1. James L. Szalma Department of Psychology and Institute for Simulation and Training University of Central Florida Analysis of Individual Differences Data: Alternative to ANOVA

2. Typical Approach Categorization of continuous variables Median splits Extreme groups Advantage: fits the ANOVA model well

3. Pessimism Median Split Quartile Split Loss of Data (Extreme groups) Treats individuals within a group as equivalent Grouping of ‘Individual Differences’ data A difference of one unit may result in a label of ‘high’ or ‘low’ Arbitrary group assignment

4. Alternative Approach Regression Dummy coding categorical variables Can test for interactions between continuous variables and independent variables (Attribute Treatment Interaction) No arbitrary group assignment No loss of data

5. Example: Effect of KR and Pessimism on Stress Three forms of KR: –Hit KR –False Alarm KR –Miss KR Comparison to a No-KR control and a composite-KR control

6. Dummy Coding DHDH D FA DMDM Hit KR100 FA KR010 Miss KR001 Comp KR 000

7. Regression Model Criterion/Dependent variable: Task Engagement Predictors/Independent Variable: Pessimism KR (D1, D2, D3) Pessimism x KR

8. Hierarchical Regression Model 1: TE = Pess Model 2: TE = Pess + (D H + D FA + D M ) Model 3: TE = Pess + (D H + D FA + D M ) + (D HxP + D FAxP + D MxP ) Increments in variance accounted for by terms in the model

9. Regression Equation Variablebt Pess.093.63** DHDH 2.572.13* D FA 5.253.80** DMDM 1.991.59 D HxP -.07-2.27* D FAxP -.14-3.71** D MxP -.06-1.80

10. Regression Equation TE = -3.94 +.09Pess + 2.57D H + 5.25D FA + 1.99D M -.07D HxP -.14D FAxP -.06D MxP Variablebt Pess.093.63** DHDH 2.572.13* D FA 5.253.80** DMDM 1.991.59 D HxP -.07-2.27* D FAxP -.14-3.71** D MxP -.06-1.80

11. Task Engagement as a Function of Pessimism Task-Engagement Pessimism

12. Exploring Interactions: Johnson-Neyman Procedure Simultaneous Regions of Significance Examine group differences over a range of the continuous variable Analogous to tests of simple effects in ANOVA

13. Regions of Significance -2 -1.5 -0.5 0 0.5 1 1.5 2 18243036424854606672 Regions of Significance

14. Task Engagement as a Function of Pessimism Task-Engagement Pessimism Intersection = 29.87 Lower Bound: 36.67 Upper Bound: 313.61

15. More Complex Designs Multiple independent variables can be dummy coded (factorial designs) Effect coding can also be used More than one individual differences variable can be entered into the model –problem: complex interactions (e.g., 4-way interactions

16. References Johnson-Neyman Procedure: –Pedhazur, E.J. (1997). Multiple regression in behavioral research: Explanation and prediction, 3 rd Ed. Ft. Worth: Harcourt Brace Attribute-Treatment Interaction: –Cronbach, L.J., & Snow, R.E. (1977). Aptitudes and instructional methods: A handbook for research on interactions. New York: Irvington

17. ACKNOWLEDGEMENT This work was supported in part by the Department of Defense Multidisciplinary University Research Initiative (MURI) program, P.A. Hancock, principal investigator, administered by the Army Research Office under grant DAAD19-01-1-0621. The views expressed in this work are those of the author and do not necessarily reflect official Army policy. The author wishes to thank Dr. Sherry Tove, Dr. Elmar Schmeisser, and Dr. Mike Drillings for providing administrative and technical direction for the Grant.