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.
McLaughlin, Mary E & Drasgow, Fritz. (1987). Lord's chi-square test of item bias with estimated and with known person parameters. Applied Psychological Measurement, 11, 161-173. doi:10.1177/014662168701100205
McLaughlin, Mary E.; Drasgow, Fritz.
Lord's chi-square test of item bias with estimated and with known person parameters.
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