NAEP Technical DocumentationComparisons of Means and Percentiles of Scores and Transformed Provisional Scores, Grade 8 Mathematics Combined National and State Assessment, by Scale: 2017

Original estimates are based on previous assessment data and previous assessment scaling results, transformed to the reporting metric using the transformation constants identified during the analysis of the previous assessment data. Provisional estimates are based on previous assessment data and current assessment scaling results. Prior to transformation, provisional estimates 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 current assessment scale scores on the scale used to report previous assessment scale scores. The transformed provisional estimates are based on previous assessment data and current assessment 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.

In 2017, both a paper-based assessment (PBA) and a digitally based assessment (DBA) were administered. The provisional PBA estimates were transformed based on the procedures described above. Then a common population linking was used to align the 2017 paper-based assessment results with the 2017 digitally based assessment results.

Comparison of means and percentiles of 2015 PBA scores and 2015-transformed provisional PBA scores, grade 8 mathematics combined national and state assessment, by scale: 2015 and 2017

Scale	Statistic	Original 2015 PBA estimate	2015-transformed provisional PBA estimate	Difference between the provisional estimate and the original estimate
Composite scale	Mean	282.22	282.22	#
	10th percentile	234.58	232.03	-2.55
	25th percentile	257.71	256.45	-1.26
	50th percentile	282.87	283.14	0.27
	75th percentile	307.70	309.03	1.33
	90th percentile	329.00	330.95	1.95
Number properties and operations	Mean	278.78	278.78	#
	10th percentile	232.01	231.22	-0.79
	25th percentile	254.70	254.12	-0.59
	50th percentile	279.31	279.41	0.10
	75th percentile	303.79	304.23	0.43
	90th percentile	325.10	325.36	0.26
Measurement	Mean	279.00	279.00	#
	10th percentile	218.09	217.39	-0.70
	25th percentile	248.49	247.47	-1.02
	50th percentile	280.49	280.11	-0.38
	75th percentile	311.34	311.80	0.45
	90th percentile	338.18	338.99	0.81
Geometry	Mean	279.87	279.87	#
	10th percentile	236.13	235.51	-0.62
	25th percentile	257.73	257.00	-0.73
	50th percentile	280.70	280.54	-0.16
	75th percentile	302.92	303.20	0.29
	90th percentile	322.67	323.13	0.47
Data analysis, statistics, and probability	Mean	281.61	281.61	#
	10th percentile	225.82	225.00	-0.82
	25th percentile	253.42	252.66	-0.75
	50th percentile	282.88	282.76	-0.12
	75th percentile	311.27	311.84	0.57
	90th percentile	335.97	336.53	0.56
Algebra	Mean	288.00	288.00	#
	10th percentile	237.94	237.52	-0.42
	25th percentile	262.80	262.13	-0.67
	50th percentile	289.29	289.11	-0.18
	75th percentile	314.80	315.11	0.31
	90th percentile	336.56	337.05	0.49
# Rounds to zero. NOTE: The differences are based on the unrounded estimates. PBA = Paper-based assessment. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2015 and 2017 Mathematics Assessments.

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