NAEP Technical Documentation Evaluation of the Samples for the 2017 State Assessment Using State Achievement Data

The purpose of this analysis was to determine whether public schools selected for the 2017 samples were representative of the schools on the NAEP sampling frames in terms of student achievement. Percentiles of the achievement distributions were compared between the frame and sample schools for each public school jurisdiction in grades 4 and 8.

Achievement Data

For grades 4 and 8, the achievement variable used in the analysis was the same variable used in the NAEP sample design to stratify the public school frame. For most jurisdictions, the variable was an achievement score provided by the jurisdiction. However, for some jurisdictions where achievement data were not available, median household income from the 2010-2014 American Community Survey (ACS) was used. (Median household income was based on the five-digit zip code area in which the school was located.) The achievement data consisted of various types of school-specific achievement measures from state assessment programs. The type of achievement data available varied by jurisdiction. For instance, in some states, the measure was the average score for a given state assessment. In other states, the measure was a percentile rank or percentage of students above a specific score. In California for example, which has its own readily accessible achievement data system (the California Assessment of Student Performance and Progress System), we used the school mean of student mathematics achievement scores.

During frame development, not every record on the Common Core of Data (CCD) file matched to the achievement data files created for the National Center for Education Statistics (NCES), even in jurisdictions where those data were generally available. For schools that did not match, their achievement score was imputed by a mean matching imputation approach using the mean achievement score for schools with complete achievement data within the same jurisdiction-urbanicity-race/ethnicity stratum combination.

Methodology

To determine whether the distributions between the frame and sample schools were different, comparisons of percentile estimates were made for the 10th, 25th, 50th, 75th, and 90th percentile levels as well as the mean for each public school jurisdiction by grade. Frame and sample school estimates were considered statistically different if the frame value fell outside the 95 percent confidence interval of the corresponding sample estimate. The percentile values for the frame schools were calculated by weighting each school by the estimated number of students in the given grade. The percentile estimates for the sample schools were calculated using school weights and weighted by the school measure of size (estimated number of students in the given grade). The 95 percent confidence intervals for the school sample estimates were calculated in WesVar—software for computing estimates of sampling variance from complex sample survey (Westat, 2000b)—using the Woodruff method (Sarndal, Swensson, and Wretman 1992) with the use of a finite population correction factor.

Results

As mentioned above, sample and frame achievement distributions were determined to be different if at least one of the percentile estimates or the mean differed significantly at the 95 percent confidence level. Out of all the jurisdiction and grade comparisons (excluding jurisdictions where all schools in the frame were selected), only 7 of the 948 distributions compared were found to be significantly different. They are shown in the table below.

Summary of significant differences in achievement measures between the sample and the frame, state assessment, by jurisdiction and grade: 2017

Grade	Jurisdiction	Achievement data / median income	Estimate	Frame	Sample	Confidence interval
4	Arizona	Achievement data	mean	64.39	63.26	(62.18, 64.33)
	Maryland	Achievement data	75th percentile	94.93	94.85	(94.82, 94.88)
	North Dakota	Achievement data	50th percentile	83.43	83.82	(83.47, 84.85)
	Charlotte-Mecklenburg TUDA	Achievement data	90th percentile	82.57	81.76	(81.68, 81.89)
	Duval County TUDA	Achievement data	90th percentile	81.65	81.55	(81.02, 81.64)
8	Maine	Achievement data	10th percentile	46.31	46.95	(46.41, 47.34)
	Duval County TUDA	Achievement data	10th percentile	24.68	24.72	(24.69, 24.77)
	SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2017 State Assessment.

The number of significant differences found in this analysis was smaller than what would be expected to occur by chance, given the large number of comparisons that were made. Also, the number of significant differences remained small even with the added use of a finite population correction factor in the calculation of the sampling variances. Even in the statistically significant cases, the close adherence of sample values to frame values suggests there is little evidence that the school sample for NAEP 2017 is not representative of the frame from which it was selected. The achievement/median income variable is used as the fourth-level sort order variable in the school systematic selection procedure. While it may be a rather low level sort variable, it still helps control how representative the sampled schools are in terms of achievement. The close agreement between frame and sample values of these achievement/median income variables provided assurance that the selected sample is representative of the frame with respect to achievement or income status.

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