Edited by: Salvador ChacónMoscoso, Universidad de Sevilla, Spain
Reviewed by: Fernando MarmolejoRamos, University of Adelaide, Australia; Michael Roy, Elizabethtown College, United States
*Correspondence: Anatoly A. Peresetsky
This article was submitted to Quantitative Psychology and Measurement, a section of the journal Frontiers in Psychology
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Confidence and overconfidence are essential aspects of human nature, but measuring (over)confidence is not easy. Our approach is to consider students' forecasts of their exam grades. Part of a student's grade expectation is based on the student's previous academic achievements; what remains can be interpreted as (over)confidence. Our results are based on a sample of about 500 secondyear undergraduate students enrolled in a statistics course in Moscow. The course contains three exams and each student produces a forecast for each of the three exams. Our models allow us to estimate overconfidence quantitatively. Using these models we find that students' expectations are not rational and that most students are overconfident, in agreement with the general literature. Less obvious is that overconfidence helps: given the same academic achievement students with larger confidence obtain higher exam grades. Female students are less overconfident than male students, their forecasts are more rational, and they are also faster learners in the sense that they adjust their expectations more rapidly.
Most people overestimate their abilities. Svenson (
The first, perhaps, to investigate this issue was Murstein (
Is overconfidence helpful or harmful for the student? There is no consensus. Overconfidence may induce a student to allocate less time to study, resulting in poor exams grades. On the other hand, Ballard and Johnson (
Does overconfidence depend on gender? Are women better forecasters? Again, there is no consensus. Guzman (
How persistent are overly optimistic expectations? Do students adjust their forecasts? Murstein (
The main focus of our paper is the expectation of the student about his or her grade, and the papers discussed above shed some light on what others have found. There exists a vast literature on the broader subject of overconfidence, both from a theoretical and an empirical viewpoint. The bias in social comparative judgments is discussed in comprehensive reviews by Chambers and Windschitl (
In our study we do not discuss a theoretical framework of our findings. We simply introduce a model which helps us to measure overconfidence in students' forecasts. Our aim is to contribute to the questions raised above by analyzing students enrolled in a secondyear undergraduate course in statistics at ICEF, Moscow, in total 592 students. During the course each student took three exams and at each exam they forecasted their grade. We address the following research questions: Are students' expectations rational? Are they overconfident? If so, is the level of overconfidence the same for male and female students? Is overconfidence helpful? Do students adjust their exam grades during the course when more information becomes available? And, if so, does the speed of adjustment depend on gender? We find that, in general, students are overconfident, especially male students; overconfidence is helpful; students adjust their forecasts with their experience of the course; and female students adjust their beliefs faster than male students.
The paper is organized as follows. The setup is described in section Methods and Participants. Rationality, overconfidence, and persistence are investigated in section Results. Section Discussion and Conclusions offers some discussion and concluding remarks.
The International College of Economics and Finance (ICEF) in Moscow was established in 1997 jointly by the London School of Economics and Political Science (LSE) in London and the Higher School of Economics (HSE) in Moscow. The college offers a 4year bachelor's program, which is considered to be one of the top programs in economics in Russia. Each year about 200 students enter the program, typically immediately after high school. In their first year the students follow, among other subjects, a course called Statistics1, and in their second year they follow Statistics2. Both courses are compulsory. Our data are obtained from students following Statistics2 over a 5year period, 2011–2015. In total, 964 students took this course during these 5 years.
In Statistics2 students take three exams every year, at the end of October (exam 1), the end of December (exam 2), and the end of March (exam 3). The exams are written exams, not multiple choice, and each consists of two parts (80 min each) with a 10 min break between the two parts. The level of the exam questions is the same in the two parts. In order to avoid cheating, students are not allowed to leave and come back during each part of the exam. At the end of part 1 and at the end of the exam the examiner collects each student's work. Each part is graded out of 50 points.
In addition, students have weekly homework assignments although these are not compulsory. All handedin assignments are graded (out of 100). The variable
After completion of the three course exams, students take two additional exams (some only take one) in early May administered by the University of London, called
where
Students fail if
At the end of the first part of each of the three exams each student was asked to forecast (out of 100) his/her grade for this exam (the two parts together). Students were told that answering this question is voluntary: they can answer or they can skip the question. They were also told that their answers could be used for research purposes anonymously. At the moment when the student writes down the forecast he/she knows the questions and his/her answers in part 1, but the student does not yet know the questions of part 2. To encourage students to fill in their forecast and to actually try their best, a bonus is promised. If the difference between the forecast and the grade is ≤ 3 in absolute value, then one bonus point is added to the grade. For example, if the forecast is 49 and the grade is 52, then the grade for this exam is marked up to 53. This procedure had to be and has been approved by the ICEF administration. As a result of the procedure and the possibility of a bonus, the response rate was extremely high (97%). The idea of giving each student an incentive to express his/her opinion was also used in a recent experiment by Blackwell (
Smart (or risk averse) students utilize this bonus in the third exam, where the grade must be ≥25. If the student chooses the forecast
The data consist of the grades
We have some background knowledge on each student, namely the grades of the firstyear calculus (
For the homework assignments we know for each student how many assignments the student handed in (
From these “raw” data we can compute the ratios
which denote, respectively, the relative number of submitted assignments for each student in period
In order to obtain a clean and complete sample, some data screening was necessary. Of the original 964 students we excluded those students who (a) did not take all three exams; or (b) had repeated the first year; or (c) had failed the course last year; or (d) had taken a break between the first and second year. This left us with 840 students.
Of these 840 students, a further 248 were excluded because they did not provide all three forecasts or we didn't have their firstyear results. As a consequence, 592 students remain on which we have complete information. The results of the University of London exams are not used in our analysis.
A summary of these “raw” and basic data is provided in Table
Basic data, averaged.
40.81  33.87  33.94  40.18  28.13  35.30  
48.41  34.49  47.50  27.35  32.70  36.90  
47.77  41.41  39.00  38.16  38.55  40.27  
36.49  43.04  39.06  34.68  38.93  38.21  
48.82  42.85  40.54  38.06  38.58  40.98  
48.49  37.86  41.69  38.00  37.41  40.06  
Observations  79  103  129  158  123  592 
40.51  36.89  41.09  39.87  47.15  41.22 
From these raw data it is not immediately clear what the answers are to our questions. To achieve this we need more sophisticated statistical techniques than simple averages. In the next section we will address each of our research questions in turn and develop the required models as we progress.
Our first question is whether our students have rational expectations about their exam grades. In the Introduction we mentioned some literature where it is found that students overestimate their abilities, that is, that they are not rational. If we also find this (as we shall) then a second question arises, namely whether male and female students are equally irrational or that perhaps female students behave more rationally than male students.
Our experimental data differ from the data in most papers in three respects: first, we use a 0–100 grade system, while other papers typically use the more discrete FDCBA (0–4) grade system; second, our students make their forecast after they have already finished half the exam; and third, our students have a real incentive to make their forecast as precise as possible, as they get a bonus for an accurate forecast.
There is, in addition, one other feature of our data, namely the fact that we collected exam results and the associated forecasts during 5 years (2011–2015). We know from the previous section that the exams are not equally difficult in each year, and these discrepancies need to be taken into account. Thus, following Hossain and Tsigaris (
where
and the female/male dummy
We define a student to be rational when the conditional expectation E(
for each of the three exams
Recall that the third exam is special because students fail the course if
Table
Rationality,
−0.106  −0.110  0.138  
(0.097)  (0.093)  (0.097)  
−0.159  −0.247 
−0.119  
(0.137)  (0.118)  (0.133)  
−0.155  0.143  −0.086  
(0.163)  (0.141)  (0.153)  
−0.773  −0.515  1.811  
(3.028)  (3.335)  (3.690)  
−0.055  −0.031  0.086 

(0.041)  (0.039)  (0.045)  
0.121 
0.141 

(0.054)  (0.058)  
−8.071 
−0.747  
(3.203)  (3.929)  
−0.032  0.002  
(0.041)  (0.049)  
−0.162 

(0.060)  
−5.741  
(3.486)  
−0.037  
(0.046)  
−4.913 
−3.060 
−2.373 

(1.381)  (1.224)  (1.293)  
constant  31.52 
18.22 
8.65 
(4.71)  (4.21)  (4.69)  
Time dummy  Yes  Yes  Yes 
Observations  414  458  393 
0.326  0.296  0.126  
0.309  0.275  0.088  
RMSE  13.50  12.48  12.10 
0  1.9·10^{−7}  0.0011 
Some preliminary conclusions can be drawn from Table
Kruger and Dunning (
To further investigate the difference in rationality between women and men, we also estimate the extended model.
for men and women separately. The results are presented in Table
Rationality, men vs. women,
−0.152  −0.114  0.032  −0.087  −0.089  0.222  
(0.135)  (0.128)  (0.129)  (0.142)  (0.139)  (0.157)  
−0.084  −0.265  −0.230  −0.277  −0.239  −0.062  
(0.194)  (0.160)  (0.171)  (0.189)  (0.176)  (0.224)  
−0.092  0.282  0.166  −0.222  −0.028  −0.308  
(0.232)  (0.193)  (0.197)  (0.224)  (0.210)  (0.254)  
−1.473  0.392  6.139  2.447  −2.430  −6.787  
(4.111)  (4.285)  (4.482)  (4.716)  (5.800)  (6.827)  
−0.071  −0.033  0.017  −0.035  −0.023  0.147 

(0.058)  (0.053)  (0.059)  (0.057)  (0.059)  (0.070  
0.0521  0.214 
0.207 
0.047  
(0.075)  (0.078)  (0.081)  (0.095)  
−9.627 
−1.213  −5.095  4.109  
(4.104)  (4.831)  (5.467)  (7.193)  
0.006  0.052  −0.090  −0.106  
(0.053)  (0.060)  (0.066)  (0.091)  
−0.240 
−0.001  
(0.074)  (0.108)  
−10.776 
0.281  
(4.419)  (5.826)  
0.019  −0.102  
(0.058)  (0.083)  
Constant  28.38 
11.40 
3.48  30.83 
23.76 
16.26 
(6.75)  (5.79)  (6.15)  (6.62)  (6.32)  (7.46)  
Time dummy  Yes  Yes  Yes  Yes  Yes  Yes 
Observations  244  268  234  170  190  159 
0.251  0.302  0.140  0.418  0.301  0.164  
0.222  0.269  0.0812  0.386  0.253  0.076  
RMSE  14.62  13.21  12.14  11.85  11.41  11.99 
3.6·10^{−5}  0.0060  0.0060  1.4·10^{−7}  0.0002  0.0434 
By including the
Our preliminary conclusions still hold in this extended framework. Women are more cautious than men. Good students are more cautious than notsogood students in their predictions, at least for the first exam. If the student does well in the first exam, then he/she becomes too optimistic in predicting the second exam, but doing well in the second exam does not lead to such optimism. The
It is often thought that women behave more rationally than men, and this is indeed what we find. But there is no consensus in the literature. Ballard and Johnson (
In the previous section we rejected rationality in predicting exam results and we saw that there is a difference between male and female students. Our next step is to try and explain this lack of rationality, and our hypothesis is that students (especially male students) are too confident about their abilities. When a student has more confidence than is justified by his or her grades, we call this student “overconfident”; see i.e., Windschitl and O'Rourke Stuart (
It makes sense that a student who does well in exams gains in confidence. But perhaps the opposite is also true, that is, a confident studentother things being equalperforms better than one lacking in confidence (Ballard and Johnson,
An overconfident student will produce a forecast which is higher than can be explained by previous academic results. We write the forecast as
which is the same as Equation (3), except that the dependent variable is now the forecast
The reason for not including the
where
Overconfidence, thus defined, may include some information which is not available to us, such as private lessons taken before the exam or certain psychological features of the student. Since this information is not available to us we ignore it.
In the first step of the estimation procedure we thus estimate
The results of the twostep procedure are presented in Table
Overconfidence results.
0.225 
0.282 
0.345 

(0.050)  (0.055)  (0.067)  
1.329  0.750  0.204  
(1.064)  (0.986)  (1.071)  
0.171 
−0.00955  −0.187  
(0.087)  (0.097)  (0.116)  
0.443 
0.325 
0.083  0.529 
0.411 
−0.068  
(0.090)  (0.078)  (0.077)  (0.073)  (0.074)  (0.079)  
0.223 
−0.032  0.055  0.377 
0.218 
0.178  
(0.128)  (0.101)  (0.107)  (0.103)  (0.094)  (0.109)  
0.0796  0.123  −0.046  0.270 
0.004  0.060  
(0.152)  (0.120)  (0.122)  (0.122)  (0.112)  (0.126)  
−1.074  −0.651  −0.197  0.798  0.287  −2.511  
(2.818)  (2.837)  (2.960)  (2.274)  (2.657)  (3.062)  
0.0191  −0.008  0.058  0.072 
0.017  −0.030  
(0.038)  (0.033)  (0.036)  (0.031)  (0.031)  (0.037)  
0.305 
0.268 
0.186 
0.122 

(0.046)  (0.047)  (0.043)  (0.048)  
−1.125  −3.813  7.416 
−2.436  
(2.723)  (3.150)  (2.547)  (3.221)  
0.055  −0.005  0.088 
−0.005  
(0.035)  (0.039)  (0.032)  (0.040)  
0.394 
0.550 

(0.048)  (0.049)  
1.658  7.836 

(2.797)  (2.857)  
−0.012  0.020  
(0.037)  (0.038)  
Constant  7.12  14.79 
18.08 
−24.24 
−3.25  10.11 
(4.42)  (3.59)  (3.77)  (3.54)  (3.36)  (3.85)  
Year dummy  Yes  Yes  Yes  Yes  Yes  Yes 
Observations  414  458  393  414  458  393 
0.353  0.525  0.642  0.719  0.734  0.682  
0.338  0.512  0.627  0.710  0.725  0.667  
RMSE  12.67  10.64  9.72  10.13  9.92  9.91 
The right panel (
The
Thus we conclude that (a) overconfidence helps in getting a better grade; (b) the impact of information deteriorates quickly over time; (c) homework results are important for the grades, but unimportant for the forecasts; and (d) gender is
We next ask: does overconfidence depend on gender? To answer this question we consider the regression
where we note that
Overconfidence results.
−5.036 
−2.987 
−2.699 

(1.228)  (0.987)  (0.971)  
Constant  2.068 
1.239 
1.092 
(0.787)  (0.636)  (0.618)  
Observations  414  458  393 
0.039  0.020  0.019  
0.037  0.018  0.017  
RMSE  12.30  10.41  9.45 
Table
In the previous section we predicted and studied overconfidence as measured by the residuals
To answer this question we estimate the dynamic regressions
If θ_{2} < 1 then learning takes place between exams 1 and 2. Similarly, if θ_{3} < 1 then learning takes place between exams 2 and 3. We run these regressions separately for men and women, because we have seen that overconfidence is not the same for men and women.
The results are presented in Tables
Persistence from exam 1 to exam 2.
0.349 
0.185 

(0.054)  (0.062)  
−1.252  −3.063  
(2.564)  (2.420)  
−1.956  −1.422  
(2.542)  (2.436)  
−1.461  −2.097  
(2.494)  (2.252)  
−0.922  −3.309  
(2.578)  (2.394)  
Constant  2.040  0.719 
(2.025)  (1.826)  
Observations  206  152 
0.177  0.076  
0.156  0.0448  
RMSE  10.31  8.55 
Persistence from exam 2 to exam 3.
0.351 
0.431 

(0.050)  (0.072)  
−0.431  2.050  
(2.029)  (2.275)  
2.052  −2.218  
(2.008)  (2.216)  
1.487  −1.562  
(1.904)  (2.086)  
1.978  −1.416  
(2.042)  (2.216)  
Constant  −0.855  −0.322 
(1.513)  (1.641)  
Observations  213  143 
0.201  0.238  
0.181  0.210  
RMSE  8.68  7.87 
Thus we conclude that (a) confidence adjustment occurs for both male and female students; (b) the adjustment from exam 1 to exam 2 is stronger than the adjustment from exam 2 to exam 3; (c) female students are faster learners, certainly in the step from exam 1 to exam 2; and (d) overconfidence persists (since the values of θ_{j} are all positive) and this persistency is stronger for men than for women.
We can go one step further. In the above regressions we estimated the average values of the adjustment coefficient for male and female students. But each student is different and the adjustment coefficient may vary from student to student. In order to estimate the individual values of the adjustment coefficient we model θ_{j} as a function of the individual characteristics of a student:
Inserting Equation (10) in Equation (9) then gives.
Instead of estimates
Kernel density plots for the distribution of the adjustment coefficient are presented in Figure
Persistence from exam 1 to exam 2.
Persistence from exam 2 to exam 3.
The figures provide further (and more detailed) confirmation of our previous conclusions, namely that (a) adjustment takes place; (b) women are faster learners that men; and (c) there is a persistency of overconfidence from one exam to the next, which is stronger for men than for women.
In this paper we studied secondyear undergraduate students in a statistics course over a period of 5 years, comparing their grades with their forecasts. As expected, we find that the students' grade expectations are not rational and that most students are overconfident, which is in agreement with the general literature. Our study had the advantage of a relatively large number of students and a high response rate, and thus contributes to various issues (many of them unresolved) in the general area of rationality, overconfidence, and persistence. The following conclusions emerge.
First, overconfidence decreases during the course and is smallest at the third exam, which shows that students adjust their expectations as information accrues (Grimes,
Second, female students have a lower level of overconfidence than male students, thus exhibiting more rational behavior. This is of interest because the literature is not in agreement on this issue. Our results are similar to what Guzman (
Third, female students are not only better forecasters, they are also faster learners than male students, showing a faster adjustment of their grade expectations. We did not find difference in
Fourth, overconfidence has a positive effect on exam grades. Some studies suggest that overconfident students are less successful at exams since they allocate less time and efforts to study. This may be the case for some students, but we find that for most students overconfidence is advantageous, possibly because it increases ambition, morale, resolve, persistence, and hence the probability of success (Ballard and Johnson,
Finally, a suggestion to teachers based on our findings. Don't wait too long in setting your first test. This will help students to adjust their expectations at an early stage, and this in turn will be of use to them in their allocation of time and effort for the course.
All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We are grateful to two referees and to seminar participants at the Department of Applied Economics, Higher School of Economics, Moscow for constructive comments.
The Supplementary Material for this article can be found online at: