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Rasch-transformed raw scores and Two-way ANOVA: a simulation analysis.
Joseph Romanoski1, Graham Douglas
1University of Western Australia, WA, Australia. JoeRomanoski400@hotmail.com
Journal of Applied Measurement
|December 18, 2002
Summary
Untransformed 0-1 raw scores are inadequate for Two-Way analysis of variance (ANOVA). Rasch transformations are suitable for ANOVA, especially when accounting for item difficulty distributions and data fit.
Area of Science:
- Psychometrics
- Statistical analysis
Background:
- Untransformed 0-1 raw scores can lead to underestimated variable effects or spurious interactions in Two-Way ANOVA.
- Previous research by Dr. Susan Embretson highlighted issues with raw score analysis.
Purpose of the Study:
- To demonstrate the inadequacy of untransformed 0-1 raw scores for Two-Way ANOVA.
- To show the suitability of Rasch transformations for Two-Way ANOVA.
- To identify psychometric conditions where raw scores and Rasch transformations differ significantly in Two-Way ANOVA.
Main Methods:
- Utilized Monte Carlo simulations to compare raw scores and Rasch transformations.
- Investigated the impact of uniform, skewed, and normal item difficulty distributions.
- Examined the effects of fitting versus misfitting data on analysis outcomes.
Main Results:
- Confirmed the inadequacy of untransformed 0-1 raw scores in Two-Way ANOVA.
- Demonstrated the effectiveness of Rasch transformations for Two-Way ANOVA.
- Quantified underestimation and spuriousness under various item difficulty distributions and data fit conditions.
Conclusions:
- Rasch transformations are superior to raw scores for Two-Way ANOVA.
- Careful consideration of item difficulty distribution and data fit is crucial for accurate psychometric analysis.