NAEP Technical DocumentationQuadratic Function Coefficients Used for Linking Variance Calculation, Mathematics Combined National and State Assessment, by Grade, Scale, and Type of Statistic: 2017

Quadratic function coefficients used for linking variance calculation, mathematics combined national and state assessment, by grade, scale, and type of statistic: 2017

Grade	Scale	Type of statistic	A	B	C
4	Composite	Mean and percentiles	0.0000839000	-0.0404100000	4.9735200000
	Composite	Standard deviation	0.0000840500	-0.0000079000	0.0000473200
	Composite	Achievement level: At or above NAEP Basic	-0.0001521100	0.0157020000	-0.0995700000
	Composite	Achievement level: At or above NAEP Proficient	-0.0001201800	0.0120700000	-0.0626500000
	Composite	Achievement level: Below NAEP Basic	-0.0001521100	0.0147200000	-0.0504700000
	Composite	Achievement level: At NAEP Basic	0.0000000000	0.0000000000	0.1875850000
	Composite	Achievement level: At NAEP Proficient	0.0000000000	0.0000000000	0.1166560000
	Composite	Achievement level: At NAEP Advanced	-0.0001157200	0.0171400000	-0.0215500000
	Number properties and operations	Mean and percentiles	0.0000881800	-0.0432500000	5.4386900000
	Number properties and operations	Standard deviation	0.0000881800	-0.0000000007	-0.0000001901
	Measurement	Mean and percentiles	0.0001265900	-0.0602900000	7.3896000000
	Measurement	Standard deviation	0.0001265900	0.0000000082	0.0000000564
	Geometry	Mean and percentiles	0.0001119100	-0.0522000000	6.1708900000
	Geometry	Standard deviation	0.0001119100	-0.0000000124	0.0000000373
	Data analysis, statistics, and probability	Mean and percentiles	0.0001070000	-0.0510800000	6.2070200000
	Data analysis, statistics, and probability	Standard deviation	0.0001070000	0.0000000523	-0.0000005738
	Algebra	Mean and percentiles	0.0000857900	-0.0413200000	5.0794800000
	Algebra	Standard deviation	0.0000857900	0.0000000019	-0.0000000834
8	Composite	Mean and percentiles	0.0000574400	-0.0335800000	5.0711400000
	Composite	Standard deviation	0.0000574000	-0.0000005746	0.0000332900
	Composite	Achievement level: At or above NAEP Basic	-0.0001641300	0.0165360000	-0.0975700000
	Composite	Achievement level: At or above NAEP Proficient	-0.0001082800	0.0105900000	-0.0427600000
	Composite	Achievement level: Below NAEP Basic	-0.0001641300	0.0162900000	-0.0852700000
	Composite	Achievement level: At NAEP Basic	0.0000000000	0.0000000000	0.1278110000
	Composite	Achievement level: At NAEP Proficient	0.0000000000	0.0000000000	0.0761480000
	Composite	Achievement level: At NAEP Advanced	-0.0000692900	0.0108900000	-0.0136800000
	Number properties and operations	Mean and percentiles	0.0000722500	-0.0407400000	5.9318400000
	Number properties and operations	Standard deviation	0.0000722500	-0.0000000077	0.0000001385
	Measurement	Mean and percentiles	0.0000667700	-0.0394800000	6.1726700000
	Measurement	Standard deviation	0.0000667700	0.0000000236	-0.0000001796
	Geometry	Mean and percentiles	0.0000857300	-0.0497100000	7.3532600000
	Geometry	Standard deviation	0.0000857300	-0.0000000438	0.0000005899
	Data analysis, statistics, and probability	Mean and percentiles	0.0000645200	-0.0358100000	5.2298900000
	Data analysis, statistics, and probability	Standard deviation	0.0000645200	-0.0000000122	0.0000002111
	Algebra	Mean and percentiles	0.0000677000	-0.0407000000	6.2912600000
	Algebra	Standard deviation	0.0000677000	0.0000000227	-0.0000002125
NOTE: The column headers A, B, and C stand for the coefficients of the quadratic equation which has the general form Ax2 + Bx + C. The term x represents the point estimation of the statistic. In 2017, grade 12 was not assessed. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2017 Mathematics Assessment.

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