An important difference between CTT and IRT is the treatment of measurement error, indexed by the standard error of measurement.
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Since the standard error of measurement for most IQ tests is approximately 5, the ceiling may go up to 75.
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The Sobel test uses the magnitude of the indirect effect compared to its estimated standard error of measurement to derive a t statistic
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But most score changes fell within the test's standard error of measurement, which is about 30 points up or down on each section, the study found.
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Among other advantages, IRT provides a basis for obtaining an estimate of the location of a test-taker on a given latent trait as well as the standard error of measurement of that location.
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The confidence interval will be smaller when the standard error of measurement is smaller, and the standard error of measurement will be smaller when there is more information at the theta level of the examinee.
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The confidence interval will be smaller when the standard error of measurement is smaller, and the standard error of measurement will be smaller when there is more information at the theta level of the examinee.
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Maximizing information at the ability estimate is more appropriate for the confidence interval approach because it minimizes the conditional standard error of measurement, which decreases the width of the confidence interval needed to make a classification.
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