Weighted and Unweighted Correlation Methods for Large-Scale Educational Assessment: wCorr Formulas. AIR--NAEP Working Paper No. 2018-01. NCES Data R Project Series #02

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.