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12 Apr 2018
Report

Weighted and Unweighted Correlation Methods for Large-Scale Educational Assessment: wCorr Formulas

AIR - NAEP Working Paper #2018-01, NCES Data R Project Series #02

Paul Bailey, Ahmad Emad, and Ting Zhang, AIR
Qingshu Xie, MacroSys
Emmanuel Sikali, National Center for Education Statistics

Correlation analysis has been used widely by researchers and analysts when analyzing large-scale assessment data. Limit research provided reliable methods to estimate various correlations and their standard errors with the complex sampling design and multiple plausible values taken into account. This report introduces the methodology used by the wCorr R package (Emad & Bailey, 2017) for computing the Pearson, Spearman, polyserial, and polychoric correlations, with and without weights applied. The methodology treats tetrachoric correlation as a specific case of the polychoric correlation and biserial correlation as a specific case of the polyserial correlation.

Simulation evidence is presented to show correctness of the methods, including an examination of the bias and consistency. Overall, the simulations show first-order convergence for each unweighted correlation coefficient with an approximately linear computation cost. Further, under our simulation assumptions, the weighted correlation performs better than the unweighted correlation for all correlation coefficients.

We show the first-order convergence of the weighted Pearson, polyserial, and polychoric correlation coefficient. The Spearman is shown to not consistently estimate the population Pearson correlation coefficient but is shown to consistently estimate the population Spearman correlation coefficient—under the assumptions of our simulation.

PDF icon Weighted and Unweighted Correlation Methods for Large-Scale Educational Assessment: wCorr Formulas (PDF)

Related Projects

Project

NCES Data R Project - EdSurvey

The released EdSurvey Version 2.6 is designed for the analysis of national and international education data from the National Center for Education Statistics (NCES). EdSurvey gives users the ability to process and analyze these data efficiently, taking into account their complex sample survey design and the use of plausible values. EdSurvey is an R statistical package developed by AIR, tailored to the processing and analysis of NCES large-scale education data with appropriate procedures.

Related Work

1 Feb 2021
Spotlight

NAEP Data in Focus: Examining the Research

The NAEP Data in Focus working papers combine AIR’s expertise and experience not only with the National Assessment of Educational Progress (NAEP), but with other large-scale assessments and survey-based longitudinal studies.
Topic: 
Education, NAEP

Further Reading

  • NCES Data R Project- EdSurvey
  • NAEP Data in Focus: Examining the Research
  • NAEP Validity Studies (NVS) Panel
  • Analyses Using Achievement Levels Based on Plausible Values
  • Effects of Visual Representations and Associated Interactive Features on Student Performance on National Assessment of Educational Progress (NAEP) Pilot Science Scenario-Based Tasks
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Paul Bailey

Senior Economist

Ting Zhang

Senior Researcher

Topic

Education
NAEP

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