We explore the relationship between sleep and student performance on standardized tests. We model test scores as a nonlinear function of sleep, which allows us to compute the hours of sleep associated with maximum test scores. We refer to this as “optimal” hours of sleep. We also evaluate how the sleep and student performance relationship changes with age. We use the Panel Study of Income Dynamics-Child Development Supplement, which includes excellent control variables that are not usually available in sleep studies. We find a statistically significant relationship between sleep and test scores. We also find that optimal hours of sleep decline with age.
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We experimented with using the CDS time diary data in order to check the robustness of the relation between sleep and academic achievement with a second sleep measure, and one that separates sleep into weekday and weekend sleep. A complication with the time diary data is that it includes time spent in bed but not asleep, and therefore the time diary measure overestimates sleep time. The regression estimates were generally insignificant and in some cases the coefficients showed wrong signs. We have more confidence in the self-reported sleep variable and we continue to focus on it in our analysis.
There is heaping of sleep hours in the data on 0s and 5s. The distributions are computed with a smoothing parameter of 0.85.
There are 6 missing income values, 111 missing education values, and 2 missing region values. We use the MI set of procedures in Stata 11 with 10 imputations [StataCorp 2009]. Results are not materially different when we drop those observations with missing values. Standard errors for all statistical tests account for the imputation procedure.
We also experimented with estimating the regressions separately for males and females. With the smaller sample sizes, standard errors increased significantly. We tested for differences between males and females for the sleep and sleep-age variables and could not reject the null hypothesis that the coefficients were the same (10 percent level). With larger sample sizes, closely examining differences between males and females would be an important topic to explore in more detail.
The formula is: optimal sleep=−(B1+B2*age)/(2*(B3+B4*age)), where B1 is the coefficient on sleep, B2 is the coefficient on sleep*age, B3 is the coefficient on sleep-squared, and B4 is the coefficient on sleep-squared*age.
We did substantial testing of the quadratic assumption, comparing it with a local polynomial smooth regression. The quadratic did well in all specifications. The results of these additional tests can be obtained by request from the authors.
We also interact the sleep dummies with age and find similar patterns by age, although the patterns are not as distinct for the youngest ages and few parameters are significant.
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We received very useful comments from participants at the 2007 International Health Economics Association meetings in Copenhagen, Denmark. Taft Foster provided excellent research assistance. We also appreciate the excellent suggestions from two anonymous referees and the editor. This work was partially funded by a grant from the College of Family, Home, and Social Science at Brigham Young University.
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Eide, E., Showalter, M. Sleep and Student Achievement. Eastern Econ J 38, 512–524 (2012). https://doi.org/10.1057/eej.2011.33
- test scores
- academic achievement