Descriptive Statistics III REVIEW Variability Range variance standard

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

Correlation and Prediction HPHE 3150 Dr. Ayers

Variables Dependent • • • (ordinal/continuous: #) Presumed effect Consequence Measured by researcher Predicted Criterion Y Y dv X iv Independent • • • (categorical: name) Presumed cause Antecedent Manipulated by researcher Predicted from Predictor X

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 • 1 measure of 2 separate variables or 2 measures of 1 variable • Provides support for a test’s validity and reliability

Attributes of r magnitude & direction

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

Scatterplot of correlation between body weight and pull-ups Pull-ups (#completed) (indirect/inverse relationship/-) Weight (lb)

Scatterplot of zero correlation (r = 0) Figure 4. 4 Y X

Correlation Formula (page 60)

Correlation issues • Correlation ≠ causation • -1. 00 < r < +1. 00 • Coefficient of Determination (r 2) (shared variance) • r=. 70 r 2=. 49 49% variance in Y accounted for by X Y dv X iv

• Negative correlation possibly due to: • Opposite scoring scales • True negative relationship • Linear or Curvilinear (≠ no relationship; fig 4. 6) • Range Restriction (fig 4. 7; ↓ r) • Prediction (relationship allows prediction to some degree) • Error of Prediction (for r ≠ 1. 0) • Standard Error of Estimate (prediction error)

Limitations of r Figure 4. 6 Curvilinear relationship Example of variable? Figure 4. 7 Range restriction

Limitations of r

Correlation & Prediction I REVIEW • Bivariate nature of correlations • X (iv) & Y (dv) • +/- relationships • Range of r? • Coefficient of Determination (r 2) (shared variance) • Coefficient of variation (S/M): 2 data sets • Low V (. 1 -. 2=homo): M accounts for most variability in scores • Curvilinear relationship? • Correlation/Causation? Fitness/PA

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

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

Correlation and prediction % Fat Skinfolds

Sample Correlations Excel document

Standard Error of Estimate (SEE) Average error in the process of predicting Y from X Standard Deviation of error As r ↑, error ↓ As r ↓, error ↑ Is ↑r good? Why/Not? Is ↑ error good? Why/Not?