Table of Contents | Search Technical Documentation | References
NAEP Analysis and Scaling → Estimation of Population and Student Group Distributions → Examining the Population-Structure Models Used in NAEP → Proportion of Variance Accounted for by Principal Components Used in NAEP Population-Structure Models → Proportion of Variance of the Group-Defining Contrasts Accounted for by the Principal Components Used in the Population-Structure Model, Grade 12 Mathematics National Assessment, by Type of Contrast: 2019
NAEP Technical DocumentationProportion of Variance of the Group-Defining Contrasts Accounted for by the Principal Components Used in the Population-Structure Model, Grade 12 Mathematics National Assessment, by Type of Contrast: 2019
| Type of contrast | Number of contrasts | Mean | Minimum | Maximum | Number of contrasts by proportion of variance explained | ||||
|---|---|---|---|---|---|---|---|---|---|
| .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. | |||||||||
| DBA = Digitally based assessment. SD/EL = Students with disabilities/English learners. | |||||||||
| U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment. | |||||||||
| All contrasts | 1414 | .90 | .72 | .99 | 0 | 40 | 599 | 577 | 198 |
| Student questionnaire | 530 | .91 | .75 | .98 | 0 | 13 | 166 | 252 | 99 |
| Major reporting variables | 78 | .92 | .82 | .99 | 0 | 0 | 31 | 23 | 24 |
| Interactions between reporting variables | 323 | .89 | .72 | .98 | 0 | 24 | 125 | 139 | 35 |
| School questionnaire | 452 | .89 | .78 | .97 | 0 | 3 | 263 | 153 | 33 |
| SD/EL questionnaire | 31 | .89 | .80 | .96 | 0 | 0 | 14 | 10 | 7 |
| Type of contrast | Number of contrasts | Mean | Minimum | Maximum | Number of contrasts by proportion of variance explained | ||||
|---|---|---|---|---|---|---|---|---|---|
| .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. | |||||||||
| PBA = Paper-based assessment. SD/EL = Students with disabilities/English learners. | |||||||||
| U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment. | |||||||||
| All contrasts | 1444 | .90 | .71 | .99 | 0 | 45 | 591 | 619 | 189 |
| Student questionnaire | 553 | .91 | .72 | .98 | 0 | 24 | 165 | 271 | 93 |
| Major reporting variables | 83 | .92 | .78 | .99 | 0 | 1 | 29 | 28 | 25 |
| Interactions between reporting variables | 329 | .90 | .71 | .98 | 0 | 17 | 121 | 153 | 38 |
| School questionnaire | 449 | .89 | .79 | .98 | 0 | 1 | 264 | 159 | 25 |
| SD/EL questionnaire | 30 | .89 | .77 | .97 | 0 | 2 | 12 | 8 | 8 |
Last updated 05 October 2023 (SK)