Appendix A3. Table A3.1. General linear model results for RMSE under the unconditional model. Source DF SS Mean Square

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1 Appendix A3 Table A3.1. General linear model results for RMSE under the unconditional model. Source DF SS F Value Pr > F Model <.0001 Error Corrected Total R- Coeff Var Root MSE Proportion of Variation Accounted for Eta-d 0.94 ω % CI (0.94,0.95) Source DF Type III SS F Value Pr > F Semipartial Eta-d SS < NI < IM < DF < PD < SS*NI SS*IM SS*DF SS*PD NI*IM < NI*DF < NI*PD < IM*DF < IM*PD < DF*PD < SS*NI*IM SS*NI*DF SS*NI*PD SS*IM*DF SS*IM*PD SS*DF*PD NI*IM*DF < NI*IM*PD < NI*DF*PD < IM*DF*PD SS*NI*IM*DF SS*NI*IM*PD SS*NI*DF*PD SS*IM*DF*PD NI*IM*DF*PD SS*NI*IM*DF*PD Note: Under Source, the following abbreviations are used: SS =sample size; NI = number of items; IM = impact condition; DF = DIF magnitude; PD = percent of items with DIF.

2 Table A3.2. General linear model results for RMSE under the impact-only model. Source DF SS F Value Pr > F Model <.0001 Error Corrected Total R- Coeff Var Root MSE Proportion of Variation Accounted for Eta-d 0.92 ω % CI (0.91,0.92) Source DF Type III SS F Value Pr > F Semipartial Eta-d SS < NI < IM < DF < PD < SS*NI < SS*IM < SS*DF < SS*PD < NI*IM < NI*DF < NI*PD < IM*DF < IM*PD < DF*PD < SS*NI*IM < SS*NI*DF < SS*NI*PD < SS*IM*DF SS*IM*PD SS*DF*PD < NI*IM*DF NI*IM*PD NI*DF*PD < IM*DF*PD < SS*NI*IM*DF SS*NI*IM*PD SS*NI*DF*PD SS*IM*DF*PD NI*IM*DF*PD SS*NI*IM*DF*PD Note: Under Source, the following abbreviations are used: SS =sample size; NI = number of items; IM = impact condition; DF = DIF magnitude; PD = percent of items with DIF.

3 Table A3.3. General linear model results for RMSE under the impact-and-dif model. Source DF SS F Value Pr > F Model <.0001 Error Corrected Total R- Coeff Var Root MSE Proportion of Variation Accounted for Eta-d 0.93 ω % CI (0.93,0.93) Source DF Type III SS F Value Pr > F Semipartial Eta-d SS < NI < IM < DF < PD < SS*NI < SS*IM < SS*DF SS*PD < NI*IM < NI*DF NI*PD < IM*DF < IM*PD DF*PD SS*NI*IM < SS*NI*DF SS*NI*PD < SS*IM*DF SS*IM*PD < SS*DF*PD NI*IM*DF NI*IM*PD < NI*DF*PD IM*DF*PD SS*NI*IM*DF SS*NI*IM*PD SS*NI*DF*PD SS*IM*DF*PD NI*IM*DF*PD SS*NI*IM*DF*PD Note: Under Source, the following abbreviations are used: SS =sample size; NI = number of items; IM = impact condition; DF = DIF magnitude; PD = percent of items with DIF.

4 Table A3.4. Average RMSE across all scoring models and design factors at N = Items Unconditional Score Impact-Only Score Impact-and-DIF Score 33% Small DIF % Small DIF % Large DIF % Large DIF % Small DIF % Small DIF % Large DIF % Large DIF Large /Small Variance SD SD SD 33% Small DIF % Small DIF % Large DIF % Large DIF Items Unconditional Score Impact-Only Score Impact-and-DIF Score 33% Small DIF % Small DIF % Large DIF % Large DIF % Small DIF % Small DIF % Large DIF % Large DIF Large /Small Variance SD SD SD 33% Small DIF % Small DIF % Large DIF % Large DIF Items Unconditional Score Impact-Only Score Impact-and-DIF Score 33% Small DIF % Small DIF % Large DIF % Large DIF % Small DIF % Small DIF % Large DIF % Large DIF Large /Small Variance SD SD SD 33% Small DIF % Small DIF % Large DIF % Large DIF

5 Table A3.5. Average RMSE across all scoring models and design factors at N = Items Unconditional Score Impact-Only Score Impact-and-DIF Score 33% Small DIF % Small DIF % Large DIF % Large DIF % Small DIF % Small DIF % Large DIF % Large DIF Large /Small Variance SD SD SD 33% Small DIF % Small DIF % Large DIF % Large DIF Items Unconditional Score Impact-Only Score Impact-and-DIF Score 33% Small DIF % Small DIF % Large DIF % Large DIF % Small DIF % Small DIF % Large DIF % Large DIF Large /Small Variance SD SD SD 33% Small DIF % Small DIF % Large DIF % Large DIF Items Unconditional Score Impact-Only Score Impact-and-DIF Score 33% Small DIF % Small DIF % Large DIF % Large DIF % Small DIF % Small DIF % Large DIF % Large DIF Large /Small Variance SD SD SD 33% Small DIF % Small DIF % Large DIF % Large DIF

6 Table A3.6. Average RMSE across all scoring models and design factors at N = Items Unconditional Score Impact-Only Score Impact-and-DIF Score 33% Small DIF % Small DIF % Large DIF % Large DIF Medium /Medium Variance 33% Small DIF % Small DIF % Large DIF % Large DIF Large /Small Variance 33% Small DIF % Small DIF % Large DIF % Large DIF Items Unconditional Score Impact-Only Score Impact-and-DIF Score 33% Small DIF % Small DIF % Large DIF % Large DIF Medium /Medium Variance 33% Small DIF % Small DIF % Large DIF % Large DIF Large /Small Variance 33% Small DIF % Small DIF % Large DIF % Large DIF Items Unconditional Score Impact-Only Score Impact-and-DIF Score 33% Small DIF % Small DIF % Large DIF % Large DIF Medium /Medium Variance 33% Small DIF % Small DIF % Large DIF % Large DIF Large /Small Variance 33% Small DIF % Small DIF % Large DIF % Large DIF

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