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

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