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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 Variance of the Group-Defining Contrasts Accounted for by the Principal Components Used in NAEP Student Group Distribution Models → Proportion of Variance of the Group-Defining Contrasts Accounted for by the Principal Components Used in the Population-Structure Model, Grade 4 Mathematics Combined National and State Main Assessment: 2003

NAEP Technical DocumentationProportion of variance of the group-defining contrasts accounted for by the principal components used in the population-structure model, grade 4 mathematics combined national and state main assessment: 2003

Type of contrast	Number of contrasts	Mean	Minimum	Maximum	Number of contrasts by proportion of variance explained
					0.00 - 0.70	0.70 - 0.80	0.80 - 0.90	0.90 - 0.95	0.95 - 1.00
NOTE: A value of 1.00 in the table does not imply that all of a single contrast's variance is accounted for by the set of principal components. Rather, the proportion of variance accounted for is high and is closer to 1.00 than any other number when expressed with two decimals of precision. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003 Mathematics Assessment.
All contrasts	1518	0.90	0.59	1.00	11	103	503	579	322
Student questionnaire	135	0.87	0.59	0.99	3	21	54	33	24
Major reporting variables	104	0.92	0.71	1.00	0	6	25	35	38
Interactions between reporting variables	824	0.91	0.70	0.98	0	32	240	361	191
Teacher questionnaire	228	0.89	0.67	0.99	6	23	72	84	43
School questionnaire	227	0.87	0.65	0.98	2	21	112	66	26

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