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NAEP Analysis and Scaling → Estimation of NAEP Score Scales → NAEP Assessment Item Response Theory Parameters → Mathematics Assessment Item Response Theory Parameters → IRT Parameters for the Number Sense, Properties, and Operations Scale, by Block and Item, Grade 8 Mathematics Combined National and State Main Assessment: 2003

NAEP Technical DocumentationIRT parameters for items in the number sense, properties, and operations scale, by block and item, grade 8 mathematics combined national and state main assessment: 2003

Block	Item	NAEP ID	aj	bj	cj	dj1	dj2	dj3	dj4
M3	8	M066401	0.72	-0.41	0.14	†	†	†	†
	9	M020101	1.27	-0.67	0.00	†	†	†	†
	16	M086001	0.93	1.03	0.19	†	†	†	†
	17	M051901	1.84	0.59	0.08	†	†	†	†
M4	1	M046001	0.51	-2.83	0.00	†	†	†	†
	5	M046901	0.88	-1.82	0.00	†	†	†	†
	8	M046801	0.65	-1.36	0.00	†	†	†	†
	9	M067801	0.87	-1.65	0.06	†	†	†	†
	18	M053001	0.73	1.97	0.00	†	†	†	†
M5	7	M020001	0.72	-0.49	0.00	†	†	†	†
	8	M046301	0.89	-1.07	0.28	†	†	†	†
	10	M046501	0.92	-0.23	0.33	†	†	†	†
	16	M051501	1.20	1.22	0.20	†	†	†	†
M6	1	M017401	0.25	-5.16	0.19	†	†	†	†
	2	N202831	0.75	-2.58	0.25	†	†	†	†
	7	M018201	0.52	-1.21	0.03	†	†	†	†
	9	M017701	1.00	-1.01	0.16	†	†	†	†
	11	M018401	1.11	-1.03	0.24	†	†	†	†
	12	M017901	1.15	-0.93	0.15	†	†	†	†
	16	M020501	0.72	-0.62	0.00	†	†	†	†
	17	M018501	1.64	0.34	0.26	†	†	†	†
	19	M018601	0.78	0.90	0.12	†	†	†	†
M7	2	M011131	0.79	-1.00	0.43	†	†	†	†
	6	M0734CL	0.26	1.49	†	-5.51	5.51	†	†
	9	M012531	0.72	0.49	0.16	†	†	†	†
	11	M012931	1.28	0.57	0.22	†	†	†	†
	16	M075901	0.53	0.95	0.14	†	†	†	†
M8	3	M073001	1.36	-0.10	0.14	†	†	†	†
	5	M073101	0.93	0.76	0.36	†	†	†	†
	14	M012431	0.81	-0.07	0.12	†	†	†	†
	15	M091901	0.56	0.05	0.19	†	†	†	†
	19	M073601	0.58	1.13	†	-0.13	-0.24	0.38	-0.01
M9	1	M013431	0.96	-0.31	0.09	†	†	†	†
	6	M091501	1.38	0.46	0.19	†	†	†	†
	7	M091601	1.12	0.21	0.24	†	†	†	†
	9	M052401	0.65	0.36	0.00	†	†	†	†
	12	M013631	1.59	0.29	0.06	†	†	†	†
	15	M013531	0.70	1.05	0.08	†	†	†	†
M10	1	M051201	0.64	-1.23	0.00	†	†	†	†
	2	M051601	0.87	-0.73	0.00	†	†	†	†
	5	M052901	0.68	-0.08	0.00	†	†	†	†
	10	M093101	1.05	0.07	0.19	†	†	†	†
M11	1	M105601	0.93	-0.03	0.16	†	†	†	†
	3	M105901	0.65	-1.94	0.20	†	†	†	†
	5	M106101	0.81	-1.13	0.16	†	†	†	†
	9	M106501	1.15	-0.26	0.26	†	†	†	†
	19	M107601	1.56	0.56	0.07	†	†	†	†
M12	1	M109801	0.96	-0.38	0.14	†	†	†	†
	11	M110901	1.34	1.12	0.12	†	†	†	†
	12	M111001	0.76	0.85	0.16	†	†	†	†
	18	M111801	0.52	-0.26	†	-0.46	0.46	†	†
† Not applicable; c parameters are not estimated for generalized partial credit models. NOTE: For item j, aj represents the discriminatory power of the item, bj represents a location parameter related to item difficulty, cj represents the guessing parameter, and dji is the category threshold parameter for category i. The c parameter value is exactly zero for items scaled with the two-parameter logistic model. For item j, dji may not sum to zero because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 Mathematics Assessment.

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