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Licensed Unlicensed Requires Authentication Published by De Gruyter January 9, 2020

Marathon, Hurdling, or Sprint? The Effects of Exam Scheduling on Academic Performance

Sofoklis Goulas ORCID logo EMAIL logo and Rigissa Megalokonomou

Abstract

Would you prefer a tighter or a more prolonged exam schedule? Would you prefer to take an important exam first or last? We exploit quasi-random variation in exam schedules across cohorts, grades and subjects from a lottery to identify distinct effects of the number of days between exams, the number of days since the first exam, and the exam order on performance. Scheduling effects are more pronounced for STEM exams. We find a positive and a negative relationship between STEM scores and exam order (warm-up) and number of days since the first exam (fatigue), respectively. In STEM, warm-up is estimated to outweigh fatigue. Marginal exam productivity in STEM increases faster for boys than for girls. Higher-performing students exhibit higher warm-up and lower fatigue effects in STEM than lower-performing students. Optimizing the exam schedule can improve overall performance by as much as 0.02 standard deviations.

JEL Classification: I20; I24

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Appendices

A Example of Exam Schedule

Figure 7: 
            Example of exam schedule.
            Note: The picture above shows the exam schedule for students in the 11th grade in May–June 2005. The first and second columns show the date and day of the week of the exam, respectively. The third column shows the subject tested. The fourth column shows the time the exam starts. On some days students in different concentrations take exams in different subjects (e. g. May 23, May 30, June 10). Since all concentration electives are tested on the same date, the choice of elective courses does not affect students’ exam schedule. For example, on May 2, three concentration subjects (one for each concentration) were testes for students of the same grade: Latin, chemistry, and communications technology.
Figure 7:

Example of exam schedule.

Note: The picture above shows the exam schedule for students in the 11th grade in May–June 2005. The first and second columns show the date and day of the week of the exam, respectively. The third column shows the subject tested. The fourth column shows the time the exam starts. On some days students in different concentrations take exams in different subjects (e. g. May 23, May 30, June 10). Since all concentration electives are tested on the same date, the choice of elective courses does not affect students’ exam schedule. For example, on May 2, three concentration subjects (one for each concentration) were testes for students of the same grade: Latin, chemistry, and communications technology.

B Supplementary Descriptive Statistics

In this section, we provide supplementary descriptive tables of student-level data. Table 11, Table 12, and Table 13 provide student-level summary statistics for each cohort for students in the 10th grade, 11th grade, and overall, respectively. We find that students characteristics are substantially similar across cohorts and grades.

Table 11:

Summary statistics for 10th graders.

Year Female Age GPA Midterm score Final exam score Retained
2002 Mean 0.60 15.84 14.69 16.76 12.81 0.00
SD 0.49 0.43 2.81 1.80 3.80 0.00
N 91 91 91 91 91 91
2003 Mean 0.50 15.76 15.33 17.18 13.50 0.00
SD 0.50 0.48 2.99 1.79 4.21 0.00
N 86 86 86 86 86 86
2004 Mean 0.66 15.88 15.88 17.40 14.21 0.01
SD 0.47 0.55 2.43 1.61 3.55 0.10
N 101 101 100 101 101 101
2005 Mean 0.48 15.81 14.98 16.68 13.05 0.02
SD 0.50 0.44 3.04 2.12 4.14 0.14
N 95 95 93 95 95 95
2006 Mean 0.53 15.95 15.10 17.06 13.14 0.01
SD 0.50 0.35 2.49 1.62 3.44 0.10
N 108 108 107 108 108 108
2007 Mean 0.57 16.06 15.30 17.09 12.90 0.04
SD 0.50 0.36 2.73 1.99 4.35 0.20
N 116 116 111 116 116 116
2008 Mean 0.55 16.03 15.24 17.32 13.20 0.00
SD 0.50 0.17 2.98 1.92 4.03 0.00
N 98 98 98 98 98 98
2009 Mean 0.47 16.02 15.99 17.62 14.38 0.00
SD 0.50 0.15 2.22 1.44 3.03 0.00
N 92 92 92 92 92 92
2010 Mean 0.57 16.04 15.99 17.71 14.09 0.01
SD 0.50 0.19 2.52 1.52 3.84 0.09
N 113 113 112 113 113 113
Total Mean 0.55 15.94 15.40 17.21 13.47 0.01
SD 0.50 0.38 2.72 1.79 3.87 0.10
N 900 900 890 900 900 900
  1. Notes: This table presents the mean, standard deviation, and number of observations for a set of variables by year (2002–2010) for students in 10th grade. Variables include gender, age, GPA (between 0 and 20), midterm score (between 0 and 20), final exam score (between 0 and 20), and a dummy that indicates whether a student is retained.

Table 12:

Summary statistics for 11th graders.

Year Female Age GPA Midterm score Final exam score Retained
2002 Mean 0.61 16.70 12.05 16.54 10.82 0.12
SD 0.49 0.46 3.17 1.86 3.65 0.32
N 102 102 90 102 102 102
2003 Mean 0.63 16.85 14.83 17.18 12.16 0.06
SD 0.49 0.48 2.80 1.87 4.11 0.24
N 84 84 79 84 84 84
2004 Mean 0.52 16.78 15.34 17.44 12.59 0.06
SD 0.50 0.47 3.04 2.04 4.99 0.25
N 79 79 74 79 79 79
2005 Mean 0.66 16.93 15.13 16.81 13.08 0.05
SD 0.48 0.82 2.69 1.93 4.18 0.22
N 99 99 94 99 99 99
2006 Mean 0.50 16.86 15.09 16.88 13.26 0.02
SD 0.50 0.63 3.12 2.16 4.27 0.15
N 88 88 86 88 88 88
2007 Mean 0.56 17.01 15.39 17.39 13.46 0.02
SD 0.50 0.60 2.43 1.52 3.69 0.14
N 103 103 101 103 103 103
2008 Mean 0.58 17.01 15.79 17.76 14.08 0.00
SD 0.50 0.10 2.59 1.49 3.62 0.00
N 103 103 103 103 103 103
2009 Mean 0.59 17.03 15.74 17.72 13.85 0.01
SD 0.49 0.18 2.84 1.72 4.02 0.11
N 90 90 89 90 90 90
2010 Mean 0.47 17.05 15.84 17.93 14.23 0.00
SD 0.50 0.26 2.47 1.33 3.38 0.00
N 88 88 88 88 88 88
Total Mean 0.57 16.92 15.03 17.29 13.06 0.04
SD 0.50 0.51 2.99 1.83 4.10 0.19
N 836 836 804 836 836 836
  1. Notes: This table presents the mean, standard deviation, and number of observations for a set of variables by year (2002–2010) for students in 11th grade. Variables include gender, age, GPA (between 0 and 20), midterm score (between 0 and 20), final exam score (between 0 and 20), and a dummy that indicates whether a student is retained.

Table 13:

Summary statistics for all students in the sample.

Year Female Age GPA Midterm score Final exam score Retained
2002 Mean 0.61 16.29 13.38 16.65 11.76 0.06
SD 0.49 0.62 3.26 1.83 3.84 0.24
N 193 193 181 193 193 193
2003 Mean 0.56 16.29 15.09 17.18 12.84 0.03
SD 0.50 0.73 2.90 1.83 4.20 0.17
N 170 170 165 170 170 170
2004 Mean 0.60 16.28 15.65 17.41 13.50 0.03
SD 0.49 0.69 2.71 1.80 4.30 0.18
N 180 180 174 180 180 180
2005 Mean 0.57 16.38 15.05 16.75 13.06 0.04
SD 0.50 0.87 2.86 2.02 4.15 0.19
N 194 194 187 194 194 194
2006 Mean 0.52 16.36 15.10 16.98 13.19 0.02
SD 0.50 0.67 2.78 1.88 3.83 0.12
N 196 196 193 196 196 196
2007 Mean 0.57 16.51 15.34 17.23 13.16 0.03
SD 0.50 0.68 2.59 1.79 4.05 0.18
N 219 219 212 219 219 219
2008 Mean 0.57 16.53 15.52 17.55 13.65 0.00
SD 0.50 0.51 2.79 1.72 3.84 0.00
N 201 201 201 201 201 201
2009 Mean 0.53 16.52 15.87 17.67 14.12 0.01
SD 0.50 0.53 2.54 1.58 3.56 0.07
N 182 182 181 182 182 182
2010 Mean 0.52 16.48 15.93 17.81 14.15 0.00
SD 0.50 0.55 2.49 1.44 3.64 0.07
N 201 201 200 201 201 201
Total Mean 0.56 16.41 15.23 17.25 13.27 0.02
SD 0.50 0.66 2.85 1.81 3.99 0.15
N 1736 1736 1694 1736 1736 1736
  1. Notes: This table presents the mean, standard deviation, and number of observations for a set of variables by year (2002–2010) for students in 10th and 11th grade. Variables include gender, age, GPA (between 0 and 20), midterm score (between 0 and 20), final exam score (between 0 and 20), and a dummy that indicates whether a student is retained.

Table 14 shows exam-level descriptive statistics for males and females for STEM subjects, non-STEM subjects, and overall. We find that males and females seem to have similar midterm and final exam scores in STEM subject, while females have slightly higher average midterm and final exam scores in non-STEM subjects than males.

Table 14:

Summary statistics for midterm and final exam scores by gender.

STEM exams
Non-STEM exams
Gender Midterm Final exam Midterm Final exam
Male Mean 16.96 12.26 16.93 13.32
SD 2.54 6.00 2.52 4.93
N 5680 5036 5214 5233
Female Mean 17.18 12.39 17.78 14.59
SD 2.46 6.04 2.18 4.76
N 6651 5995 7138 7150
All Mean 17.08 12.33 17.42 14.05
SD 2.50 6.02 2.36 4.87
N 12331 11031 12352 12383
  1. Note: This table presents the mean, standard deviation, and number of observations for STEM and non-STEM exams, for males and females (but also combined), separately, for the following variables: midterm score (between 0 and 20) and final exam score (between 0 and 20).

C Balancing Tests

One potential concern is whether exam scheduling is consistent with a random process and orthogonal to student characteristics. We deploy balancing tests to examine whether there is any systematic association between the exam scheduling variables and student characteristics, such as age, gender, or prior performance in each subject. Exam scheduling varies across year and grade configurations. To answer whether student characteristics vary along the same dimensions as exam scheduling, we regress each student characteristic on the full set of year by grade dummies. Table 15 presents the results across all students. Columns 1, 2, and 3 show the variation of midterm score, gender, and age, respectively, across all year by grade configurations. Columns 3 controls for grade fixed effects, as age is anticipated to change with grade. The coefficients of the year by grade dummies across all columns of Table 15 are in general small and not statistically significant. The F test for the collective equivalence of the coefficients of the year by grade dummies to zero accepts the null hypothesis of equivalence in each column. We conclude that there is no significant association between exam scheduling and students’ prior characteristics, reinforcing our confidence in the randomization process of exam scheduling.

Table 15:

Balancing tests.

Variables (1) (2) (3)
Midterm score Female Age
2002 × Grade 10 0.000 0.000 0.000
(0.000) (0.000) (0.000)
2002 × Grade 11 –0.058 0.003
(0.141) (0.108)
2003 × Grade 10 –0.037 –0.104 0.000
(0.092) (0.089) (0.000)
2003 × Grade 11 –0.038 0.027 –0.028
(0.088) (0.087) (0.018)
2004 × Grade 10 –0.057 0.059 0.004
(0.123) (0.073) (0.004)
2004 × Grade 11 –0.015 –0.085 –0.015*
(0.113) (0.130) (0.009)
2005 × Grade 10 –0.085 –0.120* 0.000
(0.105) (0.067) (0.000)
2005 × Grade 11 0.003 0.052 0.041
(0.130) (0.084) (0.036)
2006 × Grade 10 –0.008 –0.077 –0.000
(0.131) (0.060) (0.000)
2006 × Grade 11 –0.065 –0.104* 0.014
(0.085) (0.059) (0.013)
2007 × Grade 10 –0.078 –0.035 –0.002
(0.132) (0.056) (0.004)
2007 × Grade 11 –0.006 –0.041 0.009
(0.120) (0.060) (0.034)
2008 × Grade 10 –0.126 –0.053 –0.000
(0.128) (0.064) (0.000)
2008 × Grade 11 0.035 –0.022 –0.007
(0.073) (0.062) (0.006)
2009 × Grade 10 –0.067 –0.137* –0.000
(0.108) (0.073) (0.000)
2009 × Grade 11 –0.012 –0.016 –0.021*
(0.090) (0.076) (0.012)
2010 × Grade 10 –0.061 –0.038 –0.000
(0.086) (0.058) (0.000)
2010 × Grade 11 –0.020 –0.138* –0.010
(0.079) (0.074) (0.015)
Observations 1,736 1,736 1,736
R-squared 0.002 0.014 0.939
F-Stat P-value 0.982 0.296 0.640
Grade FE No No Yes
  1. Notes: The dependent variable in column (1) is the standardized midterm score, in column (2) the gender of each student, and in column (3) the age of each student. Results in each column come from a separate OLS regression across all students. Cluster-robust standard errors at the classroom by year level are reported in parentheses. * p < 0.1; ** p < 0.05; *** p < 0.01.

D Variation Sufficiency

Exam scheduling variables vary across years, grades, and subjects. There are two grades (10th and 11th) and nine cohorts. Each subject is tested once for each grade in a given year. Therefore, each scheduling variable takes 18 (two grades × nine cohorts) values for each subject in our data. We illustrate the variation in exam scheduling in Table 16, Table 17, and Table 18. Table 16 shows how Days between Exams varies across subjects. Each entry in Table 16 shows how frequently the subject in that column was tested in the number of days since the previous exam shown in that row. The maximum number of days students have between exams is 5 days, as shown in the first column of Table 16. As an illustration, algebra was tested on the same day as the previous exam zero times, 2 days after the previous exam seven times, and so on. History was tested on the same day as the previous exam zero times, 1 day after the previous exam twice, and so on. At the bottom of Table 16 we report the mean and standard deviation of the number of days elapsed since the previous exam for each subject. We observe considerable within-subject variation in the time since the previous exam. On average, English and modern Greek have the shortest average time since the previous exam compared to other subjects, although we do not see any systematic differences in the testing pattern of STEM and non-STEM subjects in terms of the number of days lapsed since the previous exam.

Table 16:

How Does Days Between Exams Vary across Subjects?

Days between exams Ancient Greek Literature Modern Greek History Algebra Geometry Physics Chemistry English
4 0 2 4 2 0 2 0 0
0 1 0 0 0 0 0 0 0 0
1 0 9 9 2 0 0 0 6 13
2 6 6 4 5 7 7 8 10 4
3 4 3 3 5 5 9 4 1 1
4 3 0 0 2 2 0 2 1 0
5 0 0 0 0 2 2 2 0 0
Total 18 18 18 18 18 18 18 18 18
Mean 2.57 1.67 1.63 2.50 2.94 2.83 2.89 1.83 1.33
SD 1.09 0.77 0.81 0.94 1.06 0.92 1.09 0.79 0.59
  1. Notes: The table presents the variation of the scheduling variable Days Between Exams across subjects. Each entry shows how frequently the subject in that column was tested in the number of days since the previous exam shown in that row. The variable Days Between Exams takes values from 0 to 5, indicating that from 0 up to 5 days might intervene between two consecutive exams in the sample. For example, modern Greek was tested 1 day after the previous exam nine times and 3 days after the previous exam three times. The first line corresponds to the times each subject was tested first, and thus the Days Between Exams variable is set to missing.

Table 17:

How Does Days Since First Exam Vary across Subjects?

Days since first start Ancient Greek Literature Modern Greek History Algebra Geometry Physics Chemistry English
4 0 2 4 2 0 2 0 0
2 0 3 0 1 3 0 2 2 1
3 0 1 0 0 0 0 0 0 0
4 1 0 1 0 0 1 1 1 0
5 2 0 0 1 0 1 1 0 0
7 0 0 1 0 2 1 3 1 2
9 4 2 0 0 0 2 2 2 0
10 0 0 0 0 0 0 0 0 0
11 0 0 0 1 0 1 0 1 0
12 0 0 0 0 3 1 0 0 0
13 0 0 0 1 0 0 1 0 0
14 0 0 3 1 3 2 2 1 0
15 0 2 1 0 0 1 0 0 1
16 1 1 0 2 0 1 1 0 3
17 1 1 0 0 0 1 0 0 1
18 0 0 2 1 1 2 0 0 0
19 1 0 1 1 0 0 0 0 1
20 1 0 0 0 1 0 1 0 1
21 0 4 2 1 2 0 1 1 1
22 2 0 1 0 0 0 0 3 2
23 0 1 1 0 0 0 0 2 2
24 0 1 2 1 0 1 1 1 1
25 0 0 1 0 1 0 0 0 0
26 0 0 0 0 0 1 0 1 0
27 0 0 0 1 0 2 0 1 1
28 1 2 0 1 0 0 0 0 1
29 0 0 0 1 0 0 0 1 0
Total 18 18 18 18 18 18 18 18 18
Mean 13.86 15.39 17.69 17.36 12.69 15.17 10.89 16.50 18.06
SD 7.64 8.92 6.07 8.16 7.24 7.26 6.83 9.15 7.00
  1. Notes: The table presents the variation of the scheduling variable Days Since the First Exam across subjects. Each entry shows how frequently the subject in that column was tested in the number of days since the beginning of the exam season shown in that row. The variable Days Since the First Exam takes values from 2 to 29, indicating that students take compulsory exams for a maximum duration of 29 days after the first exam. For example, modern Greek was tested 4 days after the exam season started once times and 25 days after the exam season started once. The first line corresponds to the times each subject was tested first, and thus the Days Since the First Exam variable is set to missing.

Table 18:

How Does Exam Order Vary across Subjects?

Exam order Ancient Greek Literature Modern Greek History Algebra Geometry Physics Chemistry English
1 4 0 2 4 2 0 2 0 0
2 0 4 0 1 3 0 2 2 1
3 3 0 1 1 1 3 2 1 0
4 1 0 1 0 1 0 4 2 2
5 3 2 0 2 1 2 3 1 0
6 0 1 1 0 3 4 0 1 0
7 0 0 3 1 1 2 1 1 0
8 1 3 1 2 1 1 2 0 4
9 3 0 1 1 1 2 1 0 1
10 2 2 2 2 2 0 0 1 3
11 0 3 2 1 2 0 1 4 3
12 0 1 1 0 0 1 0 2 2
13 0 0 3 0 0 2 0 0 0
14 0 1 0 0 0 1 0 2 1
15 1 0 0 3 0 0 0 1 1
16 0 1 0 0 0 0 0 0 0
Total 18 18 18 18 18 18 18 18 18
Mean 5.67 7.94 8.11 7.06 5.78 7.50 4.78 8.56 9.28
SD 4.03 4.32 3.94 5.00 3.49 3.52 2.82 4.41 3.39
  1. Notes: The table presents the variation of the scheduling variable Exam Order across subjects. Each entry shows how frequently the subject in that column was tested in the order shown in that row. The variable Exam Order takes values from 1 to 16 indicating the order of the tested subject. For example, modern Greek was tested first twice, while it was tested seventh three times. The first line corresponds to the times each subject was tested first, and thus the Exam Order variable is set to missing.

Table 17 shows how Days lapsed since the Exam Season started varies across subjects. Each entry in Table 17 shows how frequently the subject in that column was tested in the number of days since the beginning of the exam season shown in that row. Students take compulsory exams for a maximum duration of 29 days, after the first exam, as shown in the first column of Table 17. For illustrative purposes, algebra was tested on the first day twice, 2 days after the first exam three times, and so on. History was tested on the first day four times, 2 days after the first exam once, and so on. Physics was never tested more than 24 days after the first exam, and algebra was never tested more than 25 days after the first exam. At the bottom of Table 17 we report the mean and standard deviation of the number of days elapsed since the first exam for each subject was administered. We observe considerable within-subject variation in the number of days since the first exam for each subject. On average, physics and ancient Greek were tested closer to the first exam than the other subjects. We do not see any systematic differences in the testing patterns for STEM and non-STEM subjects in terms of the number of days elapsed since the first exam.

Table 18 shows how the scheduling variable Exam Order varies across subjects. Each entry in Table 18 shows how frequently the subject in that column was tested in the order shown in that row. Students take a maximum of 16 exams (including electives), as shown in the first column of Table 18. For illustrative purposes, algebra was tested first twice, second three times, third once, fourth once, and so on. History was tested first four times, second once, third once, fourth zero times, and so on. Physics and ancient Greek were the only subjects that were never tested later than the 11th place in the order of exams. At the bottom of Table 18 we report the mean and standard deviation of the place in the exam order at which each subject was tested. We observe considerable within-subject variation in the order in which each subject was tested across years and grades. On average, physics and ancient Greek were tested at a later place of order than the other subjects. We do not see any systematic differences in the testing patterns for STEM and non-STEM subjects.

E Overall Scheduling Effects

In this section we provide estimates of overall scheduling effects, without differentiating between STEM and non-STEM subjects. Table 19 shows estimates from the following model:

(3)Si,s,g,t=α0+α1DaysBetweens,g,t+α2DaysSinceFirsts,g,t+α3ExamOrders,g,t+α4Mi,s,g,t+α5Xi,s,g,t+κsg+λgt+ζt+ηi,s,g,t,

where the coefficients α1, α2, α3 reflect the average impact of Scheduling Effects I, II, and III, respectively, across STEM and non-STEM subjects. As shown earlier, STEM and non-STEM subjects exhibit substantially different scheduling effects. These largely cancel out in an overall analysis of scheduling effects, with the exception of Scheduling Effect I. Table 19 shows that as the number of days between exams increases, the final exam score decreases, on average across subjects.

Table 19:

Overall effect of exam timing on performance.

Variables (1) (2) (3)
Scheduling Effect III 0.031 0.003 –0.010
(0.023) (0.003) (0.011)
Scheduling Effect II –0.013 –0.001 0.001
(0.011) (0.002) (0.005)
Scheduling Effect I –0.045** –0.007** –0.024***
(0.017) (0.003) (0.008)
Scheduling Effect III2 0.000
(0.000)
Scheduling Effect II2 0.000
(0.000)
Scheduling Effect I2 0.003**
(0.001)
Observations 14,258 14,258 14,258
R-squared 0.026 0.985 0.985
Student controls No Yes Yes
  1. Notes: The dependent variable in each specification is the standardized final exam score at the subject and grade level. Cluster-robust standard errors at the classroom by year level are reported in parentheses. Specification includes grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, and a full set of birth year by cohort fixed effects. Columns 2 and 3 include individual controls. Individual controls include indicators for students’ gender, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.

F Non-linear Scheduling Effects

In this section, we explore non-linear scheduling effects on exam performance using the quadratic form of each scheduling variable. Specification 4 is an augmented version of specification 1, and includes the square of each scheduling variable.

(4) S i , s , g , t = α 0 + α 1 c D a y s B e t w e e n s , g , t + α 2 c D a y s S i n c e F i r s t s , g , t + α 3 c E x a m O r d e r s , g , t + α 4 c D a y s B e t w e e n s , g , t 2 + α 5 c D a y s S i n c e F i r s t s , g , t 2 + α 6 c E x a m O r d e r s , g , t 2 + α 7 M i , s , g , t + α 8 X i , s , g , t + κ s g + λ g t + ζ t + η i , s , g , t .

Column 1 of Table 20 shows the effects for STEM and non-STEM subjects separately (using specification 1), while column 2 focuses on the difference in each scheduling effect for STEM relative to non-STEM subjects. Intuitively, the main effects shown in column 2 correspond to the scheduling effects of non-STEM subjects in column 1, while the coefficients of the interaction terms reflect the additional (marginal) scheduling effects of STEM subjects compared to non-STEM subjects.

Column 3 of Table 20 shows the estimated nonlinear effects of three distinct channels of exam scheduling on performance separately for STEM and non-STEM subjects (using specification 4), while column 4 of Table 20 focuses on the differences of nonlinear scheduling effects between STEM and non-STEM subjects. Scheduling Effect I is found to have nonlinear effects only on exam performance in non-STEM subjects. The positive coefficient on the squared variable associated with Scheduling Effect I reveals the downward curvature of the effect of the underlying mechanism. Exams in non-STEM subjects taken further in days from the previous exam are associated with decreasingly lower performance, while controlling for other influences. Scheduling Effect III is found to have nonlinear effects only on exam performance in STEM subjects. The positive coefficient on the squared variable associated with Scheduling Effect III reveals the upward curvature of the effect of the underlying mechanism. Exams in STEM subjects taken at a later place in the exam order are associated with increasingly higher performance, while controlling for other influences. In contrast to the other scheduling effects, Scheduling Effect II is found not to have nonlinear effects in either STEM or non-STEM subjects.

Table 20:

The effect of exam scheduling on performance.

Variables (1) (2) (3) (4)
Scheduling Effect III for non-STEM –0.002 –0.016
(0.004) (0.015)
Scheduling Effect III for STEM 0.016*** –0.024
(0.005) (0.017)
Scheduling Effect III for non-STEM2 0.000
(0.001)
Scheduling Effect III for STEM2 0.002**
(0.001)
Scheduling Effect II for non-STEM 0.002 0.005
(0.002) (0.006)
Scheduling Effect II for STEM –0.006*** 0.004
(0.002) (0.006)
Scheduling Effect II for non-STEM2 –0.000
(0.000)
Scheduling Effect II for STEM2 –0.000
(0.000)
Scheduling Effect I for non-STEM –0.012*** –0.038***
(0.004) (0.011)
Scheduling Effect I for STEM 0.002 0.016
(0.003) (0.023)
Scheduling Effect I for non-STEM2 0.006**
(0.002)
Scheduling Effect I for STEM2 –0.003
(0.003)
Scheduling Effect III –0.002 –0.004
(0.002) (0.004)
Scheduling Effect II 0.002 0.003
(0.002) (0.002)
Scheduling Effect I –0.012*** –0.012***
(0.004) (0.004)
STEM × Scheduling Effect III 0.019*** –0.015
(0.005) (0.017)
STEM × Scheduling Effect II –0.008** –0.001
(0.002) (0.007)
STEM × Scheduling Effect I 0.013*** 0.024
(0.003) (0.022)
STEM × Scheduling Effect III2 0.002*
(0.001)
STEM × Scheduling Effect II2 –0.000
(0.000)
STEM × Scheduling Effect I2 –0.002
(0.003)
Observations 14,258 14,258 14,258 14,258
R-squared 0.985 0.985 0.985 0.985
  1. Notes: The dependent variable in each specification is the standardized final exam score at the subject and grade level. Cluster-robust standard errors at the classroom by year level are reported in parentheses. All specifications include midterm score, grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include indicators for students who are female, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.

G Differential Scheduling Effects by Student Prior Performance

We interact each scheduling effect for STEM and non-STEM subjects in specification 1 with a continuous variable that captures the standardized prior performance of each student in each subject. Results are relegated to Table 21. For Scheduling Effect I, the interaction of interest is positive and statistically significant for non-STEM subjects, whereas it is negative and significant for STEM subjects. This indicates that the gap in the effect of an additional day between exams between STEM and non-STEM subjects decreases with prior performance.

The estimated coefficient of the interaction of interest for Scheduling Effect II in non-STEM subjects is zero, while the coefficient of the interaction for STEM subjects with prior performance is positive and significantly different from zero. For STEM subjects, higher-achieving students benefit more from an additional day since their first exam for STEM subjects; this is not the case for exams in non-STEM subjects.

The estimated coefficient of the interaction of Scheduling Effect III in non-STEM subjects with prior performance is zero, while the coefficient of the interaction for STEM subjects is negative and statistically significant. Higher-achieving students benefit less from taking a STEM exam one additional place later in the order of exams in the schedule, whereas for non-STEM subjects, the exam order does not seem to play any important role.

Table 21:

Differential effects of exam timing on performance by STEM and prior performance.

Variables (1)
Midterm score 0.470***
(0.005)
Scheduling Effect I for STEM –0.012***
(0.004)
Scheduling Effect II for STEM 0.018***
(0.003)
Scheduling Effect III for STEM –0.044***
(0.007)
Scheduling Effect I for non-STEM 0.025***
(0.005)
Scheduling Effect II for non-STEM –0.015***
(0.004)
Scheduling Effect III for non-STEM 0.038***
(0.007)
Scheduling Effect I for non-STEM × Midterm score 0.016***
(0.002)
Scheduling Effect I for STEM × Midterm score –0.004***
(0.001)
Scheduling Effect II for non-STEM × Midterm score –0.000
(0.002)
Scheduling Effect II for STEM × Midterm score 0.008***
(0.001)
Scheduling Effect III for non-STEM × Midterm score 0.001
(0.003)
Scheduling Effect III for STEM × Midterm score –0.020***
(0.003)
Observations 14,258
R-squared 0.992
  1. Notes: The dependent variable is the standardized final exam score at the subject and grade level. Cluster-robust standard errors at the classroom by year level are reported in parentheses. Specification includes grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a linear time trend, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include indicators for students’ gender, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.

Table 22 shows the estimated Scheduling Effects by STEM and non-STEM subjects for four quantiles of prior performance, proxied by standardized midterm score. The estimates are presented graphically in Figure 5.

Table 22:

Differential effects of exam timing on performance by STEM and prior performance.

Non-STEM
STEM
Difference
Coef. Std. Err. Coef. Std. Err. Coef. Std. Err.
Scheduling Effect I
Quantile 1 –0.060*** (0.008) 0.004 (0.004) 0.064*** (0.007)
Quantile 2 –0.028*** (0.004) –0.003 (0.003) 0.025*** (0.004)
Quantile 3 0.005* (0.003) –0.003 (0.003) –0.008* (0.004)
Quantile 4 0.027*** (0.005) –0.014*** (0.004) –0.041*** (0.006)
Scheduling Effect II
Quantile 1 0.006 (0.006) –0.021*** (0.004) –0.027*** (0.006)
Quantile 2 0.005* (0.003) 0.000 (0.001) –0.005* (0.003)
Quantile 3 0.002* (0.001) 0.012*** (0.002) 0.009*** (0.002)
Quantile 4 0.001 (0.004) 0.024*** (0.005) 0.022*** (0.006)
Scheduling Effect III
Quantile 1 –0.014 (0.012) 0.052*** (0.008) 0.066*** (0.013)
Quantile 2 –0.015*** (0.005) 0.001 (0.003) 0.016*** (0.006)
Quantile 3 –0.005* (0.003) –0.031*** (0.005) –0.026*** (0.005)
Quantile 4 –0.001 (0.008) –0.059*** (0.010) –0.058*** (0.011)
  1. Notes: The dependent variable is the standardized final exam score at the subject and grade level. The sample includes 14,258 observations. Cluster-robust standard errors at the classroom by year level are reported in parentheses. Specification includes grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include indicators for students’ gender, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.

H Differential Scheduling Effects By Exam History

In this section, we provide estimates of differential scheduling effects by exam history. Exam history is measured by the number of STEM and non-STEM exams taken prior to attempting a subsequent exam. We expand model 1 by adding interactions of each scheduling variable for STEM and non-STEM subjects with the number of STEM and non-STEM exams taken prior. Table 23 shows estimates for the interactions of interest.

Table 23:

Differential scheduling effects by exam history.

Variables (1)
Scheduling Effect III for non-STEM × No. of STEM exams taken 0.001
(0.001)
Scheduling Effect III for STEM × No. of STEM exams taken –0.001
(0.003)
Scheduling Effect III for non-STEM × No. of non-STEM exams taken 0.002
(0.001)
Scheduling Effect III for STEM × No. of non-STEM exams taken 0.004*
(0.002)
Scheduling Effect II for non-STEM × No. of non-STEM exams taken 0.001
(0.001)
Scheduling Effect II for STEM × No. of STEM exams taken 0.001
(0.001)
Scheduling Effect II for non-STEM × No. of non-STEM exams taken –0.001
(0.001)
Scheduling Effect II for STEM × No. of non-STEM exams taken –0.001
(0.001)
Scheduling Effect I for non-STEM × No. of non-STEM exams taken –0.000
(0.001)
Scheduling Effect I for STEM × No. of STEM exams taken –0.001
(0.002)
Scheduling Effect I for non-STEM × No. of non-STEM exams taken 0.003***
(0.001)
Scheduling Effect I for STEM × No. of non-STEM exams taken 0.001
(0.002)
Observations 14,258
R-squared 0.986
  1. Notes: This table presents differential scheduling effects by exam history. We interact each scheduling variable for STEM and non-STEM subjects with the number of STEM and non-STEM exams taken prior. The model includes the three scheduling variables by type of subject, controls for midterm score, grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include a female gender dummy, and a dummy that indicates whether a student is retained. This table reports only the coefficients of interactions of interest in the interest of space.

I Restricted Models of Scheduling Effects

To increase the empirical intuition behind the size and direction of omitted variable bias when one or more exam scheduling variables are excluded from the regression model, we estimate models using subsets of the exam scheduling variables. Table 24 show the estimate from restricted models across all subjects.

Table 24:

Subsets of the effects of exam timing on performance.

Variables (1) (2) (3) (4) (5) (6)
Scheduling Effect III 0.002*** 0.005* 0.002***
(0.001) (0.003) (0.001)
Scheduling Effect II 0.001*** –0.002 0.001**
(0.000) (0.001) (0.000)
Scheduling Effect I –0.009*** –0.008*** –0.008**
(0.003) (0.003) (0.003)
Observations 14,258 14,258 14,258 14,258 14,258 14,258
R-squared 0.985 0.985 0.985 0.985 0.985 0.985
  1. Notes: The dependent variable is the standardized final exam score at the subject and grade level. Cluster-robust standard errors at the classroom by year level are reported in parentheses. Specification includes grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include indicators for students’ gender, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.

J Alternative Modeling Approach to Scheduling Effect III

In this section, we explore an alternative modelling approach for Scheduling Effect III. In particular, we estimate a model using specification Table 20, where the exam order variable is replaced by the ratio of exam order over days since first exam. The estimated coefficient for the ratio of the variables associated with Scheduling Effect III and II is reported in Table 25. The results show that an additional exam per day since the first exam increases test performance by 0.047 standard deviations across all subjects, and by 0.075 standard deviations across STEM subjects. Performance in non-STEM subjects is not found to be significantly impacted by the number of exams per days since the first exam. The ratio of exam order (Scheduling Effect III) over the number of days since the first exam (Scheduling Effect II) has a positive and significant coefficient for STEM subjects, as does the number of days since first exam variable for STEM subjects. This suggests that providing students with more time to study may be optimal for STEM subjects.

Table 25:

Scheduling Effect III relative to Scheduling Effect II.

Variables (1) (2)
Scheduling Effect III/II for non-STEM 0.031
(0.030)
Scheduling Effect III/II for STEM 0.075***
(0.026)
Scheduling Effect II for non-STEM 0.001*
(0.000)
Scheduling Effect II for STEM 0.002***
(0.000)
Scheduling Effect I for non-STEM –0.012***
(0.004)
Scheduling Effect I for STEM –0.001
(0.004)
Scheduling Effect III/II 0.047**
(0.021)
Scheduling Effect II 0.001***
(0.000)
Scheduling Effect I –0.006**
(0.003)
Observations 14,258 14,258
R-squared 0.985 0.985
  1. Notes: The dependent variable is the standardized final exam score at the subject and grade level. Cluster-robust standard errors at the classroom by year level are reported in parentheses. Specification includes grade by year fixed effects, subject by grade fixed effects, day of the week fixed effects, a full set of birth year by cohort fixed effects, and individual controls. Individual controls include indicators for students’ gender, and a dummy that indicates whether a student is retained. * p < 0.1; ** p < 0.05; *** p < 0.01.

K Day of the Week Effects

One potentially interesting aspect of exam scheduling may be the differential day-of-the-week effects associated with test performance. Table 26 shows our estimated day-of-the-week effects from different specifications ranging from no controls to controlling for subject by grade unobservable effects and scheduling variables. The estimated effects correspond to the marginal effects on test scores associated with each day of the week with respect to Monday (the omitted category). The results show that, without controls for exam scheduling, Tuesday, Thursday, and Saturday may be associated with increases test scores on subject tested on those days, relative to Monday.

Table 26:

Day of the week effects.

Variables (1) (2) (3)
Tuesday 0.088*** 0.090** 0.050
(0.033) (0.040) (0.040)
Wednesday 0.049 0.053 –0.026
(0.036) (0.036) (0.036)
Thursday 0.092** 0.076* –0.030
(0.039) (0.039) (0.046)
Friday 0.042 0.038 –0.079**
(0.035) (0.036) (0.038)
Saturday 0.289*** 0.326*** 0.223***
(0.047) (0.069) (0.073)
Scheduling variables No No Yes
Subject by Grade FE No Yes Yes
  1. Notes: Sample: 14,258 observations. The dependent variable is the standardized final exam score at the subject and grade level. Cluster-robust standard errors at the classroom by year level are reported in parentheses. Scheduling variables include exam order, days between exams, days since first exam. All specifications include grade by year fixed effects. *p < 0.1; **p < 0.05; ***p < 0.01.

Published Online: 2020-01-09

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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