bibliography - erasmus university thesis repository · web viewbesides being insignificant (p-value...

The influence of language

on ambiguity aversion

Vincent van Noort

349138

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Contents

Introduction 3

Sapir-Whorf Hypothesis 4

Questionnaire 6

Results 8

Language 9

Vienna versus The Hague 13

Gender 13

CRT Scores 14

Age 15

Degree 16

Other Regressions 17

Conclusions 19

Discussion 20

Bibliography 22

Appendix A: Questionnaire 23

Appendix B: Results 28

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Introduction

In a very well known experiment Daniel Ellsberg showed in 1961 that people dislike

ambiguous situations. He proved that in some situations people have the tendency to

behave irrational. Using data from responses under non-experimental conditions he showed

that people violate the Savage axioms when they are dealing with uncertainties. These

responses came on questions in which there are two urns; the first urn had fifty red balls and

fifty black balls. The second urn also contained hundred balls but with unknown distribution

between the two colours. Ellsberg showed that most respondents prefer the urn with known

distribution, no matter on which colour the bet. This suggests that they think the second urn

contains less red balls and less black balls than the first urn. Since the second urn also

contains hundred balls this is impossible. Ellsberg explained this by saying that people prefer

the risk of the first urn over the uncertainty of the second urn. He called this ambiguity

aversion (Ellsberg, 1961). Ambiguity is now often defined as uncertainty in the relevant

information or completely unknown relevant information. This information is often

regarding the probabilities or payoffs. Ambiguity can however also refer to information that

is misunderstood. As previous research has proven a lot of factors influence ambiguity such

as the context or the way information is obtained. Three different kinds of ambiguity can be

distinguished: uncertain probability, uncertain pay-off and situations were both are

uncertain. This research will only focus on situations where the probability is unknown.

Since Ellsberg published his findings there has been a lot of research regarding ambiguity

attitudes. Part of this research is that people are so averse to ambiguity that they would be

willing to pay to avoid ambiguous situations if a real payoff was involved (Becker &

Brownson, 1964). Besides the consequences of ambiguity aversion it has also been

investigated what factors influence ambiguity aversion. According to Fox and Tversky (1995)

ambiguity is also influenced by the context. Ambiguity aversion is strong in case of a

comparative context but disappears in the absence of a comparison (Fox & Tversky, 1995).

Others found that the way people get (ambiguous) information also influences decisions.

People who see a representative sequence seem to be less averse to the ambiguity than

when a verbal description is given (Bleaney & Humphrey, 2006).

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Because there already has been a lot research regarding ambiguity aversion this is not just a

research to show how people react to ambiguity. It will be tested whether people have a

different attitude to ambiguity in different languages. One of the reasons that it is possible

language could change the attitude comes from Sapir-Whorf hypothesis. This hypothesis

named after linguist Edward Sapir and his student Benjamin Lee Whorf states that the

language that someone speaks influences our decision making. Another reason to believe

that ambiguity attitude is affected by language is the fact that it has already been proven

that language can influence decisions. It has for instance been tested that in a foreign

language the framing effect disappears and that people tend to be less averse to losses in a

foreign language. Usually the framing effect makes it possible that the same people give

different answers to the same problem but framed differently. Because most people are risk

seeking for losses and risk averse for gains they answer differently when the problem is

framed as losses compared to the same problem framed as gains. Most famous framing

problem is the Asian disease problem. This problem is also used in a bilingual study. This

experiment showed that in the native language framing does work, leading to different

answers for the same problem. In a foreign language however this framing effect disappears.

The same study also shows that bets with positive expected value are more likely accepted

and people are less averse to losses in a foreign language than in the native language. The

writers argue that this is because the native language causes more emotional reactions

leading to biased decisions (Keysar, Hayakawa, & An, 2012).

Two questionnaires will be used to test whether this is the case with ambiguity attitudes.

Those two questionnaires will be exactly the same except one will be in Dutch and one in

English. In this questionnaire the respondents will be asked four questions regarding their

attitude to ambiguity. These questions illustrate situations in which the probability of

winning is unknown compared to situations where this probability is known. With the results

from these questionnaires it will be tested whether there is a significant different between

the answer from the Dutch questionnaire and the answers from the English questionnaire.

Sapir-Whorf Hypothesis

As said the ambiguity attitude can be influenced by for instance the context and the way of

obtaining information. Another factor that could perhaps influence ambiguity attitude is the

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language in which information is given. As said earlier ambiguity is also information that is

misunderstood. Information given in a second language could be more easily misunderstood

making people more averse to ambiguity. There is however a more important reason to

believe why the language could influence ambiguity attitudes. Some linguistics believe that

the language spoken influences our view of the world and more important our decision

making. The hypothesis these linguistics believe in is called the Sapir-Whorf hypothesis (Kay

& Kempton, 2009). This hypothesis consists of two parts:

1. Structural differences between language systems will, in general, be paralleled by

non-linguistic cognitive differences, of an unspecified sort, in the native speakers of

the two languages.

2. The structure of anyone’s native language strongly influences or fully determines the

world-view he will acquire as he learns the language (Kay & Kempton, 2009).

For this research the focus will be on the first part. This part could mean for this research

that different languages will be accompanied by different decision making. Meaning that the

results from the Dutch questionnaire could be very different from the English questionnaire.

The hypothesis does not state how each language influences the view of the world or

decision making. Therefore the results can go both ways, the Dutch results can be more

averse to ambiguity but it could also be that the English results show more ambiguity

aversion. This is dependent on the actual influences both languages have. This first part of

the Sapir-Whorf hypothesis is also called linguistic determinism. It can also be further

divided in strong and weak determinism. Strong determinism is the believe that what is said

is responsible for what is seen by the mind (Badhesha, 2002). In an Australian experiment

with deaf children it is shown that strong determinism can hold. After a doll is put in a box

with a marble the doll is removed first and after that the marble is removed. When asked

where the doll will look for the marble children with parents fluent in sign language

answered correct. The children growing up in a family with non deaf parents who are not

fluent in sign language answered incorrectly (Peterson & Siegal, 2006). Although in this

situation strong determinism holds most linguistics reject the view of strong determinism.

The version with weak determinism however is a lot more accepted. Weak determinism still

means that the language someone speaks influences our view of the world or our decisions.

But were strong determinism says that language defines this strictly; weak determinism

means that there are still other factors that influence our view or decisions (Badhesha,

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2002). Therefore weak determinism is a lot more probable than strong determinism. But

because weak determinism states that language certainly has an influence it could still lead

to differences in our decisions. These differences can perhaps also occur between a native

language in which people are fluent (Dutch) or a second language which is probably not

spoken completely fluent (English). So it is very well possible that people will show different

attitudes to ambiguity in different languages.

Questionnaire

To test whether language really affects ambiguity attitudes a questionnaire is used. Or rather

two questionnaires: one in English and one in Dutch (Appendix A). The questions in both

questionnaires are exactly the same and phrased in the same way to avoid other factors

such as framing. At first friends, family and some colleagues were asked to fill in one of the

questionnaires. Later also other students were asked to fill in one. This gives a group of

respondents that differ a lot from each other. Although a lot of respondents are in the early

twenties there are also respondents with an age in the thirties, forties or even higher. It also

gives a lot of variety in the field of study or profession despite most of the fellow students

study economics. Thanks to the other respondents there will also be enough differences

here. It was decided that all the respondents should speak Dutch as their first language.

Therefore all the respondents speak Dutch as their first language the Dutch questionnaire

gives results for first language and the English gives the results for the second language.

There are a couple of reasons why only Dutch respondents were used. First reason is that

this way it is sure that there are roughly the same amounts of results for first language as

there are for second language. Otherwise it could have happened that only people speaking

English as their native language filled in the English questionnaire. Since fluency in the

language can have an effect this could influence results. The second reason is that the switch

from Dutch to English could be different than for instance from Italian to English. This could

influence the results. Another important decision was to let every respondent fill in only one

of the questionnaires instead of both. The main reason for this was to avoid the will to be

consistent. Because the questions are exactly the same in both questionnaires respondents

would probably want to be consistent and use the same answers without thinking about it.

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Table 1: Question 1 (Red ball)Number of Balls

in Urn K K U

Number of Balls in Urn U

€100:Red

€0:Black

€100:Red

€0:Black

0 100 Urn K Urn U

Unknown Unknown

10 90 Urn K Urn U20 80 Urn K Urn U30 70 Urn K Urn U40 60 Urn K Urn U50 50 Urn K Urn U60 40 Urn K Urn U70 30 Urn K Urn U80 20 Urn K Urn U90 10 Urn K Urn U

100 0 Urn K Urn UThe first question in the questionnaires looks like the questions used by Ellsberg. There are

two urns with black and red balls. The distribution in the first urn is known and the

distribution in the second urn in unknown. Respondents have to pick an urn to draw a ball

from after they have chosen a colour. Table 1 shows the table the respondents have to fill in

if they chose a red ball. If a black ball is chosen the same table is given but with the colours

switched. The second question also uses two urns but they are filled with five different

colours. This gives the chance to see whether the ambiguity attitude stays the same when

the probability of winning in Urn K gets lower. Questions three and four are also used to

measure ambiguity attitudes. In both questions respondents have the choice between a

certain amount of money or a bet on the weather in Vienna or The Hague respectively. With

these questions it will also be tested whether a city far away (Vienna) changes the ambiguity

attitude in comparison to a city nearby (The Hague). Table 2 shows the Vienna question.

Table 2: Question 3 (Vienna)

Option A A B Option BGet €0 for sure Option A Option B

€20 if it rainsin Vienna

on Monday

Get €2 for sure Option A Option BGet €4 for sure Option A Option BGet €6 for sure Option A Option BGet €8 for sure Option A Option B

Get €10 for sure Option A Option BGet €12 for sure Option A Option BGet €14 for sure Option A Option BGet €16 for sure Option A Option BGet €18 for sure Option A Option BGet €20 for sure Option A Option B

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The questionnaire will also make use of a cognitive reflection test (CRT). Three questions will

be used to measure the cognitive ability of the respondents. The same test that Shane

Frederick used in 2005 to research the relation between cognitive ability and decision

making is also used in this research. His research proved that cognitive ability influences the

time and risk preferences. Respondents having a higher cognitive ability tend to be more

patient, more risky for gains and take less risk when it involves losses (Frederick, 2005). At

last there will be asked a couple of demographic questions. This is to make sure possible

differences are not caused by factors such as gender, age or education. The native language

of the respondents is also asked to make sure whether the results belong to first or second

language. In the English questionnaire respondents are also asked to rate their English. This

way it is also possible to remove certain results if their English is very bad and they do not

seem to understand the questions.

Results

In the end a total number of 54 respondents were reached. This was divided in 30 for the

English questionnaire and 24 for the Dutch questionnaire. However due to several reasons

some answers could not be used for research. Therefore I ended up with 21 answers to the

English questionnaire and 23 for the Dutch. First the answers given to the questions

regarding the ambiguity aversion were given numerical values. If for instance one choose a

red ball in the first question and switched between 30 red balls in Urn K and 40 red balls in

Urn K this would be given a value of 35. This was done in a similar way for the questions with

five different colours and the weather in Vienna and The Hague. Also every respondent was

given a CRT score. This varies between zero and three depending on how many CRT

questions were answered right. This research will mainly focus on possible significant

differences caused by language. This can be because of the different languages or the

proficiency in English. But it will also be tested whether other factors such as CRT scores,

gender, age or degree has an influence on ambiguity aversion.

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Table 3: Descriptive Statistics

Language 2 colours 5 colours Vienna The Hague

English N Valid 18 18 21 21

Missing 3 3 0 0

Mean 45,00 28,33 6,667 7,905

Median 45,00 25,00 7,000 7,000

Std. Deviation 8,402 12,367 4,2348 4,6250

Minimum 25 15 1,0 1,0

Maximum 55 55 20,0 20,0Dutch N Valid 23 23 22 22

Missing 0 0 1 1

Mean 45,00 32,83 8,136 8,818

Median 45,00 25,00 9,000 9,000

Std. Deviation 7,977 13,803 4,3017 4,6561

Minimum 25 15 1,0 1,0

Maximum 55 55 20,0 19,0

Language

Now the results can be analyzed. First the descriptive statistics in table 3 are examined. The

statistics have been separated by the language of the questionnaire. In the question with

two colours respondents with a value below fifty are averse to ambiguity. Higher than fifty

means they are ambiguity seeking. It is remarkable to see that most statistics for this first

question are the same in both languages. In line with ambiguity aversion the means (and

median) of both groups are below fifty. However there are apparently some respondents

who seem to be ambiguity seeking as can be seen from the maximum of 55. More

surprisingly are the results from question with urns containing five different colours. In this

case ambiguity aversion should be indicated by a value below twenty. The means are

however both above twenty and in case of the Dutch questionnaire even above the thirty. If

you take a closer look at the frequencies of this question you will see that in the English

questionnaire 72.2% of the respondents is ambiguity seeking. In the Dutch questionnaire this

percentage is even higher at 78.3% (Appendix B, Table 1). The questions about the weather

in Vienna and The Hague however give the expected results. Whether it is ambiguity

aversion or ambiguity seeking depends on the belief of the raining probability of each

respondent. Because this is not asked it is impossible to know whether respondents are

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averse to ambiguity or seeking ambiguity. But at both questions a higher value means less

aversion to ambiguity so it is possible to test whether language influences the attitude. It is

remarkable though that both have a maximum of twenty (or nineteen in the Dutch The

Hague question). This means there are respondents that prefer to win €20 only if it rains in

one of the cities above the opportunity to win €20 with certainty. This is in contrast to every

behavioural theory and more importantly also the opposite of common sense. Therefore it

could be doubted whether this person read the question well or answered it seriously. At

the last three questions there are slight differences in means between the languages. And in

the last two questions the median differs also. However whether these differences are

significant remains to be seen.

Normally an independent samples t-test is used to compare means between two groups. But

because the sample size is quite small and the distribution is not normal, it is better to use

the Wilcoxon rank sum test in this situation. This tests the difference between the groups in

distribution by comparing the sum of the ranks. The null hypothesis for this test is that there

is no difference between both groups. As the sample size is small and may be poorly

distributed it is possible that the asymptotic significance level gives a wrong indication.

Therefore the exact significance levels (2 sided) will be used to determine whether the

differences are significant or not. For these tests a confidence level of 95% will be used.

Because the tests are two sided it will be significant if the p-value is below 0.025 (0.05/2).

Now the analysis of the influence of the language of the questionnaire can start. First the

differences in answers on the first question will be tested. As is already shown in table 3

there is no difference in means or medians between both languages for this question. The

results of the Wilcoxon rank sum test support this (Appendix B, table 2 and 3). The mean

rank of the Dutch questionnaire is slightly higher. So the respondents from the Dutch

questionnaire have a higher rating meaning that they are a little less averse to ambiguity.

But with a (exact) p-value of 0.990 there is no evidence of a significant difference between

both languages for this question (Appendix B, table 3). This was expected after seeing the

descriptive statistics. For the second question those descriptive statistics do show a

difference between languages. The medians are still the same but the mean of the Dutch

questionnaire is higher than that of the English (32.83 and 28.33 respectively). This could

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indicate that the Dutch language leads to less ambiguity aversion, or in this case more

ambiguity seeking. The Wilcoxon test however still shows no significance in the differences.

Although the ranks show that the average rank of the Dutch questionnaire is higher

(Appendix B, table 4) there is still no significance to be found (Appendix B, table 5). This is

shown by a p-value of 0.327 which is still well above 0.025. Last the two questions about the

weather in Vienna and The Hague will be evaluated. The descriptive statistics show that for

both questions the mean of the Dutch questionnaire is higher, again indicating less aversion

to ambiguity. But as opposed to the first two questions there is also a difference in the

medians at the last two questions. Both medians are seven in English and nine in Dutch. The

difference at the Vienna question seems to be bigger which is also showed in the mean

ranks. The difference in mean rank for the Vienna question is five, bigger than at all the

other questions (Appendix B, table 6). This difference is however also not significant

according to the Wilcoxon test (Appendix B, table 7). Although the p-value (0.188) is getting

lower it is still not past the critical value. The differences in the The Hague question are a

little smaller (Appendix B, table 8 and 9). Besides with a p-value of 0.489 it is also not

significant. So at none of the questions the difference is significant. But all the statistics

indicate that the respondents of the Dutch questionnaire are less averse to ambiguity than

those of the English questionnaire. And as said earlier the sample size is quite small. If this

was bigger it could well be that the differences become significant. So it is too early to say

that there is no evidence consistent with the Sapir-Whorf hypothesis.

So far it is tested whether language has an influence on the decisions made by the

respondents. But as said earlier it is also possible language has another effect on ambiguity

aversion. This effect could be that information in another language is more easily

misunderstood and therefore leads to more ambiguity aversion. To test this, respondents of

the English questionnaire were asked to give an indication of their skill in the English

language on a scale from zero to ten. Zero would mean the respondent speaks no English at

all and a ten means fluent in English. The answers on this question ranged from a six to ten.

To test whether there is a relationship between proficiency in the English language and

ambiguity attitude the Spearman correlation test is used. If the result of this test is 1 or -1

there is complete correlation between both and if the result is 0 there is no correlation at all.

A positive correlation between both variables is expected, because a better proficiency of

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the English language should lead to fewer misunderstandings and a higher score on the

questions about ambiguity attitude indicates less aversion to ambiguity.

Table 4: Correlations, 2 colours, Proficiency English

2 colours

prof. English

Spearman's rho

2 colours Correlation Coefficient

1,000 0,478

Sig. (2-tailed) . 0,045

N 41 18

prof. English

Correlation Coefficient

0,478 1,000

Sig. (2-tailed) 0,045 .

N 18 21The results of the Spearman correlation test for the question with two different colours are

shown in table 4. As can be seen there is a correlation of 0,478 between both variables.

Although the strength of this relationship is not very strong it should definitely not be

ignored. Besides the p-value of 0.045 makes this correlation significant at a 5% level. This

indeed means that a higher proficiency in the English language leads to less ambiguity

aversion. However to say that there is definitely a relationship between ambiguity attitude

and English proficiency there should also be correlation with the other three question. But

this is not the case. None of the correlations between proficiency in English and the last

three questions are significant. The question of the urns with five colours has a correlation of

0.345 which is a little weaker than the first question. But the p-value of 0.161 makes it

insignificant (Appendix B, table 10). The question about Vienna is already much weaker at

0.138 and the p-value indicates also here insignificance (Appendix B, table 11). The question

about The Hague is the most extreme though. Besides being insignificant (p-value of 0.954) it

also has a correlation coefficient of only -0.013 (Appendix B, table 12). Having a negative

correlation means that in this situation a lower proficiency in English leads to more

ambiguity aversion. The correlation is however so close to zero that one could say there is no

relationship at all. The reason that the correlation at these last two questions was so low

could be that the respondents first have to decide how big the probability of rain is. These

probabilities can have a big range between all the respondents which will probably also lead

to a big range of answers. This makes it less likely there is a correlation.

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Vienna versus The Hague

Besides the possible influence of language it is also interesting to see whether ambiguity

attitude differs in the questions about the weather in Vienna and The Hague. Again a non-

parametric test is used because of the small sample size. In this situation the Wilcoxon

ranked sign test is used. The results of this test are significant if the exact p-value is lower

than 0.025. For this test every respondent’s answers of the questions about Vienna and The

Hague are compared. A negative rank is given if the value of the Vienna question exceeds

that of the question about The Hague. If the opposite is true a positive rank is given. In this

case there are five negative ranks and eighteen positive ranks (Appendix B, table 13). The

higher mean rank for positive ranks indicates that it is more likely that the value of The

Hague is higher than that of Vienna. The results of the Wilcoxon ranked sign test show that

there is a significant difference. The p-value is 0.001 which is way lower than the critical

value of 0.005 and therefore indicates significance (Appendix B, table 14). Because the Z-

value is negative (-3.141) and based on negative ranks this actually means that the answers

on the The Hague question were significantly higher than those on the Vienna question. So

respondents show less aversion to ambiguity (or in some cases more ambiguity seeking)

when asked about the weather in The Hague compared to the weather in Vienna. This is

possibly because all respondents were Dutch and for them there is ambiguity regarding

when it rains in Vienna. However it is also possible that the respondents think it is more

likely to rain in The Hague than it is in Vienna.

Gender

Now it will be examined whether there is a difference in ambiguity aversion between men

and women. To test this the Wilcoxon rank sum test will again be used. Again results will be

significant if the p-value is lower than 0.025. At the two colours question there is quite some

difference between men and women in the ranks (Appendix B, table 15). The mean rank of

the men is more than seven higher than that of the women. This shows that at least for this

question men are less averse to ambiguity. The results of the Wilcoxon test show that these

differences are insignificant, it is however very close to significant (Appendix B, table 16).

The p-value is with 0.058 closer to significance than most of the other test so far. The results

for the second question are completely the opposite. At this question women showed less

aversion to ambiguity than men although the difference is not as big as in the first question.

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This is displayed in the mean ranks of both (Appendix B, table 17). But these results are not

as close to significance as with the first question. In this case the p-value is only 0.441, not

even close to the critical value (Appendix B, table 18). The results for the third question show

bigger differences again. Here there is a difference of almost seven in mean ranks however.

And like in the previous question women also show here less aversion towards ambiguity

(Appendix B, table 19). Compared to the second question these differences are much closer

to significance but are still insignificant. This is shown by the p-value of 0.103 (Appendix B,

table 20). The results of the last question about The Hague look very similar to the previous

question about Vienna. Women are again less averse to ambiguity but the difference in

mean ranks is with six slightly smaller (Appendix B, table 21). And as could be expected from

that it is also insignificant. The p-value is with 0.143 a little but not significant (Appendix B,

table 22).

CRT scores

Next research is regarding the CRT scores. As said the cognitive ability is determined by three

questions at the end of the questionnaires. The number of questions answered right

determines the score. If all three questions are answered right this results in a score of

three. None good is a score of zero. First it could be interesting to see whether language has

an influence on the scores. The Wilcoxon rank sum test is again used to determine this. It

turns out that the mean rank for the English questionnaire is higher than that of the Dutch

questionnaire (Appendix B, table 23). So the respondents who filled in the English

questionnaire got higher CRT scores. A reason for this is perhaps that a foreign language, in

which respondents are not fluent, forces them to make more deliberate decisions. The

native language makes it easier for respondents to answer such questions quickly without

really thinking about it. The difference is however not significant according to the p-value of

0.371 (Appendix B, table 24). To test whether there is a relationship between CRT scores and

ambiguity attitude the Spearman correlation test is used again. The analysis will again be

started with the question with two colours. The correlation between this question and CRT

scores is 0.068 (Appendix B, table 25). This is so close to zero that it can be said that there is

no relationship at all between this question and CRT scores. Besides it has a p-value of 0.674

so it is insignificant as well. Between CRT scores and the second question with five colours

there seems to be a relation. Although the test shows the correlation is only -0.226

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indicating that it is still a very weak relation (Appendix B, table 26). Being negative it means

that someone with a higher CRT score shows more aversion to ambiguity than someone with

a lower CRT score. Also this relationship seems to be insignificant judging from the p-value of

0.155. CRT is also very weakly correlated to the answers on the question regarding the

weather in Vienna. The correlation of -0.238 is similar to the previous correlation (Appendix

B, table 27). Again a higher CRT score indicates more ambiguity aversion. However this

correlation is also insignificant because of the p-value of 0.125. The Spearman’s test with the

question about The Hague also gives similar results. The correlation is even a little bit weaker

though at -0.182 (Appendix B, table 28). But also this has a p-value of 0.243 and is therefore

insignificant. So the relation between CRT scores and ambiguity attitude looks to be a

negative one. Respondents scoring high on the CRT test tend to be more averse to

ambiguity. It is all insignificant but this could perhaps be due to the small sample size.

Age

Although most of the respondents are aged in the early twenties there are enough older

respondents to test whether age has an influence on ambiguity aversion. The ages varied

between twenty and sixty. To test the influence of age regressions will be used. In these

regressions the four questions which indicate ambiguity attitude will be the dependent

variables. Further there will be a constant and the independent variable will of course be

age. The calculated coefficient will show which influence age has on the ambiguity attitude.

Of course the p-value will indicate whether this is significant or not. In the first regression

the dependent variable are the answers on the question with two different colours. The

results this regression show that age does not have much influence (Appendix B, table 29).

The coefficient of the constant is 44.043. This means that a child of zero would on average

give this score on the first question. Remember that in this question a value below fifty

indicates aversion to ambiguity. The coefficient for age in this regression is 0.031. So with

every year someone grows older he becomes a little bit less averse to ambiguity. This

coefficient is however so small that it is negligible. The p-value of 0.755 also shows that this

coefficient is insignificant. In the second regression the question with five colours is the

dependent variable. In this question a value below twenty indicates ambiguity aversion and

above twenty ambiguity seeking. At this question the influence of age looks a bit bigger. The

coefficients are this time 21.709 for the constant and 0.298 for age (Appendix B, table 30).

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So in this case someone of zero years is already ambiguity seeking and this ambiguity

seeking becomes bigger with every year. The p-value of age is this time also quite close to

being significant with 0.064. The last two regressions will be made with the questions about

Vienna and The Hague as dependent variables. In these questions ambiguity aversion is

showed by a value below ten. Above ten means that person is ambiguity seeking. The results

of the regression with Vienna as dependent variable are similar to the first regression

(Appendix B, table 31). The constant coefficient of 6.762 displays that the respondents are

probably averse to ambiguity. Or they just think it will not rain in Vienna. Age however does

not seem to have any influence with a coefficient of only 0.021. That this is insignificant

according to the p-value of 0.684 does not matter much. Even if it was significant the

influence is so small that it would barely be noticed. Also the last regression shows

similarities to this regression. As is discussed earlier respondents show less aversion to

ambiguity in the The Hague question compared to the Vienna question. This is showed by

the constant coefficient of 7.708 (Appendix B, table 32). The age coefficient is however

exactly the same at these last two regression, so also here it is 0.021. So almost no influence

of age on the attitude towards ambiguity on this occasion as well. As could be expected the

p-value is 0.702. But as said earlier that does not matter much which such small coefficients.

Degree

The tests for differences caused by the highest degree received were done in a similar way

to the age. All respondents were divided into four groups again. The first group consisted of

all respondents with a high school degree or no degree at all. The second and third group

were respectively the so called MBO and HBO. And the last group consisted of everyone with

a university degree. In the last two groups there is no difference made between a bachelor

and a master. The regressions were again made with the ambiguity questions as dependent

variable and this time degree as independent variable. People without any degree would

have a value equal to the constant. The first regression gives a coefficient of 0.418 for degree

(Appendix B, table 33). That would mean that respondent with a higher degree are less

averse to ambiguity. The constant coefficient of 43.909 shows that this is really about

ambiguity aversion and not ambiguity seeking. The coefficient of degree is however not

significant with a p-value of 0.666. When a look is taken at the second regression it is seen

that at this question it is about ambiguity seeking. This is showed by the coefficient of the

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constant of 30.721 (Appendix B, table 34). This was the question with five colours so there is

ambiguity seeking at a value higher than twenty. However, more importantly the coefficient

of degree is only 0.051. This is very low so degree has barely any impact on the ambiguity

attitude in this question. Besides the very low coefficient it is also insignificant according to

the p-value (0.974). The influence of degree is already much bigger at the question about

Vienna. Although it is insignificant (p-value of 0.448) the coefficient for degree is in this

regression 0.390 (Appendix B, table 35). The constant of 6.376 indicates that the

respondents do not like ambiguity or that they think there is a very small probability that it

will rain in Vienna. Finally the last regression gives similar results regarding the influence of

degree. The coefficient of 0.409 shows this, as was the case with previous regression also

this coefficient is insignificant with the p-value at 0.460 (Appendix B, table 36). As expected

in this question about The Hague the aversion to ambiguity is a little less compared to

Vienna. This is displayed by the constant of 7.279. Although all the coefficients are

insignificant it is remarkable that in all regressions the coefficient for degree was positive. So

respondents with a higher degree showed less aversion to ambiguity at all of the four

questions.

Other Regressions

So far it is tested whether all the factors influence ambiguity attitudes one for one. It could

be interesting to see whether some of the influences found so far would change if a

regression is made with all the factors in it. In these regressions the four different questions

about ambiguity are of course still the dependent variable. But this time the language of the

questionnaire, gender CRT scores, age and degree will all be used as independent variables.

The factors language and gender will enter these regressions as dummies. These will get a

value of one respectively if the language of the questions was English and if the respondent

is female. This will mean that if the Dutch language makes people less averse to ambiguity

(or more ambiguity seeking) the coefficient should be negative. If the coefficient of gender is

positive then women are less averse to ambiguity.

17

Table 5: RegressionsDependent

Variable

2 colours 5 colours Vienna The Hague

Constant 44.132 (0.000) 28.769 (0.003) 7.644 (0.018) 8.381 (0.017)

Language 0.159 (0.953) -2.684 (0.527) -1.280 (0.338) -0.699 (0.628)

Gender -5.161 (0.089) 0.748 (0.874) 1.604 (0.292) 1.824 (0.271)

CRT -0.415 (0.816) -3.629 (0.203) -0.892 (0.291) -0.988 (0.282)

Age 0.073 (0.487) 0.289 (0.087) 0.010 (0.839) 0.010 (0.853)

Degree 0.399 (0.697) 1.024 (0.528) 0.633 (0.239) 0.670 (0.251)

The results of the four regressions can be seen in table 5 above. The p-value for each

coefficient is in between the brackets. The first regression with the question with two

colours as dependent variable does give some remarkable results. The coefficient of 0.159

for language is not in line with the first tests. First tests showed that at this question the

Dutch questionnaire had higher ranks indicating less aversion to ambiguity. In this regression

is the coefficient however positive. As said this indicates that the English questionnaire leads

to less aversion to ambiguity. Compared to earlier results there is also a switch in the

influence of CRT scores at this question. The correlation between this question and CRT was

positive, in this regression it has a negative coefficient (-0.415) though. All the other

variables show the same effect in this regression as in the other tests. Gender has a very big

influence in this regression with a coefficient of -5.161. But the difference in ranks in the first

tests was also very big at this question so this is not a very big surprise. Another result that is

seen earlier is the fact that none of these coefficients are significant. All the p-values are well

above 0.025. The second regression with the question with five different colours as

dependent variable gives no surprising results. As all other tests for this question showed

this is the only question where the respondents display ambiguity seeking behaviour. This is

showed by a constant that is with 28.769 well above the twenty. All the other results are in

line with results obtained with previous tests. Language is in this regression negative

indicating that indeed the Dutch questionnaire leads to more ambiguity seeking. The value

of -2.684 is perhaps bigger than expected but the p-value of 0.527 makes it insignificant

anyway. Also the coefficients of CRT (-3.269) and degree (1.024) are bigger than was

expected from previous tests. However these coefficients are also insignificant (p-values of

0.203 and 0.528 respectively). Next is the regression with the question about the weather in

18

Vienna as dependent variable. As with the previous regression there are here also no

unexpected signs before the coefficient. But this time also the size of the coefficients is no

surprise. Language and Gender seem to have the biggest influence on ambiguity attitude.

Earlier test with this question indeed did show the biggest differences with these variables.

When age was tested earlier it showed to have very little effect and this continues in this

regression. The coefficient of only 0.010 shows that even if this was significant it still would

have almost no influence at all on ambiguity attitude. As could be expected all the p-values

are well above 0.025 and are therefore insignificant. About the last regression with The

Hague as dependent variable can be said the same. No really surprising coefficients or p-

values in this regression. Gender has also in this regression the biggest coefficient (1.824).

But this was expected as in the first gender test there was a quite big difference in mean

ranks already. Age has again no effect at all with a coefficient of 0.010. In this last regression

CRT also seems to have a reasonable influence on ambiguity attitude. The coefficient is -

0.988 although earlier test showed a very weak correlation between CRT and this question.

As was the case with all these regressions also here there are no significant variables since all

p-values are above 0.025.

Conclusions

This research focused mainly on differences in ambiguity aversion caused by language. This

could have been caused because language determines our view of the world and more

importantly it influences our decision making as stated by the Sapir-Whorf hypothesis. It

could also have been caused by the fact that information in another language is more easily

misunderstood. Results of mean comparing and correlation tests however show that

language has no influence in either way. Only one comparison resulted in a significant effect

which could have been caused by the proficiency in the English language. Since that was the

only significant difference it seems to be a coincidence. So language does not seem to have

any relationship with ambiguity aversion. But as said multiple times before the sample size

was very small. Perhaps bigger sample sizes lead to more significant results. So it is too early

to conclude that language has no influence at all. Main reason for this is the fact that in all

the Wilcoxon tests the Dutch questionnaires led to less ambiguity aversion (or more

seeking). Also the correlations between the proficiency in English and the several questions

were mostly similar. The last question about the weather in The Hague gave a negative

19

correlation, but this was so small that it could be said that there was no correlation at all.

The other three questions all had positive correlation and were more importantly much

bigger. This could indicate that when respondents speak better English they show less

aversion to ambiguity. Besides language it was also tested whether gender, CRT scores, age

or degree had any influence on ambiguity aversion. These tests all resulted in the same

conclusion. None of these factors seemed to influence ambiguity aversion in any way.

However the same thing that can be said of the influence of language can also be said of the

variables age and degree. In all the tests they had the same positive effect. This would mean

that when people grow older or have a higher degree this results in less aversion of

ambiguity. The results of age however where so small that this does not change much.

Discussion

Despite these conclusions there should be made some side notes regarding this research.

Most important is that the research sample was not big enough to make any definite

conclusions. As is said a couple of times already the small sample size could be the cause

some of the relations turned out to be insignificant. Therefore there could be hypotheses

wrongly accepted. To make any real conclusions a way bigger number of respondents should

be use.

Also the conclusions of this research are based on tests between only two different

languages. Both are an even a Germanic language which means there are probably quite

some similarities between both languages. Besides that English is a language that is taught at

every high school in the Netherlands. This makes that most of the respondents spoke English

reasonable well. This could be seen in the grades each respondent had to give for his or her

English. Most respondents indicated that this was a nine or even a ten. Since misunderstood

information is a part of ambiguity this could possibly influence the results. If respondents

speak better English less information will be misunderstood, which could influence the

attitude towards ambiguity. Future research could be done to see whether conclusions

would change if completely other languages were added to the list, such as Italian or even

Chinese. These languages are really completely different and could therefore lead to other

results. People would not speak these languages especially well which could give other

attitudes to ambiguity. Because more information would be misunderstood, or the

20

respondents would think they understand less. Also according to the Sapir-Whorf hypothesis

the results could be different with other languages. Each language has its own influence on

decision making. Since English and Dutch are both Germanic and possibly have some

similarities the differences in decision is not that big. This could be enlarged by adding a

completely different language.

Besides that this research also did not include respondents with different native language. It

is possible that people think in their native language anyway, despite reading or hearing

information in another language. If this is the case then decisions should not change

according to the Sapir-Whorf hypothesis. Asking people these questions only in their native

language makes it possible investigate the possible influence of the Sapir-Whorf hypothesis

even better. Of course you would need enough respondents from different countries with

different languages. This was impossible to do for this research. So although this research

shows no relation between language and ambiguity aversion there are enough reasons to do

more research before the possibility is completely rejected.

21

Bibliography

Badhesha, R. S. (2002). Sapir-Whorf Hypothesis. Retrieved from

http://zimmer.csufresno.edu/~johnca/spch100/4-9-sapir.htm

Becker, S. W., & Brownson, F. O. (1964). What Price Ambiguity? Or the Role of Ambiguity in

Decision-Making. Journal of Political Economy, 62-73.

Bleaney, M., & Humphrey, S. J. (2006). An Experimental Test of Generalized Ambiguity

Aversion using Lottery Pricing Tasks. Theory and Decision, 257-282.

Ellsberg, D. (1961). Risk, Ambiguity, and the Savage Axioms. The Quarterly Journal of

Economics, 643-669.

Fox, C. R., & Tversky, A. (1995). Ambiguity Aversion and Comparative Ignorance. The

Quarterly Journal of Economics, 585-603.

Frederick, S. (2005). Cognitive Reflection and Decision Making. The Journal of Economic

Perspectives, 25-42.

Kay, P., & Kempton, W. (2009). What is the Sapir-Whorf Hypothesis? American

Anthropologist, 65-79.

Keysar, B., Hayakawa, S. L., & An, S. G. (2012). The Foreign Language Effect: Thinking in a

Foreign Tongue Reduces Decision Biases. Psychological Science, 661-668.

Peterson, C. C., & Siegal, M. (2006). Deafness, Conversation and Theory of Mind. The Journal

of Child Psychology and Psychiatry, 459-474.

22

Appendix A: Questionnaire

1 Imagine that there are two different urns, Urn K and Urn U. Both urns contain 100 balls with two different colours: red and black. The proportion of the 2 colours are always Known in Urn K. They are always Unknown in Urn U, to both you and the experimenter. The unknown Urn U has been prepared by a third party. You have to pick one colour which you would like to bet on and then you can choose one of the urns to draw a ball from. You get €100 if the colour of the drawn ball is the same as the colour you bet on.

The left two columns describe the proportions of the coloured balls in Urn K. The first left column specifies the number of balls of the colour you choose, and the second column specifies the number of balls of the other colour. The total number of balls in Urn K is always 100.As regards the two columns to the right, the proportions are always unknown for Urn U. The total number of balls in Urn U is always 100 also. Each row represents a choice scenario with two options: Urn K and Urn U. You can indicate your preference between Urn K and Urn U for each row by circle “Urn K” or “Urn U” in the middle two columns in each row. Please indicate your preferences for all rows.

You can choose the colour you prefer to bet on. If you bet on a red ball you can indicate your preferences in the first table. If you bet on a black ball you can skip the first table and use the second table.

If you choose to bet on Red:Number of Balls in Urn K

K UNumber of Balls in Urn U

€100:Red

€0:Black

€100:Red

€0:Black

0 100 Urn K Urn U

Unknown Unknown

10 90 Urn K Urn U20 80 Urn K Urn U30 70 Urn K Urn U40 60 Urn K Urn U50 50 Urn K Urn U60 40 Urn K Urn U70 30 Urn K Urn U80 20 Urn K Urn U90 10 Urn K Urn U100 0 Urn K Urn U

23

If you choose to bet on Black:Number of Balls in Urn K


€100:Black

€0:Red

€100:Black

€0:Red

0 100 Urn K Urn U

Unknown Unknown


2 Again imagine two urns, Urn K and Urn U. Both contain 100 balls but this time there are five different colours: black, red, blue, yellow and green. The proportion in Urn K will again be known to everyone and the proportion in Urn U is unknown to you and the experimenter. Pick a colour to bet on and pick an urn to draw a ball from. If the colour of your bet matches to colour of the drawn ball you get €100.

In the tables below the columns on the far left indicate how much balls of the colour you bet on are in Urn K. The second column from the left shows how much balls of the four other colours combined are in Urn K. The two columns on the right show the distribution of colours in Urn U which is unknown. You can indicate your preference for each row by circling either “Urn K” or “Urn U” in the two columns in the middle. Please give your preference for all rows. You only have to do this in the table that corresponds with the colour you would like to bet on.

If you choose to bet on Red:Number of Balls in Urn K


€100:Red

€0:Other colours

€100:Red

€0:Other colours

0 100 Urn K Urn U

Unknown Unknown


24

If you choose to bet on Black:Number of Balls in Urn K


€100:Black

€0:Other colours

€100:Black

€0:Other Colours

0 100 Urn K Urn U

Unknown Unknown


If you choose to bet on Blue:Number of Balls in Urn K


€100:Blue

€0:Other colours

€100:Blue

€0:Other colours

0 100 Urn K Urn U

Unknown Unknown


If you choose to bet on Yellow:Number of Balls in Urn K


€100:Yellow

€0:Other colours

€100:Yellow

€0:Other colours

0 100 Urn K Urn U

Unknown Unknown


25

If you choose to bet on Green:Number of Balls in Urn K


€100:Green

€0:Other colours

€100:Green

€0:Other colours

0 100 Urn K Urn U

Unknown Unknown


26

3 Consider two options you can choose from, Option A and Option B. Option A assures that you get some money. Option B is that you get €20 if it rains in Vienna on Monday.

The column on the far left states the amount of money you will get if you choose Option A. The column on the right describes Option B which is the same in each occasion. Each row gives the choice between Option A and Option B. You can indicate your preference between both options for each row by circle “Option A” or “Option B” in the middle two columns in each row. Please indicate your preferences for all rows.

Option A A B Option B

Get €0 for sure Option A Option B

€20 if it rainsin Viennaon Monday

Get €2 for sure Option A Option BGet €4 for sure Option A Option BGet €6 for sure Option A Option BGet €8 for sure Option A Option BGet €10 for sure Option A Option BGet €12 for sure Option A Option BGet €14 for sure Option A Option BGet €16 for sure Option A Option BGet €18 for sure Option A Option BGet €20 for sure Option A Option B

4 Consider the same situation as in the previous question. But this time Option B means that you get €20 if it rains in The Hague on Monday.

Which option do you prefer now? Please indicate your preferences for all rows.

Option A A B Option B

Get €0 for sure Option A Option B

€20 if it rainsin The Hagueon Monday

Get €2 for sure Option A Option BGet €4 for sure Option A Option BGet €6 for sure Option A Option BGet €8 for sure Option A Option BGet €10 for sure Option A Option BGet €12 for sure Option A Option BGet €14 for sure Option A Option BGet €16 for sure Option A Option BGet €18 for sure Option A Option BGet €20 for sure Option A Option B

27

5 A bat and a ball cost €1,10 in total. The bat costs €1,00 more than the ball. How much does the ball cost? …………………………..

6 If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets? …………………………..

7 In a lake, there’s a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?…………………………..

At last I would like you to answer some questions about yourself:

Gender: o Male o FemaleAge: …………………………..First Language: …………………………..How good is your English on a scale from 0 to 10? (0 means that you don’t speak English and 10 means that English is your first language):

………………………….. Education (Highest degree received): …………………………..Field of study/Profession: …………………………..

Appendix B: Results

Table 1: Frequincies, 5 colours

Language Frequency Percent Valid PercentCumulative

Percent

English Valid 15 5 23,8 27,8 27,8

25 7 33,3 38,9 66,7

35 2 9,5 11,1 77,8

45 3 14,3 16,7 94,4

55 1 4,8 5,6 100,0

Total 18 85,7 100,0

Missing System 3 14,3

Total 21 100,0Dutch Valid 15 5 21,7 21,7 21,7

25 7 30,4 30,4 52,2

35 1 4,3 4,3 56,5

45 8 34,8 34,8 91,3

55 2 8,7 8,7 100,0

Total 23 100,0 100,0

28

Table 3: Test Statisticsa, 2 colours

2 colours

Mann-Whitney U 205,500Wilcoxon W 376,500Z -0,045Asymp. Sig. (2-tailed) 0,965Exact Sig. (2-tailed) 0,990Exact Sig. (1-tailed) 0,522Point Probability 0,020

a. Grouping Variable: Language

Table 4: Ranks, 5 colours

Language N Mean Rank Sum of Ranks

5 colours English 18 18,94 341,00

Dutch 23 22,61 520,00

Total 41


5 colours


29



2 colours English 18 20,92 376,50

Dutch 23 21,07 484,50

Total 41


Table 6: Ranks, Vienna


Vienna English 21 19,45 408,50

Dutch 22 24,43 537,50

Total 43

30

Table 7: Test Statisticsa, Vienna

Vienna



Table 8: Ranks, The Hague


The Hague English 21 20,64 433,50

Dutch 22 23,30 512,50

Total 43

Table 9: Test Statisticsa, The Hague

The Hague



Table 10: Correlations, English Proficiency and 5 colours

prof. English 5 colours

Spearman's rho prof. English Correlation Coefficient 1,000 0,345

Sig. (2-tailed) . 0,161

N 21 18

5 colours Correlation Coefficient 0,345 1,000

Sig. (2-tailed) 0,161 .

N 18 41

31

Table 11: Correlations, English Proficiency and Vienna

prof. English Vienna

Spearman's rho prof. English Correlation Coefficient 1,000 0,138

Sig. (2-tailed) . 0,550

N 21 21

Vienna Correlation Coefficient 0,138 1,000

Sig. (2-tailed) 0,550 .

N 21 43

Table 12: Correlations, English Proficiency and The Hague

prof. English The Hague

Spearman's rho prof. English Correlation Coefficient 1,000 -0,013

Sig. (2-tailed) . 0,954

N 21 21

The Hague Correlation Coefficient -0,013 1,000

Sig. (2-tailed) 0,954 .

N 21 43

Table 13: Ranks, The Hague, Vienna

N Mean Rank Sum of RanksThe Hague - Vienna Negative Ranks 5a 7,80 39,00

Positive Ranks 18b 13,17 237,00Ties 20c

Total 43

a. The Hague < Viennab. The Hague > Viennac. The Hague = Vienna

Table 14: Test Statisticsa, The Hague, Vienna

The Hague - Vienna

Z -3,141b

Asymp. Sig. (2-tailed) 0,002Exact Sig. (2-tailed) 0,001Exact Sig. (1-tailed) 0,001Point Probability 0,000

a. Wilcoxon Signed Ranks Testb. Based on negative ranks.

32


Gender N Mean Rank Sum of Ranks

2 colours Female 12 15,96 191,50

Male 29 23,09 669,50

Total 41


2 colours

Mann-Whitney U 113,500Wilcoxon W 191,500Z -1,958Asymp. Sig. (2-tailed) 0,050Exact Sig. [2*(1-tailed Sig.)]

0,083b

Exact Sig. (2-tailed) 0,058Exact Sig. (1-tailed) 0,033Point Probability 0,005

a. Grouping Variable: Genderb. Not corrected for ties.



5 colours Female 12 23,25 279,00

Male 29 20,07 582,00

Total 41


5 colours


0,453b



33

Table 19: Ranks, Vienna


Vienna Female 12 26,96 323,50

Male 31 20,08 622,50

Total 43

Table 20: Test Statisticsa, Vienna

Vienna


0,108b



Table 21: Ranks, The Hague


The Hague Female 12 26,46 317,50

Male 31 20,27 628,50

Total 43

Table 22: Test Statisticsa, The Hague

The Hague


0,149b



34

Table 23: Ranks, CRT scores


CRT English 21 24,21 508,50

Dutch 23 20,93 481,50

Total 44

Table 24: Test Statisticsa, CRT scores

CRT



Table 25: Correlations, CRT and 2 colours

2 colours CRT

Spearman's rho 2 colours Correlation Coefficient 1,000 0,068

Sig. (2-tailed) . 0,674

N 41 41

CRT Correlation Coefficient 0,068 1,000

Sig. (2-tailed) 0,674 .

N 41 44

Table 26: Correlations, CRT and 5 colours

CRT 5 colours

Spearman's rho CRT Correlation Coefficient 1,000 -0,226

Sig. (2-tailed) . 0,155

N 44 41

5 colours Correlation Coefficient -0,226 1,000

Sig. (2-tailed) 0,155 .

N 41 41

35

Table 27: Correlations, CRT and Vienna

CRT Vienna


Sig. (2-tailed) . 0,125

N 44 43

Vienna Correlation Coefficient -0,238 1,000

Sig. (2-tailed) 0,125 .

N 43 43

Table 28: Correlations, CRT and The Hague

CRT The Hague


Sig. (2-tailed) . 0,243

N 44 43

The Hague Correlation Coefficient -0,182 1,000

Sig. (2-tailed) 0,243 .

N 43 43

Table 29: Regression 2 colours, Age

Model

Unstandardized CoefficientsStandardized Coefficients

t Sig.B Std. Error Beta

1 (Constant) 44,043 3,305 13,326 0,000

Age 0,031 0,099 0,050 0,314 0,755

a. Dependent Variable: 2 colours

Table 30: Regression 5 colours, Age

Model



1 (Constant) 21,709 5,191 4,182 0,000

Age 0,298 0,156 0,292 1,909 0,064


36

Table 31: Regression Vienna, Age

Model



1 (Constant) 6,762 1,733 3,903 0,000

Age 0,021 0,050 0,064 0,410 0,684

a. Dependent Variable: Vienna

Table 32: Regression The Hague, Age

Model



1 (Constant) 7,708 1,865 4,134 0,000

Age 0,021 0,054 0,060 0,385 0,702

a. Dependent Variable: The Hague

Table 33: Regression 2 colours, Degree

Model



1 (Constant) 43,909 2,813 15,607 0,000

Degree 0,418 0,962 0,069 0,435 0,666


Table 34: Regression 5 colours, Degree

Model



1 (Constant) 30,721 4,626 6,641 0,000

Degree 0,051 1,581 0,005 0,032 0,974


Table 35: Regression Vienna, Degree

Model



1 (Constant) 6,376 1,512 4,217 0,000

Degree 0,390 0,509 0,119 0,766 0,448

a. Dependent Variable: Vienna

37

Table 36: Regression The Hague, Degree

Model



1 (Constant) 7,279 1,627 4,473 0,000

Degree 0,409 0,548 0,116 0,746 0,460

a. Dependent Variable: The Hague

38

bibliography - erasmus university thesis repository · web viewbesides being insignificant (p-value...

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