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NAEP Analysis and Scaling → Estimation of NAEP Score Scales → Checks for Violations of Assumptions → Comparisons of Empirical and Theoretical Item Response Functions → Items Showing Good Item Fit → Dichotomous Item With Data for One Assessment Year

NAEP Technical DocumentationDichotomous Item With Data for One Assessment Year

This figure contains a plot of the empirical and theoretical item response functions (IRFs) for a dichotomous item from the 2000 grade 4 national main reading assessment. In the plot, the horizontal axis represents the provisional theta (θ) scale with mean 0 and standard deviation 1, while the vertical axis represents the probability of a correct response. The solid curve is the theoretical IRF based on the item parameter estimates and the equation for the three-parameter IRT model. The centers of the symbols represent the empirical proportions correct. The size of the symbols is proportional to the sum of the posteriors at each point on the θ scale for all of those who received the item; this is related to the number of students contributing to the estimation of that empirical proportion correct.

Dichotomous item exhibiting good model fit

SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP).

Centers of the inverted triangles represent 2000 grade 4 reading assessment data. This item has four alternatives. The curve indicates the estimated IRF assuming a logistic form.

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