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 8 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 8 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	282.91	282.91	#
	10th percentile	235.81	233.83	-1.98
	25th percentile	259.25	257.91	-1.34
	50th percentile	284.11	283.91	-0.20
	75th percentile	308.16	309.04	0.88
	90th percentile	328.64	330.80	2.16
Number sense, properties, and operations	Mean	280.39	280.39	#
	10th percentile	232.88	232.63	-0.25
	25th percentile	257.12	256.27	-0.85
	50th percentile	282.11	281.54	-0.57
	75th percentile	305.73	305.89	0.16
	90th percentile	325.79	326.65	0.86
Measurement	Mean	279.92	279.92	#
	10th percentile	218.87	218.56	-0.31
	25th percentile	249.61	248.85	-0.76
	50th percentile	281.63	281.29	-0.34
	75th percentile	312.45	312.63	0.18
	90th percentile	338.94	339.57	0.63
Geometry and spatial sense	Mean	279.49	279.49	#
	10th percentile	235.22	235.10	-0.12
	25th percentile	257.43	256.66	-0.77
	50th percentile	280.62	280.10	-0.52
	75th percentile	302.92	303.01	0.09
	90th percentile	322.33	323.03	0.70
Data analysis, statistics, and probability	Mean	284.69	284.69	#
	10th percentile	229.86	229.42	-0.44
	25th percentile	257.63	256.84	-0.79
	50th percentile	286.68	286.10	-0.58
	75th percentile	313.98	314.27	0.29
	90th percentile	337.29	338.21	0.92
Algebra and functions	Mean	287.47	287.47	#
	10th percentile	239.92	239.95	0.03
	25th percentile	263.79	262.96	-0.83
	50th percentile	288.67	288.15	-0.52
	75th percentile	312.86	312.89	0.03
	90th percentile	333.64	334.44	0.80

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