Lord's Chi-Square Test of Item Bias With Estimated and With Known Person Parameters

Properties of Lord’s chi-square test of item bias studied in a computer simulation. 0 parameters drawn from a standard normal distribution and to a 50-item test were generated using SAT-v parameters estimated by Lord. One hundred independent were generated under each of the combinations of two sample sizes (N = 1,000 N = 250) and two logistic models (two- and -parameter). LOGIST was used to estimate item person parameters simultaneously. For each of the 50 items, 50 independent chi-square tests of the equality item parameters were calculated. Proportions of chi-squares were calculated over items and , at alpha levels of .0005, .001, .005, .01, .05, and .10. The overall proportions significant were high as 11 times the nominal alpha level. The proportion for some items was as high as .32 the nominal alpha level was .05. When person were held fixed at their true values and item parameters were estimated, the actual rejection were close to the nominal rates.