Achievement in Cognitive Domains (Grade 4)

Relative Achievement in Mathematics Cognitive Domains

Exhibit 1.1.14 shows countries’ average achievement estimates in the knowing, applying, and reasoning cognitive domains relative to their overall average achievement estimates (sorted from highest to lowest overall average achievement as the default sort). The exhibit also flags differences based on a test of statistical significance between the average domain score and the overall mathematics score using an alpha level of 0.01. A smaller alpha level was used to flag statistical significance of subdomain differences to reduce the number of false positives that can be expected due to multiple comparisons across multiple countries and dependent sub-scores. Differences are computed for each student and averaged across the country, rather than comparing different groups of students as in previous exhibits in this section. This within student dependency leads to considerably smaller standard errors (given in parentheses and reported together with the estimates in the exhibit) and more narrow confidence intervals.