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NAEP Technical DocumentationComparisons of Means and Percentiles of Scores and Transformed Provisional Scores, Grade 12 Mathematics National Assessment, by Scale: 2019
In 2019, both a paper-based assessment (PBA) and a digitally based assessment (DBA) were administered. PBA estimates are based on the PBA sample scale score results on the reporting metric. Provisional DBA estimates are based on DBA sample scaling results. These are on the theta metric specified by the scaling program. The PBA estimates and provisional DBA estimates are used to find the transformation constants necessary to place the DBA sample scale scores on the scale used to report previous assessment scale scores. The transformed DBA estimates are based on DBA sample scaling results, transformed to the reporting metric using the transformation constants calculated from the PBA estimates and provisional DBA estimates. If the transformation constants are correct, the PBA and transformed DBA means should be the same.
Original estimates are based on previous assessment data and previous assessment scaling results, transformed to the reporting metric using the transformation identified during the analysis of the previous assessment data. Provisional estimates are based on previous assessment data and 2019 PBA sample scaling results. These are on the theta metric specified by the scaling program. The original and provisional estimates for the linking sample are used to find the transformation constants necessary to place the 2019 PBA sample scale scores on the scale used to report previous assessment scale scores. The transformed provisional estimates are based on previous assessment data and 2019 PBA sample scaling results, transformed to the reporting metric using the transformation constants calculated from the original and provisional estimates for the linking sample. If the transformation constants are correct, the original and transformed provisional means should be the same.
| Statistic | Original 2019 PBA estimate | 2019 DBA-transformed provisional estimate | Difference between the provisional estimate and the original estimate |
|---|---|---|---|
| Rounds to zero. | |||
| PBA = Paper-based assessment. DBA = Digitally based assessment. The differences are based on the unrounded estimates. Since 2005, the measurement and geometry scales are combined at grade 12. | |||
| U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2019 Mathematics Assessment. | |||
| Composite scale | |||
| Mean | 150.28 | 150.28 | |
| 10th percentile | 104.84 | 103.91 | -0.93 |
| 25th percentile | 125.46 | 124.98 | -0.48 |
| 50th percentile | 150.04 | 150.55 | 0.51 |
| 75th percentile | 175.24 | 175.39 | 0.15 |
| 90th percentile | 196.59 | 196.01 | -0.58 |
| Number properties and operations | |||
| Mean | 144.49 | 144.49 | |
| 10th percentile | 94.69 | 94.95 | 0.26 |
| 25th percentile | 117.93 | 117.66 | -0.27 |
| 50th percentile | 144.39 | 144.25 | -0.14 |
| 75th percentile | 171.46 | 171.35 | -0.11 |
| 90th percentile | 194.59 | 194.20 | -0.39 |
| Measurement and geometry | |||
| Mean | 149.33 | 149.33 | |
| 10th percentile | 105.52 | 105.13 | -0.39 |
| 25th percentile | 125.89 | 125.66 | -0.23 |
| 50th percentile | 149.56 | 149.82 | 0.26 |
| 75th percentile | 173.38 | 173.14 | -0.24 |
| 90th percentile | 193.16 | 192.46 | -0.70 |
| Data analysis, statistics, and probability | |||
| Mean | 150.06 | 150.06 | |
| 10th percentile | 99.59 | 98.95 | -0.64 |
| 25th percentile | 123.06 | 122.26 | -0.80 |
| 50th percentile | 150.13 | 150.04 | -0.09 |
| 75th percentile | 177.76 | 177.68 | -0.08 |
| 90th percentile | 201.27 | 200.85 | -0.42 |
| Algebra | |||
| Mean | 152.91 | 152.91 | |
| 10th percentile | 106.84 | 105.86 | -0.98 |
| 25th percentile | 127.73 | 127.48 | -0.25 |
| 50th percentile | 152.30 | 153.24 | 0.94 |
| 75th percentile | 177.74 | 178.28 | 0.54 |
| 90th percentile | 200.37 | 199.11 | -1.26 |
| Statistic | Original 2015 PBA estimate | 2015 PBA-transformed provisional estimate | Difference between the provisional estimate and the original estimate |
|---|---|---|---|
| Rounds to zero. | |||
| PBA = Paper-based assessment. The differences are based on the unrounded estimates. Since 2005, the measurement and geometry scales are combined at grade 12. | |||
| U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2015 and 2019 Mathematics Assessments. | |||
| Composite scale | |||
| Mean | 151.52 | 151.52 | |
| 10th percentile | 107.41 | 107.41 | |
| 25th percentile | 128.02 | 128.06 | 0.04 |
| 50th percentile | 151.71 | 151.71 | |
| 75th percentile | 175.48 | 175.46 | -0.02 |
| 90th percentile | 195.99 | 195.92 | -0.07 |
| Number properties and operations | |||
| Mean | 146.98 | 146.98 | |
| 10th percentile | 100.76 | 100.66 | -0.10 |
| 25th percentile | 122.53 | 122.58 | 0.05 |
| 50th percentile | 146.72 | 146.96 | 0.24 |
| 75th percentile | 171.78 | 171.82 | 0.05 |
| 90th percentile | 194.09 | 193.85 | -0.24 |
| Measurement and geometry | |||
| Mean | 151.55 | 151.55 | |
| 10th percentile | 108.08 | 108.08 | |
| 25th percentile | 128.77 | 128.76 | -0.01 |
| 50th percentile | 152.17 | 152.14 | -0.03 |
| 75th percentile | 175.03 | 175.02 | -0.01 |
| 90th percentile | 194.70 | 194.66 | -0.04 |
| Data analysis, statistics, and probability | |||
| Mean | 150.69 | 150.69 | |
| 10th percentile | 100.88 | 100.82 | -0.06 |
| 25th percentile | 124.60 | 124.71 | 0.11 |
| 50th percentile | 151.17 | 151.32 | 0.15 |
| 75th percentile | 177.61 | 177.67 | 0.06 |
| 90th percentile | 200.38 | 200.26 | -0.12 |
| Algebra | |||
| Mean | 153.39 | 153.39 | |
| 10th percentile | 109.00 | 109.04 | 0.04 |
| 25th percentile | 129.81 | 129.77 | -0.04 |
| 50th percentile | 153.56 | 153.41 | -0.15 |
| 75th percentile | 177.47 | 177.40 | -0.07 |
| 90th percentile | 198.18 | 198.27 | 0.09 |
Last updated 05 October 2023 (SK)