NAEP Technical DocumentationComparisons of Means and Percentiles of Scores and Transformed Provisional Scores, Grade 4 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 4 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	Mean	240.39	240.39	#
	10th percentile	201.55	199.84	-1.71
	25th percentile	221.26	220.39	-0.87
	50th percentile	241.71	241.76	0.05
	75th percentile	260.84	261.65	0.80
	90th percentile	277.30	278.82	1.52
Number properties and operations	Mean	242.52	242.52	#
	10th percentile	199.56	199.41	-0.15
	25th percentile	221.55	221.25	-0.30
	50th percentile	244.21	244.05	-0.16
	75th percentile	265.09	265.14	0.05
	90th percentile	283.05	283.35	0.30
Measurement	Mean	238.25	238.25	#
	10th percentile	190.37	189.75	-0.62
	25th percentile	214.40	214.02	-0.38
	50th percentile	239.59	239.60	0.01
	75th percentile	263.48	263.71	0.23
	90th percentile	284.34	284.64	0.30
Geometry	Mean	235.91	235.91	#
	10th percentile	203.05	202.67	-0.38
	25th percentile	219.37	219.10	-0.26
	50th percentile	236.58	236.59	0.01
	75th percentile	253.24	253.41	0.17
	90th percentile	267.94	268.22	0.28
Data analysis, statistics, and probability	Mean	238.35	238.35	#
	10th percentile	198.30	197.76	-0.54
	25th percentile	218.76	218.30	-0.46
	50th percentile	239.76	239.66	-0.10
	75th percentile	259.44	259.72	0.29
	90th percentile	276.54	276.99	0.45
Algebra	Mean	243.40	243.40	#
	10th percentile	205.61	205.15	-0.46
	25th percentile	224.77	224.57	-0.20
	50th percentile	244.58	244.69	0.11
	75th percentile	263.19	263.45	0.26
	90th percentile	279.67	279.76	0.09
# 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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