Class Attendance and Exam Performance: A Randomized Experiment

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Class Attendance and Exam Performance: A Randomized Experiment

*

Jennjou Chen Department of Economics National Chengchi University

Taipei City 116, Taiwan (JENNJOU@NCCU.EDU.TW)

And

Tsui-Fang Lin

Department of Public Finance National Taipei University

Taipei City 104, Taiwan (TFLIN@MAIL.NTPU.EDU.TW)

This Version: April 2006

* Prepared for the Society of Labor Economists (SOLE) Eleventh Annual Meetings, May 5-6, 2006, Cambridge, Massachusetts, U.S.A. We thank Kumiko Imai for helpful comments. All errors are our own.

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Abstract

The study of determinants of a college student’s academic performance is an important issue in higher education. Among all factors, whether or not attending lectures affects a student’s exam performance has received considerable attention. In this paper, we conduct a randomized experiment to study the average attendance effect for students who have chosen to attend lectures, which is the so-called the average treatment effect on the treated in program evaluation literature. This effect has long been neglected by researchers when estimating the impact of lecture attendance on students’ academic performance. Under the randomized experiment approach, least squares, fixed effects, and random effects models all yield similar estimates for the average treatment effect on the treated. We find that, class attendance has produced a positive and significant impact on students’ exam performance. On average, attending lecture corresponds to a 7.66% improvement in exam performance.

Keywords: class attendance, exam performance, random experiment

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I. Introduction

The study of determinants of a college student’s academic performance is an important

issue in higher education. Among all factors, whether or not attending lectures and classroom

discussions affects a student’s exam performance has received considerable attention. In light

of the importance of the attendance effect, many researchers have explored the impact of a

student’s class attendance on his or her exam performance. Most studies find that attending

lectures yields a positive and significant impact on exam performance (Anikeeff, 1954;

Schmidt,1983; Jones,1984; Buckalew, et al., 1986; Brocato, 1989; Park and Kerr, 1990; Van

Blerkom, 1992; Romer, 1993; Gunn,1993; Durden and Ellis, 1995; Devadoss and Foltz,1996;

Marburger, 2001; Bratti and Staffolani, 2002; Dolton, et al., 2003; Kirby and McElroy, 2003;

Rodgers, 2001; Rocca, 2003; Stanca, 2006; Lin and Chen, 2006).

The investigation of the attendance effect is indeed an estimation of the treatment effect in

policy evaluation. In the program evaluation literature, two kinds of treatment effects are

frequently mentioned. They are the average treatment effect and the average treatment effect

on the treated. In the application of lecture attendance, the average treatment effect refers to the

expected effect of attendance on academic performance for a randomly drawn student from the

population. The average treatment effect on the treated refers to the mean attendance effect for

those who actually participated (or not participated) in the classroom.

Literature is prolific in the area of the exploration of the average treatment effect when

estimating the impact of a student’s class attendance on his or her exam performance. In the

estimation of the average treatment effect, it is of particular note that whether or not students

choose to attend classes is an endogenous choice. Therefore, the estimated coefficient of

attendance will suffer from the endogeneity bias and become inconsistent if researchers fail to

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econometric models including instrumental variable (IV), proxy variable and panel data methods

are used to obtain consistent estimates in prior research (see Stanca (2006) for more details).

In stark contrast, existing studies in the area of attendance effect has not examined the

average treatment effect on the treated. As discussed above, the average treatment effect is the

expected effect of treatment on a randomly drawn student from the population while the average

treatment effect on the treated measures the average benefits a student could receive given that

he or she attends lectures. Most researchers focus on the estimation of the average treatment

effect since the issue of whether or not to make attendance compulsory has received great

attention in higher education. However, in the investigation of the attendance effect, we also

want to evaluate the lecture participation benefits for students who actually choose to attend

classes. This is similar to the example of job training program; what researchers and

policymakers want to know is the impact of job training on labor outcomes for program

participants but not for people from the population who probably would never be eligible for

such programs. Hence, to complement current attendance effect literature, the focus of this

paper is to investigate the average treatment effect on the treated.

One difficulty in the estimation of the average treatment effect on the treated arises from

finding the desired counterfactuals. In this case, we will need to estimate what would have

been the grades had the students not attended the class for those who actually do participate in

the classroom. One way to circumvent the problem of finding desired counterfactual is to run a

randomized experiment.

Burtless (1995) and Heckman and Smith (1995) both discuss advantages and disadvantages

of social experiments. The foremost advantage of controlled experimentation is that the

random assignment provides us with the clear causal link between treatment and outcome. In

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outcome. Random assignment also eliminates systematic correlation between treatment status

and participants’ observed or unobserved characteristics. In addition, experimentation is simple

to understand to social scientists and policymakers. Some disadvantages of experimentation

include expensive costs, ethical issues of experimentation with human beings, limited duration,

attrition and interview non-response, partial equilibrium results and program entry effects.

In this study, we propose and implement a randomized experiment to estimate the average

treatment effect on the treated. This paper will provide useful insights on the issue of the

average treatment effect on the treated in the application of class attendance. Our empirical

results demonstrate that least squares model will provide a consistent estimator under the

randomized experiment. Class attendance has produced a positive and significant impact on

students’ exam performance. On average, attending lectures corresponds to a 7.66%

improvement in exam performance.

The details of the random experiment will be discussed in the next section. In section III,

the statistical models will be presented. In section IV, the data used for this study will be

examined. The estimation results are reported in Section V, and the conclusion is summarized

in Section VI.

II. The Random Experiment

The main goal here is to construct a random experiment to estimate the average treatment

effect on the treated. The following notation is similar to the ones in Heckman and Smith

(1995).

Y1: grade outcomes associated with attending the lecture

Y0: grade outcomes associated with not attending the lecture

d = 1, attending the lecture; d = 0, not attending the lecture

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students who choose to attend classes. The average treatment effect on the treated can be

shown below:

E(Y1|d=1) – E(Y0|d =1) (1)

In order to estimate the average treatment effect on the treated, we need to know what

would have been the grades had the students not attended the class. This implies that we will

need an estimate for E(Y0|d=1) because it is unobserved by researchers. In general, E(Y0|d=0)

can not be used as a proxy for E(Y0|d=1) since students who choose not to attend lectures might

be different from those who choose to attend classes in many ways such as the unobserved

individual intelligence and motivation. As a result, the selection process to attend or not to

attend classes might become an issue and it will bias our results if we use E(Y0|d =0) to replace

E(Y0|d=1).

Our main focus then is to construct a randomized experiment to solve the problem of

selection bias. The goal is to generate an experimental group of students who would have

participated but were randomly denied access to the treatment. By doing so, we could use this

randomly selected group to be our control group and obtain their responses as the desired

counterfactuals, E(Y0|d=1).

Here is how the randomized experiment works. The instructor taught the same course in

two sections, section A and section B, in the spring semester of 2005. The course, Public

Finance, is a required course for all junior students who major in Industrial Economics at

Tamkang University in Taiwan. Students are allowed to register in any of these two sections1. At each class meeting, the same PowerPoint presentation is used in both sections, and the lecture

slides are posted on the course web site after each class meeting. During the sample semester,

the instructor randomly selects the dates, sections, and some materials/topics to cover or not to

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cover in only one section. However, students are told to be responsible for those

materials/topics shown in the slides including the ones skipped by the instructor. This implies

that materials/topics not covered by the instructor might appear in the two exams, and students

will need to prepare and study those materials by themselves to be able to answer corresponding

exam questions. In this study, about 10% of the exam questions were not covered by the

instructor but yet appeared in the exams.

Let d* = 1 denote the students who would participate in a lecture in the presence of random

assignment, and d* = 0 for everyone else. Also, let r =1 denote the group of students who are

randomly assigned to the treatment group for particular corresponding exam questions (i.e. the

materials/topics corresponding to exam questions have been covered by the instructor), and r = 0

denote the group of students who are denied access to the treatment for particular corresponding

exam questions (i.e. the materials/topics corresponding to exam questions have been randomly

skipped by the instructor).

By introducing variables d* and r, we can re-write equation (1) as

E(Y1|d* = 1, r = 1) - E(Y0|d* = 1, r = 1), (1’)

where d = 1 is replaced by d* = 1, r = 1. As mentioned above, the instructor randomly selects

the dates, sections, and materials to cover or not cover. Also, when some materials are skipped

in the lectures, students are asked to study the materials by themselves. They are told again

about this information in their last class meeting before each exam. Thus, we could reasonably

expect that

E(Y0|d* = 1, r = 1) = E(Y0|d* = 1, r = 0). (2)

E(Y0|d* = 1, r = 0) is the expected grades for students who choose to attend lectures but do not

actually get the treatments since some materials/topics are randomly skipped for corresponding

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E(Y0|d* = 1, r = 1) is the average grades that would have been obtained had students not

attended the lecture. This partial observation issue is a common problem in estimating the

average treatment effect on the treated. By running the randomized experiment, we can now

observe E(Y0|d* = 1, r = 0) and use it as a replacement for E(Y0|d* = 1, r = 1). Hence, by

using equation (2), the average treatment effect on the treated can be shown below:

E(Y1- Y0|d =1) = E(Y1- Y0|d* =1, r =1)

= E(Y1|d* = 1, r = 1) - E(Y0|d* = 1, r = 1)

= E(Y1|d* = 1, r = 1) - E(Y0|d* = 1, r = 0) (3)

Thus, randomization serves as an instrumental variable by creating variations among

students who choose to attend lectures, because some of them do receive the treatment randomly

while some of them do not receive the treatment. In so doing, we will be able to estimate the

average treatment effect on the treated accurately.

III. Statistical Models

In prior research, various econometric techniques including IV, proxy, and panel data

models are usually used to remedy the endogeneity bias problem when estimating the average

treatment effect. This paper sheds lights on the estimation of the average treatment effect on

the treated by employing a randomized experiment. Under our randomized experiment, the

mean outcomes of the experimental treatment group and the control groups provide estimates of

the average treatment effect on the treated without getting into the trouble of sample selection

bias.

This study uses a micro level data to explore the impact of a student’s attendance on his or

her exam performance. We use the following linear function to describe the relationship

between students’ exam performance and various input variables for learning.

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I is the total number of students and J is the total number of exam questions. Yij corresponds to

student i’s exam performance on question j; xij is student i’s set of observed inputs in learning

question j. β represents the student input effect vector. rij is equal to one if student i attends

the lecture when question j is covered. η is the attendance effect. αi represents student i’s

time-invariant individual effect and εij is the random disturbance term.

To estimate the average treatment effect on the treated (i.e. η), Least Squares (LS), Fixed Effects (FE) and Random Effects (RE) models will be employed. In this paper, we employ a

linear probability model instead of a nonlinear probit model when estimating the individual

effects. The main reason for doing so is that we are concerned about the incidental parameters

problem in a typical nonlinear panel model (see Woldridge (2002) and Greene (2003) for

details).

The estimation results of LS, FE and RE models are all listed for the use of comparisons.

Under the experimental design, we would expect that all three models produce consistent

estimators. By the definition of a randomized experiment, the treatment is randomly assigned

within the estimation sample and will not be correlated with xij , αi and εij. This implies that LS

estimation of the attendance effect can produced consistent result. Also, LS, FE and RE will

produce similar estimates and all these three are consistent estimators.

IV. Data

We conduct a survey of 114 students who attended the Public Finance course at Tamkang

University in Taiwan in the Spring of 2005. All students who major in Industrial Economics

are required to take this course in their third-year of study. The students are in two separate

sections. There are 67 students in one section, and 47 students in the other section.

Attendance is recorded at each class meeting during the sample semester. There are 12 2-hour

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Students’ demographic variables are collected form the survey distributed in the very first

class of the sample semester. They include students’ gender, average grades before taking this

course, living arrangement and family economic condition. Also, the commuting time between

students’ apartment and school, and the working hours for each student are

recorded. Moreover, two questions: hours students spent preparing for the exam and hours they

spent studying every week, are asked when students took their midterm and final exams. Table

1 reports the summary statistics of students’ characteristics.

In this paper, the dependent variable is a binary variable indicating students’ exam

performance. 50 multiple choice questions are asked in the midterm exam while 57 multiple

choice questions are asked in the final exam. There are 12,028 observations which come from

114 students and their responses to the 107 exam questions2. We assign 1 to the binary variable if students answer the exam question correctly; otherwise the binary variable is 0.

The binary variable, Actual Attendance, is coded as 1 if students have attended the lecture in

which the class material covered that day was relevant to the corresponding exam question, i.e.

dij = 1 as discussed in the random experiment section. Actual Attendance is coded as 0 if

students miss the class that day, i.e. dij = 0 as discussed in the random experiment section.

Among students who have attended lectures, we create a binary variable, Experimental

Attendance. Experimental Attendance is coded as 1 if students have attended the lecture and the instructor has taught the material in that lecture, i.e. d*ij = 1 and rij = 1 as discussed in the

random experiment section. Experimental Attendance is coded as 0 if students have attended

the lecture but the instructor has randomly choose not to cover some materials for corresponding

exam questions in that lecture i.e. d*ij = 1 and rij = 0 as discussed in the random experiment

2 There are two students missing the final exam (57*2), and some questions are not answered by some students (56). So 114 * 107 – 57*2 - 56 = 12,028.

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section.

Table 2 reports the means and standard deviations of students’ actual attendance,

experimental attendance, and their exam performance by students’ demographic variables.

The average actual attendance rate is about 91% which is higher than that in some previous

studies (Romer (1993), Margurger (2001)). It is worth noting that the sample course, Public

Finance, is a required course for students in their junior year. In addition, students are more

likely to attend lectures when they are in their junior and senior years as pointed out by Rocca

(2003). Therefore, a 91% class attendance rate seems reasonable. If we further restrict our

sample to students who have chosen to attend lectures, we find that the experimental attendance

is about 92%.

V. Estimation Results

Table 4 presents the estimation results for the average treatment effect. In this regression

model, the independent variable is a binary variable indicating whether or not students answer

the exam question correctly. The dependent variables include Actual Attendance, exam

question dummies and individual time-invariant dummies. The number of observations is

12,028 in this case. The coefficient of Attendance in the panel linear probability model is about

4.32%, and it is about 7.03% in the least squares model. Thus, after controlling for individual

unobserved characteristics, the consistent fixed effects estimator obtains a much smaller estimate

on the attendance effect. Generally, our average treatment effect estimation results are

comparable to prior studies. For instance, Stanca (2006) also finds that the OLS estimates

overestimate the impact of attendance on exam performance.

Table 5 provides the estimation results for the average treatment effect on the treated. We

restrict our sample to those students who have chosen to attend lectures. The sample size is

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whether or not students answer exam questions correctly. The dependent variables include

Experimental Attendance, exam question dummies and individual time-invariant dummies. The principle finding of Table 5 is that the coefficients of Experimental Attendance in LS,

FE ad RE models are almost the same. As mentioned earlier, randomization acts an instrument

variable, and simply running the least square models will give us a consistent estimator. Hence,

as we expected, LS, FE and RE models all produce similar results in the estimation of the

average treatment effect on the treated under our randomized experiment. We find that, among

students who choose to attend lectures, attending lectures yields a positive and significant impact

on students’ exam performance. On average, attending lectures corresponds to a 7.66%

improvement in exam performance.

From Tables 4 and 5, we also find that the average treatment effect is lower than the average

treatment effect on the treated. Our results suggest that the mean attendance effect for the

population of students who choose to attend classes is greater than the mean attendance effect

when students are randomly selected to attend lectures. This finding seems reasonable since we

would expect that students who decide to attend lectures should or might have a higher return

from attending classes than the ones who are randomly selected to attend lectures.

Some might be concerned about issues regarding the random assignment of treatment in this

study. For instance, our estimation results may still suffer from some biases since students

might expect that materials not covered by the instructor will be less likely to appear in the

exams even though they are told to be responsible for those skipped materials in the exams. In

order to examine whether students’ perception might become an issue and bias our results, we

further divide our sample into two sets: the midterm exam sample and the final exam sample.

If students think that materials not covered by the instructor are less likely to appear in the

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example, in the midterm, if students assume that materials not covered by the instructor will not

appear in the exam and they realize that they were wrong after the midterm, then they will pay

the same attention to those skipped materials when preparing for the final exam. If this is the

case, we would expect to see different results in the midterm and final samples. Otherwise, we

would expect to find similar estimation results in the midterm and final exam samples.

Table 6 presents the estimation results for the average treatment effect on the treated in the

midterm and final samples. In these two models, the independent variable is a binary variable

indicating whether or not students answer exam questions correctly; the dependent variables

include Experimental Attendance, exam question dummies and individual time-invariant

dummies. It is of note that we find similar results in both cases. For the midterm exam, the

average treatment effect on the treated is 7.51%; for the final exam, the average treatment effect

on the treated is 7.91%. Taken together, we would not need to worry about the perception issue

here. Moreover, this also assures us of the robustness of our estimation results.

VI. Conclusion

In this paper, a randomized experiment is designed to control for students’ endogeneous

class attending choices when exploring the impact of class attendance on exam performance.

Under our randomized experiment, the mean outcomes of the experimental treatment and control

groups provide estimates of the average treatment effect on the treated without getting into the

trouble of sample selection bias.

Our estimation results show that, under the randomized experiment, simply running the

least squares model will yield a consistent estimator. In addition, the LS, FE and RE models all

produce similar estimates of the attendance effects. On average, attending lectures corresponds

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References

Anikeeff, M. (1954), The Relationship Between Class Absences and College Grades, Journal of

Educational Psychology, 45, 244-249.

Bratti, M. and S. Staffolani (2002), Student Time Allocation and Educational Production

Functions, Working Paper Number 170, Economics Department, University of Ancona.

Brocato, J. (1989), How Much Does Coming to Class Matter? Some Evidence of Class

Attendance and Grade Performance, Educational Research Quarterly, 13, 2-6.

Buckalew, W., Daly, D., and K. Coffield (1986), Relationship of Initial Class Attendance and

Seating Location to Academic Performance in Psychology Classes, Bulletin of the

Psychonomic Society, 24, 63-64.

Burtless, G. (1995), The Case for Randomized Field Trials in Economic and Policy Research,

Journal of Economic Perspectives, 9, 63-84.

Devadoss, S. and J. Foltz (1996), Evaluation of Factors Influencing Student Class Attendance

and Performance, American Journal of Agriculture Economics, 78, 499-507.

Dolton, P., Marcenaro, D. and L. Navarro (2003), The Effective Use of Student Time: a

Stochastic Frontier Production Function Case Study, Economics of Education Review, 22,

547-560.

Durden, C. and V. Ellis (1995), The Effects of Attendance on Student Learning in Principles of

Economics, American Economic Review, 85, 343-346

Greene, W. (2003), Econometric Analysis, 5th. ed., New Jersey: Pearson Education Upper Saddle River.

Gunn, P. (1993), A Correlation between Attendance and Grades in a First-year Psychology

Course, Canadian Psychology, 34, 201-202.

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Economic Perspectives, 9, 85-110.

Jones, H. (1984), Interaction of Absences and Grades in a College Course, The Journal of

Psychology, 116, 133-136.

Kirby, A. and B. McElroy (2003), The Effect of Attendance on Grade for First Year Economics

Students in University College Cork, The Economic and Social Review, 34, 311-326.

Lin, T. and J. Chen (2006), Cumulative Class Attendance and Exam Performance, Applied

Economics Letters, forthcoming.

Marburger, R. (2001), Absenteeism and Undergraduate Exam Performance, Journal of Economic

Education, 32, 99-110.

Park, H. and P. Kerr (1990), Determinants of Academic Performance: a Multinomial Logit

Approach, Journal of Economic Education, 21, 101-111.

Rocca, A. K. (2003), Student Attendance: A Comprehensive Literature Review, Journal on

Excellence in College Teaching, 14, 85-107

Rodgers, R. (2001), A Panel-data Study of the Effect of Student Attendance on Academic

Performance, unpublished manuscript.

Romer, D. (1993), Do Students Go to Class? Should they?, Journal of Economic Perspectives, 7,

167-174.

Schmidt, R. (1983), Who Maximizes What? A Study in Student Time Allocation, American

Economic Review Papers and Proceedings, 73, 23-28.

Stanca, L. (2006), The Effects of Attendance on Academic Performance: Panel Data Evidence for

Introductory Microeconomics, forthcoming, Journal of Economic Education.

Van Blerkom, L. (1992), Class Attendance in an Undergraduate Course, Journal of Psychology,

126, 487-494.

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Test for Heteroshedasticity, Econometrica, 48, 817-838.

Wooldridge, J. (2002), Econometric Analysis of Cross Section and Panel Data, Cambridge: MIT

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Sample Size % Mean Standard Deviation All Students 114 1.000 Gender Female 65 57.02 Male 49 42.98

Average Grade Before Entering the Course 72.047 7.7553

60-70 40 35.09

70-80 47 41.23

80-90 27 23.68

Housing

Live with Relatives 43 37.72

Not Live with Relatives 71 62.28

Family Economic Condition (1 to 5) 2.8596 0.5781

Poor (1) 4 3.509 Below Average (2) 15 13.16 Average (3) 89 78.07 Above Average (4) 5 4.386 Wealthy (5) 1 0.877 Commute Time 29.355 32.425

less than 10 Minutes 37 32.46

30-10 Minutes 41 35.96

60-30 Minutes 7 6.140

more than 60 Minutes 29 25.44

Work Hours 6.9599 10.546

zero 65 57.02

10-zero Hours 15 13.16

20-10 Hours 15 13.16

30-20 Hours 13 11.40

more than 30 Hours 6 5.263

Hours Studied Before the exam 8.6327 6.4431

Below 5 Hours 25 21.93

5-10 Hours 58 50.88

10-15 Hours 20 17.54

Above 15 hours 11 9.649

Hours Studied Every Week 1.5035 1.9138

Below 1 Hours 41 35.96

1-2 Hours 47 41.23

Above 2 hours 26 22.81

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Mean Standard Deviation Mean Standard Deviation Mean Standard Deviation Mean Standard Deviation All Students 0.9088 0.0026 0.6313 0.0044 0.9198 0.0026 0.6347 0.0046 Gender Female 0.9261 0.0032 0.6387 0.0058 0.9165 0.0035 0.6404 0.0060 Male 0.8860 0.0044 0.6215 0.0067 0.9243 0.0039 0.6267 0.0071

Average Grade Before Entering the Course

60-70 0.8425 0.0056 0.5914 0.0076 0.9209 0.0045 0.5950 0.0083

70-80 0.9296 0.0036 0.6259 0.0069 0.9177 0.0040 0.6256 0.0071

80-90 0.9654 0.0034 0.6978 0.0086 0.9225 0.0051 0.6996 0.0087

Housing

Live with Relatives 0.9143 0.0032 0.6306 0.0056 0.9216 0.0032 0.6353 0.0058

Not Live with Relatives 0.8996 0.0045 0.6324 0.0072 0.9167 0.0043 0.6336 0.0076

Family Economic Condition

Poor 0.8066 0.0191 0.6840 0.0226 0.9213 0.0144 0.7026 0.0247 Below Average 0.9296 0.0064 0.6258 0.0121 0.9210 0.0070 0.6232 0.0126 Average 0.9110 0.0029 0.6264 0.0050 0.9196 0.0029 0.6311 0.0052 Above Average 0.9132 0.0122 0.6811 0.0203 0.9196 0.0123 0.6722 0.0213 Wealthy 0.7925 0.0396 0.6887 0.0452 0.9048 0.0322 0.7024 0.0502 Commute Time

less than 10 Minutes 0.9070 0.0047 0.6203 0.0079 0.9160 0.0047 0.6263 0.0082

30-10 Minutes 0.8974 0.0046 0.6252 0.0074 0.9225 0.0043 0.6260 0.0078

60-30 Minutes 0.9636 0.0069 0.6806 0.0171 0.9147 0.0105 0.6783 0.0175

more than 60 Minutes 0.9125 0.0051 0.6425 0.0086 0.9213 0.0051 0.6473 0.0090

Work Hours

zero 0.9254 0.0032 0.6444 0.0059 0.9228 0.0034 0.6460 0.0061

10-zero Hours 0.9635 0.0047 0.6560 0.0119 0.9080 0.0074 0.6562 0.0121

20-10 Hours 0.8893 0.0078 0.6094 0.0122 0.9104 0.0075 0.6104 0.0130

30-20 Hours 0.8919 0.0084 0.5965 0.0132 0.9301 0.0073 0.6016 0.0140

more than 30 Hours 0.6745 0.0186 0.5849 0.0196 0.9209 0.0129 0.6047 0.0236

Hours Studied Before the exam

Below 5 Hours 0.8671 0.0067 0.6124 0.0097 0.9203 0.0057 0.6089 0.0104

5-10 Hours 0.9098 0.0037 0.6397 0.0062 0.9190 0.0037 0.6468 0.0064

10-15 Hours 0.9304 0.0058 0.6309 0.0110 0.9324 0.0059 0.6368 0.0113

Above 15 hours 0.9456 0.0060 0.6325 0.0127 0.9086 0.0078 0.6276 0.0131

Hours Studied Every Week

Below 1 Hours 0.9522 0.0037 0.6333 0.0084 0.9223 0.0048 0.6352 0.0086

1-2 Hours 0.9008 0.0041 0.6430 0.0066 0.9208 0.0039 0.6474 0.0070

Above 2 hours 0.8775 0.0056 0.6129 0.0083 0.9171 0.0050 0.6159 0.0088

Table 2: Actual Attendance, Experimental Attendance, and Exam Performance

Actural Attendance

Experimental

Attendance Exam Performance

Exam Performance

All Samples (N = 12,028)

Samples with Actural Attendance = 1 (N = 10,919)

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Mean Standard Deviation Mean Standard Deviation Number of Students Male 0.4776 0.5033 0.3617 0.4857

Average Grade Before Entering the Cou 72.097 8.1414 71.909 7.3211

Live with Relatives 0.6716 0.4732 0.5532 0.5025

Family Economic Condition 2.8358 0.5928 2.8936 0.5608

Commute Time 29.750 32.351 29.213 33.098

Work Hours 5.5758 9.3002 9.1444 11.997

Hours Studied Before the exam 8.6119 6.4894 8.5333 6.4583

Hours Studied Every Week 1.5209 2.2242 1.3222 0.8691

67 47

Table 3: Sample Statistics for Section "A" and "B"

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Fixed Effects Model Random Effects Dependant Variable Independant Variable Attendance 0.0703** 0.0432** 0.0519** (0.0142) (0.0158) (0.0151) R-squares 0.2199 0.2473 . F-value or X2 value* 53.17** 50.04** 3435.06** Sample Size 12,028 12,028 12,028

Table 4: Estimation Results for the Average Treatment Effects

Note: "**" is at 5% significant level and "*" is at 10% significant level. White (1980) robust standard errors are in parentheses. Exam question dummies are used in all regressions. *: the F-values are reported in the Least Squares and Fixed Effects model

Correctly Answer the Question (yes = 1, no = 0) Least Squares Method

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Fixed Effects Model Random Effects Dependant Variable Independant Variable Attendance 0.0779** 0.0763** 0.0766** (0.0210) (0.0202) (0.0202) R-squares 0.2228 0.2479 . F-value or X2 value* 48.69** 29.83** 3168.39** Hausman Test (X2107) Sample Size 10,919 10,919 10,919

Table 5: Estimation Results for the Average Treatment Effect on Treated

Note: "**" is at 5% significant level and "*" is at 10% significant level. White (1980) robust standard errors are in parentheses. Exam question dummies are used in all regressions. *: the F-values are reported in the Least Squares and Fixed Effects model

Correctly Answer the Question (yes = 1, no = 0) Least Squares Method

Panel Linear Probability Model

(22)

22

Fixed Effects Model Random Effects Fixed Effects Model Random Effects

Dependant Variable Independant Variable Attendance 0.0751** 0.0761** 0.0756** 0.0791** 0.0715** 0.0738** (0.0393) (0.0364) (0.0363) (0.0249) (0.0246) (0.0245) R-squares 0.2176 0.2534 . 0.2261 0.2611 . F-value or X2 value* 39.81** 29.37** 1475.63** 56.62** 30.20** 1694.86** Hausman Test (X250 or X257) Sample Size 5,247 5,247 5,247 5,672 5,672 5,672 6.53

Table 6: Estimation Results for the Average Treatment Effect on Treated by Midterm and Final Exams

Note: "**" is at 5% significant level and "*" is at 10% significant level. White (1980) robust standard errors are in parentheses. Exam question dummies are used in all regressions. *: the F-values are reported in the Least Squares and Fixed Effects model

Final Exam

Least Squares Method

Panel Linear Probability Model

Correctly Answer the Question (yes = 1, no = 0)

3.30 Correctly Answer the Question (yes = 1, no = 0) Least Squares Method

Panel Linear Probability Model Midterm Exam

數據

Table 1: Summary Statistics

Table 1:

Summary Statistics p.17
Table 2: Actual Attendance, Experimental Attendance,  and Exam Performance

Table 2:

Actual Attendance, Experimental Attendance, and Exam Performance p.18
Table 3: Sample Statistics for Section "A" and "B"

Table 3:

Sample Statistics for Section "A" and "B" p.19
Table 6: Estimation Results for the Average Treatment Effect on Treated by Midterm and Final Exams

Table 6:

Estimation Results for the Average Treatment Effect on Treated by Midterm and Final Exams p.22

參考文獻

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