NAEP Technical DocumentationComparison of Means and Percentiles of 2013 Scores and 2013-Transformed Provisional Scores, Grade 4 Mathematics Combined National and State Assessment, by Scale: 2015

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 current assessment 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 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.

Comparison of means and percentiles of 2013 scores and 2013-transformed provisional scores, grade 4 mathematics combined national and state assessment, by scale: 2015

Scale	Statistic	Original 2013 estimate	2013-transformed provisional estimate	Difference between the provisional estimate and the original estimate
Composite	Mean	241.55	241.55	#
	10th percentile	202.82	201.60	-1.21
	25th percentile	222.45	221.46	-0.98
	50th percentile	243.03	242.75	-0.29
	75th percentile	262.08	262.75	0.67
	90th percentile	278.21	279.80	1.59
Number properties and operations	Mean	241.86	241.86	#
	10th percentile	199.91	199.93	0.02
	25th percentile	221.28	220.78	-0.50
	50th percentile	243.48	243.12	-0.36
	75th percentile	264.08	264.14	0.07
	90th percentile	281.50	282.02	0.52
Measurement	Mean	238.85	238.85	#
	10th percentile	191.88	191.77	-0.12
	25th percentile	215.78	215.09	-0.69
	50th percentile	240.70	240.16	-0.54
	75th percentile	263.63	263.82	0.19
	90th percentile	283.29	284.00	0.72
Geometry	Mean	240.83	240.83	#
	10th percentile	206.82	206.35	-0.47
	25th percentile	223.53	223.24	-0.29
	50th percentile	241.41	241.46	0.05
	75th percentile	258.79	259.10	0.31
	90th percentile	274.24	274.43	0.19
Data analysis, statistics, and probability	Mean	242.04	242.04	#
	10th percentile	201.40	200.99	-0.40
	25th percentile	221.97	221.22	-0.75
	50th percentile	243.37	243.15	-0.22
	75th percentile	263.53	263.89	0.36
	90th percentile	280.88	281.44	0.56
Algebra	Mean	244.73	244.73	#
	10th percentile	207.64	207.56	-0.08
	25th percentile	226.72	226.15	-0.57
	50th percentile	246.34	245.83	-0.50
	75th percentile	264.35	264.37	0.03
	90th percentile	279.65	280.38	0.72
# Rounds to zero. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2015 Mathematics Assessment.

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