Large-scale Assessments in Education

An IERI – International Educational Research Institute Journal

Table 8 Hit rates and Type I error rates in the simulation study

From: A structural equation modeling approach for examining position effects in large-scale assessments

Simulation factors				Estimated position effect				Estimated item difficulty
Sample size	Position effect	Change in position	Total position effect (β)	\(\hat{\beta }\)	95% coverage	Hit rate	Type I error rate	RMSE	ME
1000	−.01	40	−.4	−.405	.958	.723	.051	.0058	.0033
	−.01	25	−.25	−.248	.951	.351
	−.01	10	−.1	−.097	.951	.086
	−.02	40	−.8	−.805	.947	.999
	−.02	25	−.5	−.504	.957	.892
	−.02	10	−.2	−.204	.948	.252
5000	−.01	40	−.4	−.402	.951	1	.049	.0017	.0007
	−.01	25	−.25	−.249	.953	.945
	−.01	10	−.1	−.099	.946	.279
	−.02	40	−.8	−.8	.94	1
	−.02	25	−.5	−.499	.96	1
	−.02	10	−.2	−.203	.96	.821
10,000	−.01	40	−.4	−.402	.947	1	.049	.0009	<.0001
	−.01	25	−.25	−.248	.95	.999
	−.01	10	−.1	−.099	.951	.48
	−.02	40	−.8	−.8	.942	1
	−.02	25	−.5	−.498	.961	1
	−.02	10	−.2	−.202	.954	.976

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