Fig 1. Bias reduction due to the three-way matching.

This figure shows standardized percent reduction in bias afforded by three-way matching. The key conditioning variables include sex, race, marital status, education level, cohort, and age 5-year categories. The remaining bias in standardized percent bias is less than 0.5-percent for the ‘bilingual vs. monolingual’ pair and 1-percent for the ‘late learner vs. monolingual’ pair across years. At the same time, the yearly three-way matching eliminated the bias completely in every time period.