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Comprehensive Review: Correlation & Prediction in Descriptive Statistics

Explore the concepts of correlation and prediction in descriptive statistics, including variability measures, formulae, limitations, and practical applications. Learn to assess the strength and nature of relationships between variables.

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Comprehensive Review: Correlation & Prediction in Descriptive Statistics

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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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