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NAEP Analysis and Scaling → Estimation of Population and Student Group Distributions → Examining the Population-Structure Models Used in NAEP → Proportion of Scale Score Variance Accounted for by the Population-Structure Models → Proportion of Scale Score Variance Accounted for by the Population-Structure Models, Grade 4 Mathematics Combined National and State Main Assessment, by Subscale and Jurisdiction: 2005

NAEP Technical DocumentationProportion of scale score variance accounted for by the population-structure models, grade 4 mathematics combined national and state main assessment, by subscale and jurisdiction: 2005

Jurisdiction	Number of principal components2	Proportion1 of scale score variance accounted for by the  population-structure model
		Number, properties, and operations	Measurement	Geometry	Data analysis and probability	Algebra
Alabama	232	0.54	0.56	0.56	0.55	0.55
Alaska	151	0.40	0.40	0.37	0.37	0.35
Arizona	254	0.56	0.57	0.57	0.57	0.54
Arkansas	241	0.53	0.53	0.53	0.53	0.50
California	373	0.52	0.52	0.48	0.50	0.47
Colorado	244	0.53	0.53	0.51	0.53	0.49
Connecticut	252	0.57	0.60	0.59	0.62	0.55
Delaware	211	0.49	0.53	0.52	0.52	0.49
Florida	307	0.49	0.50	0.52	0.51	0.46
Georgia	264	0.53	0.55	0.50	0.55	0.53
Hawaii	243	0.55	0.56	0.60	0.59	0.57
Idaho	245	0.49	0.49	0.48	0.50	0.51
Illinois	274	0.56	0.60	0.60	0.58	0.56
Indiana	236	0.51	0.53	0.50	0.55	0.52
Iowa	219	0.46	0.43	0.42	0.44	0.45
Kansas	227	0.46	0.50	0.47	0.48	0.45
Kentucky	229	0.44	0.46	0.47	0.47	0.46
Louisiana	233	0.55	0.59	0.56	0.55	0.60
Maine	254	0.46	0.49	0.44	0.44	0.45
Maryland	224	0.56	0.60	0.58	0.53	0.57
Massachusetts	276	0.52	0.61	0.51	0.57	0.52
Michigan	213	0.56	0.61	0.55	0.57	0.52
Minnesota	237	0.51	0.51	0.51	0.53	0.49
Mississippi	243	0.50	0.55	0.56	0.56	0.51
Missouri	244	0.48	0.53	0.48	0.53	0.48
Montana	255	0.45	0.47	0.47	0.51	0.52
Nebraska	220	0.53	0.60	0.58	0.54	0.48
Nevada	254	0.50	0.53	0.51	0.50	0.53
New Hampshire	254	0.49	0.56	0.48	0.50	0.50
New Jersey	252	0.55	0.57	0.57	0.55	0.55
New Mexico	277	0.52	0.55	0.53	0.51	0.56
New York	302	0.52	0.52	0.51	0.52	0.47
North Carolina	271	0.53	0.54	0.55	0.55	0.53
North Dakota	230	0.45	0.47	0.45	0.55	0.42
Ohio	241	0.55	0.59	0.55	0.54	0.49
Oklahoma	256	0.51	0.54	0.52	0.53	0.51
Oregon	245	0.50	0.54	0.48	0.49	0.47
Pennsylvania	229	0.54	0.59	0.56	0.56	0.51
Rhode Island	240	0.56	0.60	0.57	0.56	0.51
South Carolina	235	0.51	0.55	0.58	0.59	0.52
South Dakota	253	0.48	0.51	0.51	0.52	0.50
Tennessee	244	0.51	0.53	0.55	0.55	0.53
Texas	334	0.45	0.45	0.49	0.46	0.45
Utah	227	0.49	0.50	0.44	0.51	0.49
Vermont	223	0.42	0.54	0.49	0.44	0.47
Virginia	244	0.54	0.57	0.55	0.57	0.53
Washington	242	0.50	0.51	0.50	0.55	0.49
West Virginia	239	0.42	0.42	0.42	0.41	0.42
Wisconsin	233	0.54	0.60	0.57	0.56	0.55
Wyoming	198	0.48	0.49	0.49	0.49	0.47
Other jurisdictions
District of Columbia	164	0.51	0.55	0.58	0.52	0.52
DoDEA3	230	0.47	0.53	0.53	0.53	0.53
1 (Total Variance – Residual Variance)/Total Variance, where Total Variance consists of both sampling and measurement error variance. 2Excluding the constant term. 3 Department of Defense Education Activity. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2005 Mathematics Assessment.

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