NAEP Analysis and Scaling → Scale Linking and Transformation to the Reporting Metric → Comparisons of Distributions of Linking Samples for NAEP Assessments → Comparison of Means and Percentiles of 2009 Scores and 2009 Transformed Provisional Scores, Grade 4 Mathematics Combined National and State Assessments, By Scale: 2011

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.

NAEP Technical DocumentationComparison of means and percentiles of 2009 scores and 2009 transformed provisional scores, grade 4 mathematics combined national and state assessments, by scale: 2011

Scale	Statistics	Original 2009 estimate	2009-transformed provisional estimate	Difference between the provisional estimate and the original estimate
# Rounds to zero. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2011 Mathematics Assessment.
Composite scale	Mean	239.67	239.67	#
	10th percentile	202.05	200.44	-1.61
	25th percentile	221.25	220.38	-0.87
	50th percentile	241.19	241.28	0.09
	75th percentile	259.67	260.51	0.84
	90th percentile	275.15	276.50	1.35
Number sense, properties, and operations	Mean	238.27	238.27	#
	10th percentile	196.58	196.39	-0.19
	25th percentile	218.05	217.65	-0.40
	50th percentile	240.10	239.97	-0.13
	75th percentile	260.48	260.55	0.07
	90th percentile	277.40	277.64	0.24
Measurement	Mean	238.36	238.36	#
	10th percentile	193.23	192.64	-0.59
	25th percentile	216.27	215.93	-0.34
	50th percentile	240.38	240.23	-0.15
	75th percentile	262.36	262.59	0.23
	90th percentile	280.92	281.27	0.35
Geometry and spatial sense	Mean	238.76	238.76	#
	10th percentile	205.51	205.01	-0.50
	25th percentile	222.08	221.79	-0.29
	50th percentile	239.54	239.61	0.07
	75th percentile	256.38	256.63	0.25
	90th percentile	271.12	271.34	0.22
Data analysis, statistics, and probability	Mean	242.66	242.66	#
	10th percentile	203.83	203.26	-0.57
	25th percentile	223.72	223.22	-0.50
	50th percentile	244.10	244.29	0.19
	75th percentile	263.16	263.56	0.40
	90th percentile	279.60	279.79	0.19
Algebra and functions	Mean	244.07	244.07	#
	10th percentile	209.35	208.84	-0.51
	25th percentile	227.02	226.92	-0.10
	50th percentile	245.33	245.59	0.26
	75th percentile	262.48	262.76	0.28
	90th percentile	277.14	277.17	0.03

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