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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