Presenter:  Anli Lin
Presentation type:  Talk
Presentation date/time:  7/28  9:25-9:50
 
Standard Error Analysis with Bootstrap and IRT Model
 
Anli Lin, Harcourt Assessment, Inc
Don Meagher, Harcourt Assessment, Inc
Christina Stellato, Harcourt Assessment, Inc
 
The purposes of this study are: a) to find a relationship between standard error of scaled scores and sample size; b) to compare the standard error of scaled scores obtained by sampling the data before calibration with the standard error of scaled scores obtained by sampling the data after calibrations; c) to compare the standard error of rounding scaled scores with the standard error of un-rounding scaled scores. Standard error was calculated with bootstrapping. Rasch model was used to calibrate with SAS program. Major results: a) For standard error trend, as sample sizes are less than 500, standard error drops fast as sample size increases; as sample sizes are between 500 and 1000, standard error changes slowly as sample size changes; standard error is relative stable as sample size is lager than 1000. b) Sample size could be decided based on the tolerance of standard error; c) Confidence intervals were calculated with sample sizes for reference of sample size decision; d) Sampling with IRT will needs more samples as compared to sampling without IRT to get same standard error; e) When samples size is small, standard errors of rounding scaled scores and un-rounding scaled scores have similar patterns; When sample size is large, standard errors of rounding scaled scores and un-rounding scaled scores have significant different patterns.