James H. Austin VAllie Levine

Heather LuntzPooja Viswanath

Introduction

• Allie, James, Heather and Pooja’s favorite numbers are odd.

• Is this a random phenomenon or does the general public really favor odd numbers over evens?

• Could this be due to cultural attitudes that surround certain numbers, or does it relate to birthdays, home addresses, etc?

• Could this knowledge be used to make bets to guess people’s favorite numbers? Would knowing this give us a better chance of having less people pick the same numbers as us in the lottery?

Goals

• Our goal is NOT necessarily to determine every subjects favorite number, but rather the overall tendency to favor odds over evens, or evens over odds.

• We tried to figure out the probability of a random person’s favorite number being odd.

• More precisely, do people really prefer odd numbers to even numbers?

Protocol and Testing

For the test we tested all the students that agreed to take our survey in food court, February 16th, from 6:30-7:30, and stopped when we had received 100 numbers. (The last person actually made it an even 100 numbers. We were not going to stop them if they gave us a few more than 100).

Protocol• We walked to each table with the surveys at hand

and asked the subject to fill it out. The subject did not know that our test was to see whether people prefer odds to evens so not to influence their opinions. After they completed the survey we glanced it over to make sure that it was completely filled out.

QuestionsWe asked our subjects the following questions:

• Question 1:.List your favorite numbers (max of five numbers).

We asked each subject to list their top favorite numbers, up to five. We did not want to require them to list five numbers because some people do not have five favorite numbers and we wanted them all to be legitimate. Also, by allowing people to choose five numbers it accounts strength of preference.

• Question 2: Did you choose any of these numbers based on some special significance to you? (i.e. birthday, anniversary, age, superstition, etc) If so, which numbers and why?

We wanted to ask some background questions to see if any of this information affects preference. We contemplated that people who have birthdays that fall on odd numbers may be more likely to like their birthday number, just because it is odd.

• Question 3: What is your gender?

We asked this question to make sure we were not completely biased with all female subjects or male subjects. We also wondered if there would be a significant difference between male and female preferences for odd numbers.

Our Pretest Beliefs

• We believed that people prefer odd numbers.

• Furthermore, we speculated that of the favorite numbers we collected, about 75% of them would be odd numbers.

Hypotheses

Null Hypothesis: Overall, the chance of a random person’s favorite number being odd is equally likely to it being even.

pnull = .5

Alternate Hypothesis: The chance of a person’s favorite number being odd is more likely than the number being even. palt >.5

Power Hypothesis: podd = ppow = .75

HOLY COW!! We Were Right!

ResultsNumbers Reason Sex9 bday F

12, 7, 13, 21 lucky F

8   F

21, 25 bday, sports M

21 Bday F

13, 17, 7   M

21, 23 Bday M

32, 18 Sports M

7   M

4, 16   F

16   F

3   F

23   F

22 sports F

8, 14 sports F

4, 7, 9   M

11, 9, 97, 21, 23   M

17, 45, 101 movie M

21 sports M

7, 8, 13   M

12, 18, 69, 21 sports M

11, 20, 84 sports, luck M

3, 21 sports M

11   M

12 bday M

13, 1   F

7, 17, 41, 47, 417   F

7,11, 2 bday F

22, 2 sports M

3, 4, 69 sports M

18, 25, 31 sports M

7, 22, 88, 21 sports M

81   M

5, 7, 9 bday F

3, 21, 77   M

3, 9, 19, 35, 2 house F

7, 29, bday, lucky F

13, 27, 11, 4 sports M

2, 13   F

9, 23   F

7 sports M

19 bday F

33, 31, 37   F

Numbers Reason Sex

73 of the favorite numbers were odd while 27 were even!!!

Odds vs. Evens

73

27

0

10

20

30

40

50

60

70

80

Odds Evens

Type of Number

Percentage of Total values

Odds vs. Evens

73

27

Odds

Evens

A graph showing our power hypothesis versus our actual results.

Odds vs. Evens (Predicted vs. Actual)

75

25

73

27

0

10

20

30

40

50

60

70

80

Odds Evens

Percentage of Favorite Numbers

Predicted

Actual

Analysis of Results

• There were 73 odds and 27 evens.

• There were an overwhelming number of 7’s and 21’s.

• A majority of people had reasons for why their favorite numbers were their favorite. The most popular reason was sports numbers and the second most was birthdays.

26 people gave reasons while 18 didn’t.

Reason vs. No Reason

26

18

0

5

10

15

20

25

30

Reason No Reason

Number of Respondents

Series1

Reason for Favorite Number

9

3

14

1

18

0

2

4

6

8

10

12

14

16

18

20

Birthday Lucky # Sports # House # None

Reason

Number of Respondents

Frequency of Favorite Numbers

0

2

4

6

8

10

12

Favorite Number

Frequency

Series1

Our Calculations

Conclusion• So it turns out that people really do prefer odd

numbers to even numbers. • According to our results, 72% of people prefer

odd numbers over evens. This is very close to our power hypothesis of 75%.

• Our test is so powerful that the chance that our .75 hypothesis (power) is true, and we fail to reject the null hypothesis is totally negligible. This ends up being about a one in 5,000 chance of committing a Type II error.

Confounding Factors

• Most of the culturally popular numbers (i.e. 7, 21, 69) are odd numbers, so one might argue that these numbers should be taken out when we compile our data. On the other hand, we feel that one of the reasons why odd numbers may be more popular is because of these culturally popular numbers, therefore these numbers cannot really be disregarded.

• Also, we surveyed people in Food Court and due to the fact that we were probably annoying the diners, they may have made up arbitrary numbers to get us away. Who knows, they could have given us the price of their food, how many chicken nuggets they had, or how many people were at their table.

So, Turns out…Everyones just an ‘ODD’BALL