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Chapter 2F Statistical Tools in Evaluation

Chapter 2F Statistical Tools in Evaluation. Linear Regression. Predict one variable from others If measurement on one variable is difficult Prediction is not perfect but contains error Error (SEE) is low if r is high Equation is Y=(bX)+C Y is the predicted value

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Chapter 2F Statistical Tools in Evaluation

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  1. Chapter 2FStatistical Tools in Evaluation

  2. Linear Regression • Predict one variable from others • If measurement on one variable is difficult • Prediction is not perfect but contains error • Error (SEE) is low if r is high • Equation is Y=(bX)+C • Y is the predicted value • b is the slope of the line and X is the value of the other • C is the Y intercept (constant)

  3. Prediction-Regression Analysis • Regression – statistical model used to predict performance on one variable from another. • Simple regression – predicting a score on one variable (Y) from one other variable (X). • Multiple regression – predicting a score on one variable (Y) from two or more other variables (X1, X1, etc.)

  4. General Prediction Equation Y = (bX) + C b = slope of regression line (rate of change in Y per unit change in X) c = Y-intercept or constant (Y when X=zero)

  5. Standard Error of Estimate (SEE) • R=regression while r=correlation • Predicted Score = Y • Y will not be perfect unless r = 1 • When r  1 there is prediction error • The standard deviation of this error = SEE • SEE = Sy1 - r2

  6. Standard Error of Estimate (SEE) • Expect to find the subjects’ real score in the boundaries: Y ± 2 (SEE) 95% of the time • The equation with the lowest SEE is the most accurate.

  7. Other important measures • R = correlation between predicted and real score • Ranges between 0 and 1.00 • An index of prediction accuracy • R2 = coefficient of determination • Proportion of variance in criterion (Y scores) explained by the predictor (X scores) • An index of prediction accuracy

  8. Regression Equation • Y=(bX)+C • Y is the predicted value • b is the slope of the line and X is the value • C is the Y intercept (constant)

  9. Confidence Intervals (CI) • SEE x 2 • Determines error around the predicted score • Multiply the SEE x 2 to get 95% confidence

  10. Simple Regression • Trying to predict height from weight. • Run SPSS regression and choose linear.

  11. Simple Regression Solved • Subject #1, Y=(bx)+C • Y=(.06x115)+56.81 • Y=6.9+56.81 • Y=63.71 • Predicted score = 63.71+(SEEx2) • Answer = 63.71+6.98 • 95% of the time the real score will fall between 56.73 - 70.69

  12. Multiple Regression • Predict criterion (Y) using several predictors (X1, X2, X3, etc) • Basic multiple regression equation has one intercept (c) and several bs (one for each predictor variable). • Y = (bX1 + bX2 + bX3) + c • Important measures: R, R2, SEE

  13. Multiple Regression • Trying to predict height from weight and Rgrip. • Run SPSS regression and choose linear.

  14. Multiple Regression Solved • Subject #1, Y= (bX1) + (bX2) + C • Y=(.02x115) + (.08x18) + 56.14 • Y=2.3+1.44+56.14 • Y=59.88 • Predicted score = 59.88+(SEEx2) • Answer = 59.88+4.24 • 95% of the time the real score will fall between 55.64 – 64.12

  15. Outcomes • Simple vs. Multiple Regression • R increased • SEE decreased THEREFORE • 95% confidence intervals decreased • Prediction accuracy increased

  16. SPSS • Analyze • Regression • Linear • Dependent variable (what to predict) • Independent variable (used to predict) • Constant, B value(s) and SEE

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