NAEP Technical DocumentationProportion of Variance of the Group-Defining Contrasts Accounted for by the Principal Components and Contrast-Coded Direct Covariates Used in the Population-Structure Model, Grade 8 Mathematics Combined National and State Assessment, by Type of Contrast: 2022

Proportion of variance of the group-defining contrasts accounted for by the principal components and contrast-coded direct covariates used in the population-structure model, grade 8 mathematics combined national and state assessment, by type of contrast: 2022
Type of contrast	Number of contrasts	Mean	Total		Reportable		Number of contrasts by proportion of variance explained
Type of contrast	Number of contrasts	Mean	Minimum	Maximum	Minimum	Maximum	.00 - .70	.70 - .80	.80 - .90	.90 - .95	.95 - 1.00
(Total Variance – Residual Variance) / Total Variance, where Total Variance includes variance accounted and unaccounted for by the variables in the population-structure model.
The major reporting variables include the contrasts from the direct covariates.
U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2022 Mathematics Assessment.
All contrasts	1828	.83	.03	1.00	.03	1.00	384	67	138	257	982
Student questionnaire	469	.91	.05	1.00	.05	1.00	32	9	40	80	308
Major reporting variables	150	.66	.03	1.00	.03	1.00	71	4	6	10	59
Interactions between reporting variables	266	.72	.05	.99	.05	.99	106	17	24	55	64
Teacher questionnaire	483	.89	.11	1.00	.11	1.00	58	14	29	52	330
School questionnaire	460	.81	.08	1.00	.08	1.00	117	23	39	60	221

Last updated 24 July 2024 (SK)

​​​NAEP Technical DocumentationProportion of Variance of the Group-Defining Contrasts Accounted for by the Principal Components and Contrast-Coded Direct Covariates Used in the Population-Structure Model, Grade 8 Mathematics Combined National and State Assessment, by Type of Contrast: 2022