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 2007 Scores and 2007 Transformed Provisional Scores, Grade 8 Mathematics Combined National and State Main Assessment, by Scale: 2009

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 2007 scores and 2007 transformed provisional scores, grade 8 mathematics combined national and state main assessment, by scale: 2009

Scale	Statistic	Original 2007 estimate	2007- 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), 2009 Mathematics Assessment.
Composite scale	Mean	281.35	281.35	#
	10th percentile	234.66	232.98	1.68
	25th percentile	257.85	256.71	1.14
	50th percentile	282.61	282.45	0.16
	75th percentile	306.32	307.22	-0.90
	90th percentile	326.60	328.42	-1.82
Number sense, properties, and operations	Mean	279.31	279.31	#
	10th percentile	231.69	231.60	0.09
	25th percentile	256.16	255.22	0.94
	50th percentile	281.28	280.77	0.51
	75th percentile	304.65	304.84	-0.19
	90th percentile	324.44	325.24	-0.80
Measurement	Mean	277.80	277.80	#
	10th percentile	216.17	215.86	0.31
	25th percentile	247.48	246.40	1.08
	50th percentile	279.99	279.33	0.66
	75th percentile	310.61	310.90	-0.29
	90th percentile	336.92	337.86	-0.94
Geometry and spatial sense	Mean	277.71	277.71	#
	10th percentile	234.12	234.01	0.11
	25th percentile	256.11	255.43	0.68
	50th percentile	279.07	278.54	0.53
	75th percentile	300.79	300.86	-0.07
	90th percentile	319.68	320.39	-0.71
Data analysis, statistics, and probability	Mean	284.73	284.73	#
	10th percentile	231.39	231.18	0.21
	25th percentile	258.52	257.72	0.80
	50th percentile	286.74	286.24	0.50
	75th percentile	313.11	313.28	-0.17
	90th percentile	335.66	336.41	-0.75
Algebra and functions	Mean	285.20	285.20	#
	10th percentile	238.74	238.68	0.06
	25th percentile	261.73	261.19	0.54
	50th percentile	286.21	285.84	0.37
	75th percentile	310.05	310.23	-0.18
	90th percentile	330.76	331.30	-0.54

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