The N-effect explored

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The N-effect explored

Igor Runderkamp 10648682

Business Economics: Organization Economics 40 ECTS

Abstract

The extended N-effect states that increasing the number of competitors, while keeping the percentage of winners equal, has a detrimental effect on performance. This study tried to explain this N-effect through confidence. It turned out that confidence does not play a role within the N-effect. It could be that the variable confidence is measured in an incorrect manner. A more logical explanation is however that the number of competitors has a relative small (and in this study even insignificant) impact on confidence. People estimate their performance on factors unrelated to the number of competitors in case the percentage of winners remains equal. This phenomenon could be explained by people’s unawareness of the role of sample sizes. Limitations, potential future studies and implications are discussed as well.

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2 1. Introduction

On macroscale, increasing the number of competitors has positive consequences. An increase in competition forces firms to increase their efficiency, since only the most efficient firms are able to survive (Meggison & Netter, 2001). Consumers are believed to profit from fierce competition on macroscale in the form of lower prices and better products.

Where an increase in the number of competitors seems to enhance performance on macroscale, it is not by definition the case that an increase in the number of competitors enhances performance on microscale as well. On microscale, personnel economics prescribe that differences between people are based on relative differences instead of marginal

productivity (Lazear, 2008). Tournament models based on personnel economics are for example used to decide over the future of employees. The relative best employees will become manager one day. Employees who are relatively not performing well will never be promoted.

One of the variables influencing the motivation to perform is the number of competitors one is facing. In the example with employees, the number of competitors could influence the motivation of employees in several ways. If there are too few employees allocated in one specific section, employees might become lazy since they believe that they will be promoted anyway. If there are too many employees allocated in one specific section, employees might become frustrated since they believe that they do not even have a realistic chance to become promoted. The crux is to know the number of competitors for which people perform on their top level.

Garcia & Tor (2009) have done research to the effect of increasing the number of competitors on competitive motivation. They introduced the so-called ‘effect’ in their paper ‘The N-effect: More Competitors, Less Competition’ published in 2009. The N-effect is the discovery that increasing the number of competitors (N), while keeping the percentage of winners equal, decreases competitive motivation (Garcia & Tor, 2009). This is surprising, since statistically the chance of winning is independent from the number of competitors in case the percentage of winners remains equal. Garcia & Tor explain the N-effect by social-comparison processes. People who can identify themselves with others participating in a tournament model behave more competitive. Social-comparison processes become less important in large pools. As a consequence competitive motivation diminishes when the number of competitors grows (Garcia & Tor, 2009).

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that this is indeed the case, the range of the N-effect can be extended. Increasing the number of competitors has a detrimental effect on performance due to social-comparison processes. Although there is empirical evidence that social-comparison processes influence the

performance of people, there could as well be other factors explaining the N-effect. One of these potential factors which could influence performance is confidence based on the number of competitors. The main research question of this paper is therefore the following: What is the role of confidence within the N-effect?

This study reveals that the N-effect cannot be explained by confidence. Confidence based on the number of competitors does not have a significant impact on performance. The most logical explanation is the small (and in this study even insignificant) impact of the number of competitors on confidence.

This paper consists of in total 6 sections. The second section reviews the existing literature related to the N-effect and confidence. The methodology of the experiment held in this study is stated in section 3. The hypotheses are stated in section 4. Section 5 provides the results of this experiment. Section 6 discusses the obtained results and concludes. In the appendix there are some extra statistical tables included alongside the documents used during the experiment.

2. Related Literature

The N-effect states that increasing the number of competitors has a detrimental effect on competitive motivation (Garcia & Tor, 2009). Garcia & Tor (2009) assume a positive correlation between competitive motivation and performance. At some point in their paper they quote: “We predicted that denser test-taking environments – where more test takers are present in a testing venue – diminish competitive motivation and consequently reduce both SAT and CRT scores.” (Garcia & Tor, 2009). The assumption that (competitive) motivation is positively correlated with performance can be found in a study of Lazear (2000) as well. In Lazear’s study the motivation of workers was increased by changing from fixed wages to a pay per performance scheme, since their pay was now directly related to their performance. As a result the productivity of workers increased with 44% (Lazear, 2000). There is however as well some empirical evidence that indicates that an increase in (competitive) motivation could have a detrimental effect on performance. Ariely et al. (2009) found that if incentives become too high, there is a treat that people choke under pressure. There is a range of psychological mechanisms that explain the negative correlation between motivation and

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performance. These include increased arousal, shifting mental processes from ‘automatic’ to ‘controlled’, narrowing of attention and preoccupation with the reward itself (Ariely et al., 2009). These mechanisms are however not applicable in situations where the incentives are relatively small, as is the case in the studies done by Garcia & Tor (2009) and this paper. Therefore the N-effect in this paper is extended by assuming that increasing the number of competitors has a detrimental effect on performance. There is as well empirical evidence that the N-effect can be extended in this way. In one of the studies done by Garcia & Tor (2009), students were asked to solve 8 simple questions as quick as possible. Students competing in a pool of 10 competitors finished significantly faster than students competing in a pool of 100 competitors (Garcia & Tor, 2009).

Garcia & Tor (2009) claim that social-comparison processes explain the N-effect. They base their findings on several empirical studies discussed in their paper (Garcia & Tor, 2009). In one study participants had to answer 11 questions, which gave an indication of their social-comparison orientation (SCO). Participants were then asked to what extent they would ran faster than normal in either a pool of 50 or a pool of 500 people of similar running ability when the best 10% received a $1,000 prize. The N-effect was significantly stronger among high-SCO participants than among low-SCO participants. There was namely a positive correlation between people’s score on the social-comparison orientation and people’s

extended effort in case there were 50 contestants instead of 500 contestants. In another study, participants had to weigh their competitive feelings against a single competitor. The number of competitors consisted of either 10, 30, 50 or 100 participants. Participants felt less

competitive against a single competitor if the number of competitors grew. The importance of social-comparison processes therefore decreases as N increases. In the final study reflected in the paper by Garcia & Tor (2009), participants had to gain as many friends as possible on Facebook within one week. The pool of competitors consisted either of 10 or 10.000 competitors. Those finishing among the best 20% would receive a $100 prize. People were more motivated to compete and to compare their own progress with their competitors in a smaller pool of competitors. The results of these 3 empirical studies made Garcia & Tor (2009) conclude that the N-effect is explained by social-comparison processes.

Garcia & Tor (2009) however did not make any assumptions about the role of confidence within the N-effect. Garcia & Tor (2009) only refer to the relation between confidence and the N-effect in the ‘Facebook study’ mentioned above. In the competition to gather as many new friends on Facebook as possible within 1 week, participants felt more confident in performing among the top 20% in a pool of 10 competitors than in a pool of 10.000

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competitors. Garcia & Tor (2009) however do not include a linear relationship between confidence and performance based on the number of competitors in their study. This is remarkable, since all required data to measure the role of confidence within the N-effect is present in their ‘Facebook study’ (Garcia & Tor, 2009). As a consequence the role of confidence within the N-effect is yet to be defined.

To determine the role of confidence within the N-effect, it is first important to discuss the different effects confidence could have on performance. The relationship between confidence and performance has received a lot of attention in scientific literature. Especially in the sports world confidence plays an important role in performance. Parfitt & Pates (1999) for example studied the effect of self-confidence on the performance of basketball players. They found that self-confidence has a positive impact on both pure physical (height jumped), as partly cognitive skills (successful passes and assists) in basketball. The positive correlation between self-confidence and performance in the sports world might however be unrelated to the correlation between self-confidence and performance in pure cognitive tasks. In the sports world, performance is inter alia positively influenced by the control over the human body. Within cognitive tasks control over the human body plays only a marginal role. If confidence positively influences the sports performance through an improved control over the human body, confidence therefore does not by definition leads to a better performance in cognitive tasks.

For pure cognitive tasks there is however as well empirical evidence that confidence is positively correlated with performance. Feather (1969) found that performance is positively related to initial confidence. He constructed an experiment in which subjects had to solve anagrams. Before participants in the experiment could start solving the anagrams, participants had to rate their confidence that they would be able to solve at least 5 anagrams. It turned out that confidence was positively correlated with performance (Feather, 1969). The external validity of Feather’s study is however debatable due to a lack of external factors determining performance included. An example of including an external factor would be to include competitors in the game and measure relative performance. In this way participants’

performance is not entirely determined by their own achievements. The way through which people deal with external factors (for example in the form of competitors) when estimating their own performance gives a good indication of someone’s confidence. It could be the case that studies where external factors are absent, as is the case in Feather’s study, are not able to measure confidence in a correct manner.

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Although the studies discussed so far assume a positive correlation between confidence and performance, there is as well literature which indicates the opposite. There is namely a risk that confidence turns into overconfidence. Overconfidence is the phenomenon that someone’s subjective confidence in their judgments lays above the objective accuracy of their judgments. Overconfidence is mainly a treat in situations where there have to be made choices involving risk. There is empirical evidence that firms which are run by overconfident managers do invest more and have more debt (Ben-David et al., 2012). Another treat of overconfidence is however laziness. An overconfident person might perceive one will perform better than a competitor without having to perform on his or her top level. A study which indicates that overconfidence could have a negative effect on performance in some settings is done by Stone (1994). Stone (1994) found that inducing mildly negative expectations may improve performance more than positive expectations. He constructed an experiment in which participants had to match a student with a specific college. Participants had to base their decision on the criteria of the student and the attributes of the colleges. The participants were randomly assigned to one of three expectation conditions. In all expectation conditions, participants were told that they could use a support system that would guide them in making the most accurate choice. In the positive expectation condition participants were instructed that, due to the support system, hard work would lead to a better performance than 90% of the competitors. In the mildly negative expectation hard work would lead to a better

performance than 50% of the competitors. In the strongly negative expectation condition hard work would only lead to a better performance than 10% of the competitors.

The positive expectation condition did lead to overconfidence in choice accuracy (Stone, 1994). The positive expectation condition however did not lead to an increase in performance relative to the strongly negative expectation condition (Stone, 1994). The mildly negative expectation condition did increase performance relative to the strongly negative expectation condition (Stone, 1994).

Even though Stone’s results could be interpreted in a way which assumes that overconfidence has a negative effect on performance, it is dangerous to conclude that overconfidence has a detrimental effect on performance based on solely this study. The instructions in the study of Stone were framed in a particular way which could made participants within the positive expectation condition believe that only mediocre effort, in combination with the support system, still enables them to perform better than a substantial part of the competitors. The guarantee of performing better than a substantial part of the competitors cannot be derived from the studies used to determine the N-effect in any way (Garcia & Tor, 2009). As a

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consequence, the conclusion that (over)confidence has a detrimental effect on performance due to assumed guarantees might not be relevant when discussing the N-effect.

The primary goal of this study is to test, in an experiment that satisfies standard experimental economics criteria, whether confidence plays a role in explaining the N-effect. This

distinguishes this work from the study of Garcia & Tor (2009). Garcia & Tor (2009) only explain the N-effect by social-comparison processes and do not discuss the potential role of confidence within the N-effect.

3. Methodology

Design

An experiment was done to determine the role of confidence within the N-effect. The experiment was held on the high school Stedelijk Gymnasium Haarlem. In total 92 students participated in the experiment. The sample consisted out of 51 girls and 41 boys. All

participants were in their third year of high school. The average age of the students was 14.7 years old. The majority of the students, 61 in total, were 15 years old. The average age of the participants in this study seems to be relatively low. There are however studies which

indicate that the behavior of people at the age of 15 is representative for their behavior in later life (Webley, 2005). The relative low average age of the sample should therefore not form a problem when determining the role of confidence within the N-effect.

The experiment consisted out of two treatments. In both treatments the challenge for students was to solve as many mathematical sums as possible within 2 and a halve minute. In one treatment students competed in a pool of 10 randomly chosen competitors. In the other treatment students competed in a pool of 50 randomly chosen competitors. The experiment consisted of 2 rounds. Each student competed one round in a pool of 10 competitors and one round in a pool of 50 competitors. Students had each round the chance to win a 2€ cash price by performing among the top 20% of their random assigned pool. In both rounds, students were asked to estimate their chance of ending up in the top 20% of their random assigned pool based on the number of competitors.

There were 4 third classes which were selected to participate in the experiment. The students were informed that their pool of competitors consisted out of students randomly chosen from within- and outside their own class. This was done to make sure that the students made an

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estimation of their chances of ending in the top 20% of their pool based solely on the number of competitors they were facing. Since these students are almost 3 years together in the same class, it can be assumed that they can make a fair estimation of the capability of their

classmates in solving mathematical sums. In that case students would base their estimation not only on the size of their pool of competitors, but as well on the estimated capability of their class mates. Since competitors are now selected from outside their own class as well, this threat is less severe.

In 2 of the 4 classes, students competed the first round in a pool of 10 competitors and the second round in a pool of 50 competitors. In the other 2 classes, students competed the first round in a pool of 50 competitors and the second round in a pool of 10 competitors. The difference in order between the classes is implemented to control for learning effects. The experiment is modelled according to a combination of a between-group design and a within-subjects design. The effect of confidence on performance in different pools of competitors can therefore be measured in 2 ways; either by comparing the results between the groups for the 2 different treatments, or by comparing the differences within the subjects for the 2 different treatments.

In case of comparing between-groups, the threat of variation in the natural ability of solving sums quickly between the groups is minimalized. All subjects have namely approximately the same age and follow exactly the same education program. In case of comparing

within-subjects differences there is the threat of the learning effect. Students might be more confident in the second round regardless of the treatment due to the opportunity of learning from the first round. Students are however aware of the fact that all participants had the opportunity to learn from the first round. If the students would realize that all students could have learned from the first round, this aspect should not influence their estimation of the chance that they would end up in the top 20% of their pool in the second round. In case the learning effect causes biased results, there is always the possibility of using only data from the first round and use between-group comparisons.

To prevent a situation where students who competed in the same pool faced different circumstances, students were only allocated to pools in which they competed with students who followed the same order of treatments. So students who competed in a pool of 501

1_{In the end only 92 students participated in the experiment, divided into 2 groups of respectively 44 and 48}

students who followed the same order of treatments. As a result it was impossible to construct any pool of 50 random competitors who all follow the same order of treatments. This problem was dealt with by creating pools of 44 and 48 students, in case the pool size was supposed to be 50. The number of winners in the treatment where the pool of competitors was supposed to consist of 50 students was still based on a pool of

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competitors in the second round competed only with students whom competed with 50 competitors in their second round as well.

At the end of the second round there was a survey distributed. Participants were asked to write down their estimation of their performance in both treatments and to indicate why they choose to estimate their performance on different- or equal levels. Participants were as well asked to answer a question which could give an indication of their notion of the role of sample sizes. People namely tend to neglect the role of sample sizes (Tversky & Kahneman, 1974). In a study done by Tversky & Kahneman (1974) most students perceive the chance that on a specific day there are more than 60% boys born in a hospital to be unrelated to the size of that hospital. However, in a larger hospital the chance that the sample would stray away from an even distribution of boys and girls is lower. Therefore it would occur more often that on a specific day there are more than 60% boys born in a smaller hospital

compared to a larger hospital. In this study students had to answer an adapted version of that question to determine their notion of the role of sample sizes. Students were asked for which size of pools the chance would be higher that they would be allocated in a pool with at least 60% boys. When answering this question, students had to assume that the distribution of male and female participants in the experiment was exactly equal. The chance that students are allocated to a pool with at least 60% boys is larger in a smaller pool of competitors, since in a larger pool of competitors the distribution of male and female participants is less likely to stray away from an even distribution (Tversky & Kahneman, 1974).

Procedure

The students were given instruction forms at the beginning of the experiment. The instruction forms were in Dutch, since Dutch is the language in which participants of the experiment follow their education. An example of a mathematical sum the students had to solve (42 – 6) was given in the instructions. This was done to make the students aware of the simplicity of the sums. After reading their personal instructions of the first round, participants were asked to fill in their name, their gender and their estimation of their performance based on the number of competitors they were facing. When the students had filled in their personal information and estimation for their performance during the first round, the forms with mathematical sums were distributed. The forms were distributed upside down, so that the students were unable to already start solving the sums. Students were instructed to write

50 competitors. So in the treatment N=50, the pool consisted in the end out of 44 or 48 students. However in both pools there were still 10 winners.

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down their full name at the back of their sheet with mathematical sums and to wait for my signal to start. Students are asked to write their name at the back of their paper before the signal to start was given. This is done to prevent the risk that students forget to write down their name in their rush to solve as many sums as possible. At my signal, the students got 2 and a halve minute to turn their sheet and solve as many mathematical sums as possible. After 2 and a halve minute students had to lay down their pens. The first round of the experiment was than over.

At the time the answers of the first round of sums were collected, a second set of instructions was handed out to the participants. The set-up of the second round was identical to the first round, only the number of competitors the students were facing differed. Students, who competed in a pool of 10 competitors in the first round, competed in a pool of 50 competitors in the second round and vice versa. Students had to fill in their name and their estimation of their performance on their second set of instructions. The second round forms with

mathematical sums were than distributed. The forms were again distributed upside down, so that the students were unable to already start solving the sums. Students were instructed to write down their name at the back of their second sheet with mathematical sums and to wait for my signal to start. At my signal, the students got again 2 and a halve minute to turn their sheet and solve as many mathematical sums as possible. After 2 and a halve minute students had to lay down their pens. The second round of the experiment was than over. After the forms with the second round of sums were collected, the survey was distributed. After the surveys were filled in and collected, the experiment was over.

4. Hypotheses

In the introduction and literature review one specific research question is formulated; what is the role of confidence within the N-effect? In order to be able to answer this question, there are two additional research questions formulated. First, this study investigates whether the N-effect is actually present within this study. Second, this study measures the impact of the number of competitors on confidence. The impact of the number of competitors on

confidence could be important when explaining the role of confidence within the N-effect. Therefore there are 3 research questions with accompanying hypotheses formulated, which are listed below:

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1) Is the N-effect present in this study?

H10 : Increasing the size of the pool of competitors, while keeping the percentage of winners

in both pools equal, does not have an effect on performance.

H1a : Increasing the size of the pool of competitors, while keeping the percentage of winners

in both pools equal, has a detrimental effect on performance.

2) Does an increase in the size of the pool of competitors, while keeping the percentage of winners in both pools equal, has an effect on confidence?

H20 : Increasing the size of the pool of competitors, while keeping the percentage of winners

in both pools equal, does not have an effect on confidence.

H2a : Increasing the size of the pool of competitors, while keeping the percentage of winners

in both pools equal, has an effect on confidence.

3) Could the N-effect be explained by confidence?

H30 : Confidence does not play a role in explaining the N-effect.

H3a : Confidence does play a role in explaining the N-effect.

The N-effect states that increasing the number of competitors, while keeping the percentage of winners equal, has a detrimental effect on performance. There are 3 scenarios for the role of confidence within the N-effect based on the literature review and rational assumptions.

1. A larger pool of competitors could decrease the confidence of participants (Garcia & Tor, 2009). This could happen if participants do not believe in their chances when the pool of competitors is increased and therefore become less confident. A rational explanation for these thoughts is that in a larger pool of competitors, people have to beat a larger absolute amount of competitors to win. There is a lot of empirical evidence indicating that lower confidence has a detrimental effect on performance (Parfitt & Pates, 1999; Feather, 1969).

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2. A larger pool of competitors could as well increase the confidence of participants. In a game where there is one small pool and one big pool, the chance on either good or bad luck with the quality of the competitors is higher in a smaller pool of competitors. The reason is that the variance in the quality of the competitors is more evenly

distributed in a larger pool of competitors (Tversky & Kahneman, 1974). A risk averse person might therefore be more confident in a larger pool of competitors, since the risk of bad luck with the quality of the competitors is smaller within a large pool of competitors (Tversky & Kahneman, 1974). If participating in a large pool of competitors leads to overconfidence in the sense that competitors believe they will end up among the winners anyway, confidence could have a detrimental effect on performance (Stone, 1994).

Number of competitors ↑  Confidence ↑  Performance ↓

3. It could as well be that confidence is not determined by the number of competitors. This happens when participants estimate their performance on factors which are unrelated to the number of competitors they are facing. Participants might for example estimate their chances in both pools equal, since the actual percentage of winners remains equal in both pools. Confidence based on the number of competitors is than not likely to play a role within the N-effect.

Number of competitors ↑  Performance ↓ (Confidence does not play a role within the N-effect in this case)

5. Results

Summary statistics

The graphs below give an overview of some summary statistics based on the answers given by students in the survey at the end of the experiment.

Graph 1 gives an indication for the motives behind students’ confidence levels in both treatments.

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Below the diversification in students’ motives is discussed based on students’ considerations notated in their survey at the end of the experiment.

Equal Winning Percentage: Almost 23% of the students believed their chances of winning remained the same regardless the number of competitors. They based this believe on the fact that the percentage of winners stayed equal in both treatments.

Larger N  Smaller Chance: Almost 34% of the students believed that their chances on

winning decreased in case the number of competitors was higher. Some of the students did not realize that the percentage of winners remained equal. These participants believed that the number of winners remained equal, while the number of competitors grew. However, most students understood that the number of winners increased in ratio with the number of competitors. Students believed that they had more chance in case of a smaller N, since they than simply had to beat less absolute competitors to win.

Larger N  More Chance: Just over 13% of the students believed their chances of winning

increased for a larger N. They based this believe on the assumption that the impact of a single strong competitor is less powerful in a competition with a high number of competitors

compared to a competition with a small number of competitors. A single strong competitor is likely to be 1 of the 2 winners in a pool of 10 competitors, while a single strong competitor is only 1 of the 10 winners in a pool of 50 competitors. This assumption is correct, however

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21 _{External Factors}

Larger N --> More Chance Larger N --> Smaller Chance

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students did not seem to realize that the actual chance of being in a pool with a single strong competitor is of course higher in a larger in a smaller pool of competitors.

External Factors: The remaining 30% of the students based their confidence on ‘external factors’. They estimated their performance based on factors unrelated to competition size or percentage of winners. External factors influencing the decision making process of students mentioned most often are the following:

- Students tend to overestimate their own capabilities of solving sums quickly during the first round. These students thought the sums would be easier to solve, even though the example given in the instructions (42 – 6) was representative of the difficulty of the sums. In case their performance in the first round did not meet their expectations, students had less confidence in their performance during the second round.

- Students compared their own performance with the performance of their neighbors. Students were unaware of their exact performance at the end of the two and a halve minute, but a quick look to the number of answers gives an indication about

someone’s performance. Students either upgraded or downgraded their confidence in the second round based on their own perceived performance in the first round

compared to the perceived performance of their neighbors in the first round.

- There were students who took the wrong conclusions out of the learning effect. These students thought they would perform better during the second round, since they now knew what to expect. These students however did not seem to realize that their performance was measured on a relative scale. Since all participants had the opportunity to learn from the first round, the learning effect applied to all students. Students therefore should not have determined their confidence in the second round on the learning effect.

On the eye graph 1 indicates that there is a negative correlation between the number of competitors and confidence due to the larger fraction of people who seem to be more

confident in a smaller sample of competitors. Graph 1 is however misleading, since the actual size of the impact of the number of competitors on confidence is not measured. Graph 1 and it’s explanations below should therefore only be interpreted as an indication for the thoughts behind students diversification in confidence.

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Graph 2 gives an indication of students’ statistical notion of the role of sample sizes

Graph 2. Overview of students’ answers to the question for which size of pools the chance of ending up in a pool where at least 60% of the competitors are male is higher

More than 58% of the students consider the chance to end up in a competition with at least 60% boys to be equal for N=10 and N=50. In reality the chance that you end up in a competition with at least 60% boys is larger within a smaller pool of competitors. Only 20% of the students gave this correct answer.

Learning Effects

This study controls for the possibility of the learning effect. The order in which students competed in the different sizes of pools is mixed up. Table 1 indicates that the learning effect with regard to performance is present.

2 18 18 54 No Answer A competition with N=10 A competition with N=50

The chances are equal for a competition with either N=10 or N=50

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Table 1. Comparison of the performance in round 1 & round 22

t = -3.48

Students performed significantly better in the second round than in the first round of the experiment, regardless of the pool they were competing in. Students solved on average 2.74 sums more in the second round compared to the first round. This result is significant for a p-value of 0.01.

This result can be entirely attributed to those students who followed an order in which they competed the first round in a pool of 50 competitors and the second round in a pool of 10 competitors. Students who participated in the experiment according to this order solved on average more than 8 sums more in the second round than in the first round (p < 0.01). A table with these results can be found in table A-2 of the appendix. Students who participated in an order in which they competed the first round in a pool of 10 competitors and the second round in a pool of 50 competitors solved on average 3 sums more in the first round than in the second round. This effect is however insignificant for a p-value of 0.1. A table with these results can be found in table A-1 of the appendix.

The explanation for the presence of the learning effect with regard to performance is that students learned how to efficiently solve as many sums as possible after the first round. A major part of the students started by solving sum by sum in the first round of the experiment. After the first round there were students, solving sum by sum during the first round, who saw that other students skipped relatively difficult sums. The strategy of skipping relatively difficult sums was used by many more students in the second round compared to the first round. While this study provides no statistical evidence, it seems as if skipping relatively difficult sums has a positive impact on solving as many sums as possible in comparison with solving sum by sum.

2_{In table 1 a paired t-test is used, since everybody within the sample is tested for both treatments.}

Variable Obs. Mean Std.

Error Std. Dev. 95% Confidence Interval Performance in round 1 92 48.68 0.97 9.31 46.76 50.61 Performance in round 2 92 51.42 0.98 9.41 49.47 53.37 Difference 92 -2.74 0.79 7.55 -4.3 -1.18

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The learning effect could as well have an influence on confidence in this experiment. Table 2 indicates that this is indeed the case. The learning effect has a negative effect on confidence.

Table 2. Comparison of confidence in round 1 & round 23

t = 4.95

Students had significantly more confidence in the first round than in the second round of the experiment, regardless of the pool they were competing in. Confidence drops with 7.4 percentage points from almost 35% in the first round, to 27.5% in the second round. This effect is significant for a p-value of 0.01. Especially in the order of treatments in which students competed the first round in a pool of 10 competitors and the second round in a pool of 50 competitors this effect is forthcoming. In this order, confidence is diminished with more than 11 percentage points from more than 35% to less than 25%. This effect is significant for a p-value of 0.05. A table with these results can be found in table A-3 of the appendix. In the order of treatments in which students competed the first round in a pool of 50 competitors and the second round in a pool of 10 competitors confidence drops with on average almost 4 percentage points (from 34.19% to 30.31%). However, this effect is insignificant for a p-value of 0.1. A table with these results can be found in table A-4 of the appendix.

There are two explanations for the negative impact of the learning effect on confidence. The first explanation is that students downgraded their confidence based on the perceived score of their neighbors in the first round. The second explanation is that students overestimated their own capability in solving sums before the first round. After the first round, students were unsatisfied with their performance during the first round. The students therefore had less confidence in their performance the second round.

Error Std. Dev. 95% Confidence Interval Confidence in round 1 92 34.95 2.45 23.53 30.07 39.82 Confidence in round 2 92 27.54 2.3 22.06 22.97 32.11 Difference 92 7.4 1.5 14.36 4.43 10.38

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The N-effect

Table 3 measures the difference in performance between students competing in a pool of 10 competitors and students competing in a pool of 50 competitors.

Table 3. Comparison of performance between students competing in pools where N=10 and

students competing in pools where N=504

t = 10.24

A student solved on average 5.85 sums more in a pool of 10 competitors than in a pool of 50 competitors when data from both rounds are considered. This result is significant for a p-value of 0.01.

Since table 1 on page 16 indicates the presence of the learning effect with regard to

performance, table 4 measures the difference in performance in only the first round between students competing in pools where N=10 and students competing in pools where N=50.

Table 4. Comparison of the performance in the first round between students competing in

pools where N=10 and students competing in pools where N=505

t = 3.07

5_{In table 4 an unpaired t-test is used, since the different treatments are run on separate independent groups.}

Error Std. Dev. 95% Confidence Interval Performance N=10 92 52.98 0.91 8.76 51.16 54.79 Performance N=50 92 47.13 0.96 9.23 45.22 49.04 Difference 92 5.85 0.57 5.48 4.71 6.98

Error Std. Dev. 95% Confidence Interval Performance N=10 44 51.66 1.44 9.55 48.76 54.56 Performance N=50 48 45.96 1.2 8.28 43.55 48.36 Difference 5.7 1.86 2.01 9.4

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19

In the first round, a student solved on average 5.7 sums more in a pool of 10 competitors than in a pool of 50 competitors. This result is significant for a p-value of 0.01.

Based on tables 3 and 4, hypothesis H10 can be rejected and hypothesis H1a can be accepted.

Increasing the size of the pool of competitors, while keeping the percentage of winners in both pools equal, has a detrimental effect on performance.

Confidence

Table 5 measures the difference in confidence between students competing in a pool of 10 competitors and students competing in a pool of 50 competitors.

Table 5. Comparison of confidence between students competing in pools where N=10 and

students competing in pools where N=506

t = 2.04

Students are significantly more confident in pools of 10 competitors than in pools of 50 competitors when data from both rounds are considered. In a pool of 10 competitors, students have on average a confidence level of 3.36 percentage points higher than in a pool of 50 competitors. This result is significant for a p-value of 0.05.

It is besides interesting to notice that on average students estimate the chance that they will win above 20% (respectively 32.92% for N=10 & 29.57% for N=50), while in the end only 20% of the students in both competition sizes actually do win. This denotes the presence of structural overconfidence.

Since table 2 on page 17 indicates the presence of the learning effect with regard to

confidence as well, table 6 measures the differences within the first round of the experiment between the confidence of students in a pool of 10 competitors compared to the confidence of students in a pool of 50 competitors.

Error Std. Dev. 95% Confidence Interval Confidence N=10 92 32.92 2.33 22.39 28.29 37.56 Confidence N=50 92 29.57 2.47 23.68 24.66 34.47 Difference 92 3.36 1.65 15.82 0.08 6.63

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20 Table 6. Comparison of confidence in the first round between students competing in pools

where N=10 and students competing in pools where N=507

t = 0.32

Students are slightly more confident in pools of 10 competitors than in pools of 50

competitors. However these results are insignificant for a p-value of 0.1. Since the results of table 5 on page 19 are likely to be biased due to the learning effect and table 6 above denotes the absence of a significant difference in confidence between students competing in pools of 10 or 50 competitors, hypothesis H20 cannot be rejected. Increasing the size of the pool of

competitors, while keeping the percentage of winners in both pools equal, does not have an effect on confidence in this study.

Confidence within the N-effect

This section determines the role of confidence within the N-effect. Table 7 shows a

regression where the dependent variable performance is determined by independent variables treatment, confidence, notion of the role of sample sizes and gender. The variable treatment is a dummy variable reflected either by 0 (number of competitors = 10) or 1 (number of

competitors = 50). The notion of the role of sample sizes is as well a dummy variable, reflected by either 0 (incorrect answer on the question indicating students’ notion of the role of sample sizes) or 1 (correct answer on the question indicating students’ notion of the role of sample sizes). The parameters are estimated by the ordinary least squares method.

7_{In table 6 an unpaired t-test is used, since the different treatments are run on separate independent groups.}

Error Std. Dev. 95% Confidence Interval Confidence N=10 44 35.77 3.66 24.3 28.38 43.16 Confidence N=50 48 34.19 3.32 23.02 27.5 40.87 Difference 1.59 4.93 -8.22 11.39

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21 Table 7. Determinants of Performance

Observations 184

R2 0.13

For a p-value of 0.05, only the variables treatment and round have a significant impact on performance. The effect of both variables is strong. A student competing in a pool of 10 competitors solves on average 5.56 sums more within 2 and a halve minute than a student competing in a pool of 50 competitors. A student solves on average 2.86 sums more during the second round than during the first round of the experiment. Confidence is not significant for a p-value of 0.05, however significant for a p-value of 0.1. Performance increases with 0.05 for every percentage point increase in confidence. This means that a person which has 20 percentage points more confidence of performing among the top 20% will solve on average 1 sum more within 2 and a halve minute. Notion of the role of sample sizes is non-significant (p = 0.3), however the estimated effect of giving the correct answer to the question within the survey leads to an increase in performance of 1.74. The variable gender is

insignificant and irrelevant from any perspective. R2 is 0.13, which means that the variance in performance can be explained for 13% by the independent variables used in table 7.

Table 7 is however inconsistent due to the learning effect. In table 2 on page 17 it can be seen that confidence is influenced by the round in which students participate. As a consequence the independent variables confidence and round are not independent from each other. OLS is not consistent in case the independent variables are correlated with each other. Therefore table 8 estimates the impact of independent variables confidence, treatment, gender and notion on the dependent variable performance based on observations from the first round only. Hereby this regression controls for the learning effect. The OLS estimator in table 8 is

Variable Coef. Std. Error t P > t 95% Confidence Interval Constant 49.53 1.81 27.37 0.00 45.96 53.1 Confidence 0.05 0.03 1.7 0.09 -0.01 .11 Treatment -5.56 1.32 -4.21 0.00 -8.16 -2.95 Gender -0.04 1.33 -0.03 0.98 -2.65 2.58 Notion 1.74 1.66 1.05 0.3 -1.53 5.02 Round 2.86 1.33 2.15 0.03 0.23 5.5

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22

more likely to be consistent since the independent variables are independent from each other. Table A-5 in the appendix shows there is no treat of multicollinearity8 for the independent variables used in table 8.

Table 8. Determinants of performance in first round of experiment only

Observations 92

R2 0.12

For a p-value of 0.05 only the variable treatment has a significant impact on performance. A student competing in a pool of 10 competitors solves on average 5.68 sums more within 2 and a halve minute than a student competing in a pool of 50 competitors. Confidence is not anymore significant for a p-value of 0.1 (p-value = 0.11), while the actual impact on

performance slightly increased toward 0.06. The notion of the role of sample sizes seems to have become even less important, since the p-value is now 0.69 and the coefficient falls to 1.2. The variable gender remains insignificant and irrelevant from any perspective. R2 is now 0.12, which means that the variance in performance can be explained for 12% by the

independent variables used in table 8.

Based on tables 7 and 8, hypothesis H30 cannot be rejected. In table 7 confidence based on

the number of competitors influences performance significantly at a p-value of 0.1. However the results of table 7 are inconsistent due to the learning effect. Table 8 shows that confidence based on the number of competitors has an insignificant effect on performance when

controlled for the learning effect. Therefore this study provides no statistical evidence that confidence plays a role within the N-effect.

8_{Table A-5 in the appendix shows that there is no treat of high correlation between the independent variables}

(multicollinearity) in a regression which controls for the learning effect, since the maximum correlation between the independent variables does not exceed 0.2.

Variable Coef. Std. Error t P > t 95% Confidence Interval Constant 48.76 2.32 21 0.00 44.15 53.38 Confidence 0.06 0.04 1.61 0.11 -0.02 0.14 Treatment -5.68 1.89 -3.02 0.00 -9.43 -1.94 Gender 0.75 1.88 0.4 0.69 -2.99 4.48 Notion 1.2 2.37 0.51 0.61 -3.51 5.91

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23

Limitations

This study contains several limitations. A first limitation is that students were able to compare their own perceived performance with those of their neighbors in between rounds. The knowledge of the perceived performance of their neighbors influenced students’

confidence in the second round. There were students who indicated that they had more (less) confidence in the second round, since their perceived performance was better (worse) than their neighbors in the first round. This is a liability in the experiment, since students could base their confidence the second round on more than just the number of competitors. In hindsight it would have been better to make it impossible for students to get even a glimpse of the perceived performance of other students.

This study is as well likely to suffer from the omitted variable bias problem, since this study does not control for social-comparison processes. In determining whether confidence plays a role within the N-effect it would have been beneficial if this study controlled for social-comparison processes. Social-social-comparison processes namely have proven to be a significant determinant in explaining the N-effect (Garcia & Tor, 2009). This might be as well the reason that the independent variables in tables 7 and 8 do respectively only explain 13% and 12% of the variance in performance. It could as well be that social-comparison processes are

correlated with independent variables used in both tables. In that case there is a threat of endogeneity, since the independent variables might be correlated with the error term. OLS estimators are inconsistent in case of endogeneity.

Finally, it might be that the variable confidence is not measured correctly within this study. There are 2 reason why this could be the case. Either students were unable to make a correct estimation of their own performance within different group sizes in this particular study. This could occur if students estimate their performance on other factors than their own perceived capabilities, the percentage of winners and the number of competitors. Graph 1 on page 12 shows that 30% of the students participating in this experiment made an estimation of their performance based on external factors. It could as well be that people have difficulties rating their relative capabilities in general, especially in case the identity of their competitors is unknown.

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24 6. Discussion & Conclusion

On macroscale it is believed that increasing the number of competitors has positive effects, for example in the form of an increase in efficiency of the firms. This study however indicates that on microscale increasing the number of competitors is not likely to have any positive effects. Based on prior research, the N-effect could already be extended in the sense that increasing the number of competitors has a detrimental effect on performance next to competitive motivation (Lazear, 2000; Garcia & Tor, 2009). This study provides empirical evidence for the existence of this extended N-effect. People perform significantly better when they face a small number of competitors compared to when they face a large number of competitors.

The main question of this paper was to determine the role of confidence within the N-effect. Table 7 on page 21 shows that confidence does not play a significant role within the N-effect in this study. Garcia & Tor (2009) did not discuss a potential role of confidence within performance in their study. The fact that Garcia & Tor (2009) did not mention the role of confidence within the N-effect could denote the absence of a significant impact of confidence within the N-effect in their study as well.

The absence of a solid linear relation between confidence and performance within the N-effect might be explained by the failure of measuring confidence in the proper way. It could be the case that people are unable to properly estimate their performance on a relative scale, as discussed in the limitations. This limitation cannot be solved when the role of confidence within the N-effect has to be determined in future studies, since estimating one’s relative performance is indispensable when measuring the role of confidence within the N-effect. However, people might have problems to estimate their relative performance only in case the identity of their competitors is unknown. This study provides no statistical evidence that this is indeed the case. It is however logical to assume that people are more capable in estimating their relative chances in case the identity of their competitors is known. A setting in which people estimate their own chances based solely on the number of competitors, while the identity of their competitors is known, could be interesting for future studies. In this study students were unaware of the identity of their competitors. This was done to make sure that students estimated their performance solely on the number of competitors and not on the identity of their competitors.

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A more realistic explanation for the nonexistant role of confidence within the N-effect is the relative small impact of the number of competitors on confidence. Table 6 on page 20 shows that within this study the effect of confidence on performance is not even significant in case the regression controls for the learning effect9. These results are somewhat conflicting with the results found by Garcia & Tor (2009) in their ‘Facebook study’. In this study, the number of participants had as well a less significant effect on confidence than on performance (Garcia & Tor, 2009). However the effect of the number of competitors on confidence in Garcia & Tor (2009) was significant at a p-value of 0.05. A potential explanation for these conflicting outcomes could be the differences in the experimental setting in this study and the study done by Garcia & Tor (2009). In the study of Garcia & Tor (2009), students had to rate their confidence on a scale of 1-7 and the 2 pools consisted of either 10 or 10.000 competitors. In this study, students had to rate their confidence on a scale of 1-100 and the 2 pools consisted of either 10 or 50 competitors. It could be the case that these differences contribute to a difference in significance of the outcomes of both studies. The difference between 10 and 10.000 competitors is for example more extreme than the difference between 10 and 50 competitors. This could make students more aware of the actual difference between the numbers of competitors.

Both this study and the study done by Garcia & Tor (2009) prove however that the number of competitors has a significant smaller impact on confidence than on performance. Scenario 3 of the hypotheses seems to be correct. An increase in the number of competitors has a

detrimental effect on performance through other factors than confidence, due to the marginal effect of the number of competitors on confidence. An explanation for the smaller (and in this study even insignificant) impact of the number of competitors on confidence could be

people’s lack of statistical notion of the role of sample sizes. Only 20% of the students in this study estimated the chance to end up within a pool of at least 60% boys to be larger in a smaller pool of competitors. This denotes people’s ignorance of the role of sample sizes. People might therefore just estimate their performance on factors irrespective of the number of competitors, since they believe that their actual chances of winning are not affected by the number of competitors in case the percentage of winners remains equal. The impact of the

9_{Table 1 on page 16 and table 2 on page 17 show that the learning effect is significantly present in case of} both performance and confidence. Therefore the conclusions made are based solely on statistical tests controlled for this learning effect, since statistical tests not controlling for the learning effect might be biased.

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26

number of competitors on performance (The N-effect) could then be seen as an unconscious phenomenon. The number of competitors triggers competitive motivation subconsciously, instead of triggering confidence consciously.

Although confidence does not play a role within the N-effect, this study once again proves the existence of the N-effect in a broader sense. This broad N-effect, where an increase in the number of competitors has a detrimental effect on performance, should have implications for policy makers on microscale. People should be treated in different ways than institutions or firms. Where firms and institutions become more efficient if the number of competitors grow, the N-effect indicates that the opposite accounts for people. People perform better in smaller environments. It could therefore be detrimental for the work environment to let people compete with too many competitors in a specific setting. A possible way to take the N-effect into consideration is to keep teams within offices small. Even though it is debatable whether a small amount of competitors has a positive impact on confidence, it is statistically proven that a small amount of competitors has a positive impact on people’s performance.

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27 Appendix

The appendix consists of tables which were referred to in the thesis and documents used during the experiment.

Table A-1. Comparison of the performance in round 1 & round 2 for students who followed an order in which they competed the first round in a pool of 10 competitors and the second

round in a pool of 50 competitors10

t = 1.55

Table A-2. Comparison of the performance in round 1 & round 2 for students who followed an order in which they competed the first round in a pool of 50 competitors and the second

t = -4.99

10_{In table A-1 an unpaired t-test is used, since the different orders are run on separate independent groups.} 11_{In table A-2 an unpaired t-test is used, since the different orders are run on separate independent groups.}

Error Std. Dev. 95% Confidence Interval Performance in round 1 44 51.66 1.44 9.55 48.76 54.56 Performance in round 2 44 48.41 1.52 10.1 45.34 51.48 Difference 3.25 2.1 -0.91 7.41

Error Std. Dev. 95% Confidence Interval Performance in round 1 48 45.96 1.2 8.28 43.55 48.36 Performance in round 2 48 54.19 1.14 7.87 51.9 56.47 Difference -8.23 1.65 -11.5 -4.95

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28 Table A-3. Comparison of the confidence in round 1 & round 2 for students who followed an order in which they competed the first round in a pool of 10 competitors and the second

t = 2.2

Table A-4. Comparison of the confidence in round 1 & round 2 for students who followed an order in which they competed the first round in a pool of 50 competitors and the second

t = 0.87

Table A-5. Correlations between the independent variables used in table 8

12_{In table A-3 an unpaired t-test is used, since the different orders are run on separate independent groups.} 13_{In table A-4 an unpaired t-test is used, since the different orders are run on separate independent groups.}

Error Std. Dev. 95% Confidence Interval Confidence in round 1 44 35.77 3.66 24.30 28.38 43.16 Confidence in round 2 44 24.52 3.56 23.61 17.34 31.70 Difference 11.25 5.11 1.1 21.4

Error Std. Dev. 95% Confidence Interval Confidence in round 1 48 34.19 3.32 23.02 27.50 40.87 Confidence in round 2 48 30.31 2.94 20.39 24.39 36.23 Difference 3.88 4.44 -4.94 12.69

Confidence Gender Notion Treatment

Confidence 1

Gender -0.06 1

Notion -0.00 -0.05 1

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29

The following documents are the instruction forms handed out to the students during the experiment. The first set of instruction was for students who followed an order of treatments in which they competed the first round in a pool of 10 competitors and the second round in a pool of 50 competitors. The second set of instructions was for students who followed an order of treatments the other way around. Please take into account that the students received the different parts of the instructions on separate times. The students received the first part of the instructions before the first round of sums and the second part of the instructions after the first round of sums.

The survey handed out to the students at the end of the experiment can be found on page 34. The forms with sums can be found on pages 35 and 36.

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30

Geachte leerling,

Welkom bij mijn experiment. Lees de instructies alsjeblieft zorgvuldig door. Zet je telefoon uit of op stil gedurende het gehele experiment. Wees daarnaast ook stil gedurende het gehele experiment.

Schrijf allereerst hier je voor- en achternaam:

Het experiment zal uit 2 verschillende onderdelen bestaan. Hieronder volgen de instructies voor het eerste deel van het experiment.

Deel 1

Zo meteen zullen er formulieren worden uitgedeeld met simpele rekensommen. Een

voorbeeld van een som op het formulier is 42-6. Je wordt zo meteen geacht zoveel mogelijk sommen correct op te lossen binnen twee en een halve minuut.

4 van de 5 derde klassen doen mee aan mijn experiment. Je eigen uitwerkingen zullen worden vergeleken met uitwerkingen van 9 andere leerlingen van binnen en buiten je eigen klas. Iedereen wordt dus ingedeeld in een groep van in totaal 10 leerlingen. Mocht je binnen de voor jou samengestelde groep van 10 leerlingen bij de beste 20% horen, dan win je 2€.

De formulieren met sommen worden zo meteen ondersteboven uitgedeeld, zodat je de

sommen nog niet kunt zien. Schrijf allereerst jouw voor- en achternaam op de achterkant van het formulier met sommen.

Wacht alvorens ik het teken geef om te beginnen voordat je het formulier met sommen omdraait!

Na precies twee en een halve minuut zal ik roepen: “pennen neer”. Degene die op dat moment nog doorgaat met schrijven wordt direct gediskwalificeerd en uitgesloten van de prijzen.

Voordat de formulieren met sommen zo meteen worden uitgedeeld vraag ik je eerst onderstaande in te vullen:

Leeftijd: Geslacht:

Hoe groot acht jij de kans dat jij binnen je willekeurig samengestelde groep van 10 leerlingen bij de beste 20% hoort? (Graag in een percentage uit drukken):

Nadat de eerste ronde is afgelopen, zullen de instructies voor het tweede deel van het experiment worden uitgedeeld.

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31 Deel 2

Zo meteen zullen er weer formulieren worden uitgedeeld met simpele reken sommen. De moeilijkheidsgraad van de sommen zal hetzelfde zijn. Je wordt zo meteen wederom geacht zoveel mogelijk sommen correct op te lossen binnen twee en een halve minuut.

Je eigen uitwerkingen zullen dit keer worden vergeleken met uitwerkingen van 49 andere leerlingen binnen en buiten je eigen klas. Iedereen wordt dus ingedeeld in een groep van in totaal 50 leerlingen. Mocht je binnen de voor jou samengestelde groep van 50 leerlingen bij de beste 20% horen, dan win je 2€.

De formulieren met sommen worden zo meteen weer ondersteboven uitgedeeld, zodat je de sommen nog niet kunt zien. Schrijf wederom eerst jouw voor- en achternaam op de

achterkant van je formulier met sommen.

Voor- en achternaam:

Nadat deze ronde is afgelopen, zal er nog een korte enquête worden uitgedeeld. Jullie worden vriendelijk verzocht deze enquête waarheidsgetrouw in te vullen.

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32

Geachte leerling,

Welkom bij mijn experiment. Lees de instructies alsjeblieft zorgvuldig door. Zet je telefoon uit of op stil gedurende het gehele experiment. Wees daarnaast ook stil gedurende het gehele experiment.

Schrijf allereerst hier je voor- en achternaam:

Het experiment zal uit 2 verschillende onderdelen bestaan. Hieronder volgen de instructies voor het eerste deel van het experiment.

Deel 1

Zo meteen zullen er formulieren worden uitgedeeld met simpele rekensommen. Een

voorbeeld van een som op het formulier is 42-6. Je wordt zo meteen geacht zoveel mogelijk sommen correct op te lossen binnen twee en een halve minuut.

4 van de 5 derde klassen doen mee aan mijn experiment. Je eigen uitwerkingen zullen worden vergeleken met uitwerkingen van 49 andere leerlingen van binnen en buiten je eigen klas. Iedereen wordt dus ingedeeld in een groep van in totaal 50 leerlingen. Mocht je binnen de voor jou samengestelde groep van 50 leerlingen bij de beste 20% horen, dan win je 2€.

De formulieren met sommen worden zo meteen ondersteboven uitgedeeld, zodat je de

sommen nog niet kunt zien. Schrijf allereerst jouw voor- en achternaam op de achterkant van het formulier met sommen.

Leeftijd: Geslacht:

Nadat de eerste ronde is afgelopen, zullen de instructies voor het tweede deel van het experiment worden uitgedeeld.

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33 Deel 2

Zo meteen zullen er weer formulieren worden uitgedeeld met simpele reken sommen. De moeilijkheidsgraad van de sommen zal hetzelfde zijn. Je wordt zo meteen wederom geacht zoveel mogelijk sommen correct op te lossen binnen twee en een halve minuut.

Je eigen uitwerkingen zullen dit keer worden vergeleken met uitwerkingen van 9 andere leerlingen van binnen en buiten je eigen klas. Iedereen wordt dus ingedeeld in een groep van in totaal 10 leerlingen. Mocht je binnen de voor jou samengestelde groep van 10 leerlingen bij de beste 20% horen, dan win je 2€.

De formulieren met sommen worden zo meteen weer ondersteboven uitgedeeld, zodat je de sommen nog niet kunt zien. Schrijf wederom eerst jouw voor- en achternaam op de

achterkant van je formulier met sommen.

Nadat deze ronde is afgelopen, zal er nog een korte enquête worden uitgedeeld. Jullie worden vriendelijk verzocht deze enquête waarheidsgetrouw in te vullen.

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34 Enquête

1. Wat heb je opgeschreven in de eerste ronde toen je werd gevraagd om je eigen kansen in te schatten om bij de beste 20% van jouw groepje te horen?

2. Wat heb je opgeschreven in de tweede ronde toen je werd gevraagd om je eigen kansen in te schatten om bij de beste 20% van jouw groepje te horen?

3. Waarom heb jij gekozen voor verschillende of juist gelijke schattingen in je eerste en tweede ronde? Wees zo duidelijk mogelijk in je antwoord.

4. Veronderstel dat het aantal jongens en meisjes dat heeft mee gedaan aan mijn

experiment exact gelijk is. Gedurende dit experiment heb je een ronde gespeeld in een competitie met in totaal 10 deelnemers en in een competitie met in totaal 50

deelnemers. Voor welke competitiegrootte acht jij de kans hoger dat je in een

competitie terecht komt waarin minstens 60% van de deelnemers uit jongens bestaat? Omcirkel de letter van jouw keuze.

a. Een competitie met in totaal 10 personen. b. Een competitie met in totaal 50 personen.

c. De kansen om in een competitie met tenminste 60% jongens te zitten zijn nagenoeg gelijk in een competitie met in totaal 10 of 50 personen.

Ik wil je hartelijk danken voor je deelname aan mijn experiment. De winnaars van de cashprijzen zullen worden bekend gemaakt op het bord waar ook de cijferlijsten hangen. De winnaars kunnen dan hun prijzen komen ophalen op een nog nader te bepalen tijdstip in een nog nader te bepalen lokaal.

Mocht je vragen hebben met betrekking tot het experiment? Mijn e-mailadres: igor_p_r@hotmail.com

Met vriendelijke groet,

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35 Sommen 15 – 12 = 9 – 1 = 6 + 9 = 15 + 20 = 41 – 9 = 65 + 3 = 56 + 4 = 14 – 5 = 11 + 13 = 32 + 11 = 24 – 2 = 55 + 12 = 27 – 10 = 86 – 4 = 42 – 10 = 94 + 3 = 17 + 4 = 22 + 22 = 45 + 7 = 12 – 3 = 53 – 2 = 46 – 5 = 11 + 9 = 24 + 6 = 22 + 11 = 67 – 19 = 87 – 23 = 49 – 37 = 45 – 28 = 97 – 49 = 69 – 32 = 72 – 29 = 79 – 52 = 23 + 64 = 90 – 4 = 38 – 6 = 12 + 5 = 74 – 11 = 98 – 9 = 12 + 7 = 99 – 3 = 12 + 8 = 11 + 7 = 22 – 9 = 18 + 15 = 60 – 44 = 22 + 9 = 23 – 17 = 12 + 16 = 23 + 45 = 81 + 6 = 61 + 17 = 33 + 14 = 22 – 18 = 11 + 2 = 29 + 20 = 17 – 6 = 1 + 23 = 87 – 19 = 61 – 39 = 22 + 53 = 75 – 34 = 53 – 34 = 9 – 8 = 16 – 9 = 21 + 7 = 88 – 17 = 52 + 12 = 89 + 9 = 44 – 18 = 19 – 7 = 23 – 8 = 39 – 17 = 62 + 14 = 39 + 17 = 22 – 9 = 78 – 29 = 63 – 14 = 29 + 8 = 31 + 3 = 30 + 18 = 72 – 9 = 63 – 8 = 41 + 27 = 51 + 8 = 71 – 19 = 92 – 37 = 15 – 3 = 61 – 18 = 75 – 23 = 54 – 45 = 76 – 67 = 12 + 24 = 8 + 8 = 43 – 29 = 27 + 52 = 22 + 39 = 61 + 29 = 94 – 69 = 42 + 37 =