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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 2005 Scores and 2005 Transformed Provisional Scores, Grade 4 Mathematics Combined National and State Main Assessment, by Scale: 2007

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 2005 scores and 2005 transformed provisional scores, grade 4 mathematics combined national and state main assessment, by scale: 2007

Scale	Statistic	Original 2005 estimate	2005 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), 2007 Mathematics Assessment.
Composite scale	Mean	237.87	237.87	#
	10th percentile	200.43	198.97	1.46
	25th percentile	219.57	219.15	0.42
	50th percentile	239.39	239.74	-0.35
	75th percentile	257.53	258.24	-0.71
	90th percentile	272.94	273.67	-0.73
Number Properties and Operations	Mean	236.03	236.03	#
	10th percentile	194.95	194.50	0.45
	25th percentile	216.05	216.04	0.01
	50th percentile	237.72	237.99	-0.27
	75th percentile	257.51	257.78	-0.27
	90th percentile	274.47	274.34	0.13
Measurement	Mean	237.24	237.24	#
	10th percentile	193.72	193.06	0.66
	25th percentile	215.94	215.86	0.08
	50th percentile	238.93	239.30	-0.37
	75th percentile	260.19	260.42	-0.23
	90th percentile	278.23	278.07	0.16
Geometry	Mean	236.00	236.00	#
	10th percentile	203.21	202.73	0.48
	25th percentile	219.78	219.69	0.09
	50th percentile	237.01	237.25	-0.24
	75th percentile	253.15	253.44	-0.29
	90th percentile	267.26	267.27	-0.01
Data Analysis and Probability	Mean	241.24	241.24	0.00
	10th percentile	204.98	204.25	0.73
	25th percentile	223.34	223.34	#
	50th percentile	242.45	242.86	-0.41
	75th percentile	260.27	260.62	-0.35
	90th percentile	275.68	275.55	0.13
Algebra	Mean	243.25	243.25	#
	10th percentile	206.62	206.14	0.48
	25th percentile	225.40	225.23	0.17
	50th percentile	244.69	244.88	-0.19
	75th percentile	262.50	262.74	-0.24
	90th percentile	277.70	277.65	0.05

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