One way of measuring the achievement gap between the U.S. and other nations is to assess students’ math achievement, the strongest predictor of human capital productivity in nations. Imagine an American student who moves from U.S. to another country and attends school overseas. How well would this American student fare against native students in math (as measured by international standardized test score and percentile rank)?
Depending on the achievement gap between the two countries (i.e., the U.S. as the country of origin and other nation as the country of destination), the answers will change. The calculator below provides three metrics of the achievement gap: percentile rank, Cohen’s d and Lee & Finn’s d΄ (see calculator 1 for information on d΄).
Based on the 2007 TIMSS (The Trends in International Math and Science Study) grade 4 and grade 8 student math achievement test results for all participating countries, we convert U.S.-based percentile rank (i.e., percent students in the U.S. performing at or below the math achievement score of this hypothetical American student) into the other nation-based percentile rank (i.e., percent students in the other nation performing at or below the same hypothetical American student).
We also calculate standardized achievement gap (d) between other country and U.S. The value of d captures how much better or worse the level of typical American student’s relative math achievement is in standard deviation units; it reflects national average math achievement gap between the other country and the U.S. Positive values of d mean that the U.S. performs better than the other nation, whereas negatives values of d mean the opposite.
Further, this calculator computes time-indexed gap d΄for corresponding d values to show how much time the American child is ahead or behind in terms of the years/months of learning math compared to his counterpart in the peer nation of comparison (e.g., 3.5 = 3 years and 5 months ahead; -2.1 = 2 years and 1 month behind). This time-indexed gap (d΄) is based on the U.S. national math achievement growth norms. In short, d and d΄ produce approximate international exchange values of American math achievement in both standard deviation and school time units respectively.