Cognitive fatigue influences students’ performance on standardized tests

The table shows simple averages for subsamples across test hours. Test uncertainty is the estimated uncertainty for the test result (only available for years 2011–2013). This variable measures how precisely the individual test score was estimated by the computer. (The uncertainty comes from the fact that the test can be more or less accurate to measure the student performance. Each question contributes to the precision of the test, reducing uncertainty. That is, the test is adaptive, and the computer tries to calculate the individuals level. For instance, if the student reaches a level where every time he/she gets a harder question, he/she answers wrong, but every time he/she gets an easier question, he/she answers right, there will be very low uncertainty on test score.) Income is adjusted to the 2010 price level and adjusted for household size using the square root approach. Spring child is a child born in the period January–June of the year being considered. Because the school starting age cutoff is January 1, these children have the highest expected school starting age. The variable called school days refers to the number of days from the start of the school year to the test day, not counting weekends. Parents’ years of schooling is the years of schooling completed by the mother or father (the highest value).

Dependent variable: standardized test scores. The row break shows the point estimate for the coefficients on break and test hour in model S3. All models are estimated with the full set of covariates and fixed effects. Column 1 is for the full sample. In column 2, only tests in mathematics are included. In column 3, only tests in reading are included. In column 4, only tests for grades 2–4 are included. In column 5, only tests for grades 6–8 are included. In column 6, we only included the schools included in the break survey. In column 7, we estimated a modified version of model S2, using individual fixed effects. SEs clustered at the school level are shown in parentheses. Number of schools show the number of schools included (individuals for column 7, and thus also the level of fixed effects and clustering (Individual FE in column 7 is also clustered at the school level). Smallest/largest group shows the smallest/largest number of observations from one school/one individual. Model degrees of freedom specifies the number the degrees of freedom used by the model. AIC gives the Akaike information criteria. Smaller AICs are generally preferred. Observations refers to the number of observations included in the regressions. The dependent variable is standardized within the test year, grade, and subject cell. As fixed effects on the school level implies comparisons within schools, we only include schools with at least two tests. Regressions are based on administrative data from Statistics Denmark and the Danish Ministry for Education, for all mandatory tests 2009/10–2012/13.

↵*** P < 0.01; **P < 0.05; *P < 0.1.

Dependent variable: test score percentiles. All estimates are obtained using OLS. Column 1 shows the point estimate for α1 from estimating model S1. Columns 2–4 show results from estimating model S2 using ordinary least squares. Columns 5–7 show results from estimating model S3 using ordinary least squares. The table only shows the point estimates for the coefficients α1−α5 in model S2 and coefficient α1 and α2 for model S3. Columns 2 and 5 show results from estimating models without any control variables. Columns 3 and 6 show results from estimating simple models with only school, year, day of the week, grade, and subject fixed effects. Columns 4 and 7 show results from estimating the full models without individual fixed effects. SEs clustered at the school level are shown in parentheses. Number of schools show the number of schools included and thus also the level of fixed effects and clustering. Smallest/largest group shows the smallest/largest number of observations from one school. F-value gives the F-statistic for a test of joint significance for the hourly indicators, and P value gives the corresponding P values. Model degrees of freedom specifies the number the degrees of freedom used by the model. AIC gives the Akaike information criteria. Smaller AICs are generally preferred. Observations refers to the number of observations included in the regressions. The dependent variable is test score percentile rank (1–100) within the test year, grade, and subject cell. As fixed effects on the school level implies comparisons within schools, we only include schools with at least two tests. Regressions are based on administrative data from Statistics Denmark and the Danish Ministry for Education, for all mandatory tests 2009/10–2012/13.

↵*** P < 0.01; **P < 0.05; *P < 0.1.