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 4 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 4 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	1506	.83	.03	1.00	.03	1.00	316	62	112	192	824
Student questionnaire	295	.93	.15	1.00	.15	1.00	11	15	31	56	182
Major reporting variables	151	.63	.03	1.00	.03	1.00	72	6	6	10	57
Interactions between reporting variables	174	.73	.07	.99	.07	.99	67	8	12	32	55
Teacher questionnaire	421	.87	.08	1.00	.08	1.00	61	12	30	30	288
School questionnaire	465	.82	.06	1.00	.06	1.00	105	21	33	64	242

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 4 Mathematics Combined National and State Assessment, by Type of Contrast: 2022