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

Correlation and Prediction HPHE 3150 Dr. Ayers

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

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 (direct relationship/+) Pull-ups (#completed) Chin-ups (#completed)

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

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

Correlation Formula (page 60)

Correlation issues Correlation ≠ causation < r < Coefficient of Determination (r 2 ) (shared variance) r=.70r 2 =.4949% variance in Y accounted for by X X iv Y dv

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? Fitness/PA Correlation/Causation?

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 Skinfolds % Fat

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?