction error)

  10. Limitations of r Figure 4.5 Curvilinear relationship Example of variable? Figure 4.6 Range restriction

  11. Limitations of r

  12. Uses of Correlation • Quantify RELIABILITY of a test/measure • Quantify VALIDITY of a test/measure • Understand nature/magnitude of bivariate relationship • Provide evidence to suggest possible causality

  13. Misuses of Correlation • Implying cause/effect relationship • Over-emphasize strength of relationship due to “significant” r

  14. Correlation/PredictionREVIEW • Bivariate nature • Strength (-1 to 1) • Linear relationships (curvilinear?) • (In)Direct relationships • Coefficient of determination: what is it and what does it tell you? • Uses/Misuses of correlation?

  15. Sample Correlations Excel document

  16. Correlation and prediction % Fat Skinfolds

  17. Variables Dependent • Presumed effect • Consequence • Measured by researcher • Predicted • Criterion • Y Independent • Presumed cause • Antecedent • Manipulated by researcher • Predicted from • Predictor • X

  18. Equation for a line Y’ = bX + c b=slope C=Y intercept

  19. We have data from a previous study on weight loss. Predict the expected weight loss (Y; dependent) as a function of #days dieting (X; independent)for a new program we are starting

  20. Y=weight loss Ybar=8.0# sy=1.5# X=days dieting Xbar=65 days sx=15 days rxy=.90 To get regression equation, calculate b & c b=r(sy/sx) b=.90(1.5/15) b=.09 On average, we expect a daily wt loss of .09# while dieting c=Ybar–bXbar c=8.0-.09(65) c=2.15 Y’ = bX + c Y’ = .09x + 2.15 Predicted wt loss = .09(days dieting) + 2.15

  21. Correlation and prediction % Fat Skinfolds

  22. Correlation and prediction % Fat Skinfolds

  23. Correlation and prediction % Fat Skinfolds

  24. Standard Error of Estimate(SEE) As r ↑, error ↓ As r ↓, error ↑ Is ↑r good? Why/Not? Is ↑ error good? Why/Not?

  25. Correlation and prediction % Fat 23 20 17 SEE = 3% 40 Skinfolds

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