Transcript Odd or Even Favorite Number Test

James H. Austin V
Allie Levine
Heather Luntz
Pooja 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.
Questions
We 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!
Results
Numbers
Reason
Sex
Numbers
Reason
Sex
9
bday
F
11, 20, 84
sports, luck
M
12, 7, 13, 21
lucky
F
3, 21
sports
M
F
11
8
M
21, 25
bday, sports
M
12
21
Bday
F
13, 1
F
M
7, 17, 41, 47, 417
F
13, 17, 7
bday
M
21, 23
Bday
M
7,11, 2
bday
F
32, 18
Sports
M
22, 2
sports
M
7
M
3, 4, 69
sports
M
4, 16
F
18, 25, 31
sports
M
16
F
7, 22, 88, 21
sports
M
3
F
81
23
F
5, 7, 9
M
bday
F
22
sports
F
3, 21, 77
M
8, 14
sports
F
3, 9, 19, 35, 2
house
F
4, 7, 9
M
7, 29,
bday, lucky
F
11, 9, 97, 21, 23
M
13, 27, 11, 4
sports
M
17, 45, 101
movie
M
2, 13
F
21
sports
M
9, 23
F
M
7
sports
M
M
19
bday
F
7, 8, 13
12, 18, 69, 21
sports
33, 31, 37
F
Odds vs. Evens
80
73
70
Percentage of Total values
60
50
40
Odds vs. Evens
30
27
20
27
10
0
Odds
Evens
Type of Number
Odds
Evens
73
73 of the favorite numbers were odd while 27 were even!!!
Odds vs. Evens (Predicted vs. Actual)
80
75
73
70
Percentage of Favorite Numbers
60
50
Predicted
Actual
40
30
27
25
20
10
0
Odds
Evens
A graph showing our power hypothesis versus our
actual results.
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.
Reason vs. No Reason
30
26
25
Number of Respondents
20
18
15
Series1
10
5
0
Reason
No Reason
26 people gave reasons while 18 didn’t.
Reason for Favorite Number
20
18
18
16
14
Number of Respondents
14
12
10
9
8
6
4
3
2
1
0
Birthday
Lucky #
Sports #
Reason
House #
None
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