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Surve Data Analsis 1

Surve Data Analsis

Daniel Loa

Taft College


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Survey Data Analysis 2

Abac

Data was collected through a survey and fed into a database. From this database a

sample of 50 respondents was taken and the data analysed using techniques learned in an

introductory statistics course. This analysis was done in order to answer a series of questions

regarding the relationship of different random variables such as gender, income, political

association, handedness and opinion on several issues. Some results were inconclusive due to

the size of the sample as explained in the results section.

Inodcion

The purpose of our research here was to better understand how conduct a scientific

study and write a proper report. We also wanted to get some practice using the statistical

techniques we have learned throughout this course. We accomplished this by conducting a

study on a population constructed by collecting data from random individuals using a survey. We

took a sample from this survey and set out to answer several questions based on the data

collected.

Our first question was whether or not there is an appropriate relationship between a

persons height, weight, shoe size and ring size. It was hypothesized that such a relationship

exists since larger people will probably have all of these be greater than a smaller person. The

second question was if there was a difference in income based on gender for which it was

hypothesized that such a difference would be found.

The third part had several parts, all regarding the relationship between party association

and three other variables. The first part was to see if there was a relationship between party

association and the respondent believing Obama would be reelected. The second was if they

were in favor of the health care bill as passed and the third variable was their stance on the

death penalty. For all of these I hypothesized that a relationship existed since these issues are


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often divided along party lines.

The next question also had more than one part to it. It was whether there was a

relationship between handedness and a persons stance on the death penalty, and the amount of

water they drank. For both it was hypothesized that no relationship would be found.

After this I wanted to see who was more likely to switch to the tea party, Democrats or

Republicans. It was hypothesized that Republicans are more likely to switch because of the Tea

Partys clearly conservative ideals.

The last question that will be answered from the data collected was whether students

were less likely to work more than 30 hours a week than non-students. The hypothesis for this

was that students were less likely to work more than 30 hours a week.

How the data to answer these questions, and how the data was analyzed to answer

them, is explained in the following sections.

Mehod

Paicipan

The people that took the survey were individuals randomly selected by students in

several different statistics classes taught in Bakersfield, CA and Taft, CA. It is likely a majority of

the individuals that took the survey reside this this general area.

Maeial

Survey: This was a survey that consisted of 23 simple questions the participants were

asked to answer. A copy of this survey can be found in the appendix.

Database: We used an online database to store the data we collected.

Pocede


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Se Daa Anali 5

Heigh Hiogam and mma aiic

Mean S Min Q1 M Q3 Ma

66.7800 4.0972 53.0000 64.0000 67.0000 70.0000 74.0000

To anale he diibion of eigh in he ample I ed he ame pocede a he

peio aiable.


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Weight Histogram and summar statistics


167.9400 40.9775 85 140 169 187 290


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Se Daa Anali 7

Ring ie hiogam and mma aiic


7.4167 1.7092 3 6 8 9 10

The hoe ie daa a alo analed in he ame manne.


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Se Daa Aai 8

She ie higa ad a aiic

Mea S Mi Q1 M Q3 Ma

8.8000 2.0677 3 7.5 9 11 12.5

The ecd ei I aed ae ih hi d a, i hee a diffeece i

g ice baed gede? M hhei a e. T bee dead he daa I de a

higa ad cacaed he ae aiic f he ice f each gede. The I efed

a Wice Ra- ha eed i -ae=0.7604 hich de he hhei.


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Male income histogram and summar statistics


53068.1818

688832.8368

0 13000 30000 69000 300000


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Female income histogram and summary statistics

Mean S Min Q1 M Q3 Max

32259.4286 29747.421

4

0 4000 30000 48500 110000

Our next question was to see if there was a relationship between political party and a

respondents opinion on a series of issues. The data is summarized in a series of tables bellow

comparing the respondents party and their response to an issue. Reporting the data in this

manner makes it easier to perform tests of independence.

The first part was to see if there was a relationship between party and whether or not the

respondent believed Obama would be reelected. The hypothesis for this was that the two

variables were dependent, however, the results were inconclusive when the Independent and


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Other columns were included, even if they were combined. Further collapsing of the table was

not possible.

Obama reelection

Republican Democrat Independent Other

Yes 4 15 0 4

No 15 7 3 2

The next part was to see if there was also a relationship between party and the

respondents approval of the health care bill. The hypothesis was that a relationship existed. In

order to meet the assumptions for the test we collapsed the Independent and Other columns

together. This returned a X2 of 10.9271 and a p-value=0.0042 which supports the hypothesis.

health care Republican Democrat Other

Yes 5 13 0

No 14 9 9

The same was done about the question regarding party and stance on the death penalty.

The Independent and Other columns were combined and a test of independence was

performed. This produced a X2 of 0.1062 and a p-value=0.9483 which contradicts the

hypothesis.

death Republican Democrat Other

Yes 13 14 6

No 6 8 3


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I then wanted to see if a persons handedness had an effect on their opinion about the

death penalty and the amount of water they drank. I predicted that a persons handedness should

have no effect on either of these. To check the first part of this I collected the data on a table in

order to perform a test of independence. This resulted in X2=2.6364 and p-value=0.2676 which

supports my hypothesis, however, these values had to be disregarded because the

assumptions of the test were not met. Our results are inconclusive.

Right Left Ambidextrous

Yes 18 4 1

No 25 1 1

For the next question, I drew histograms and calculated the summary statistics for the

water drank by people of each handedness. The question was whether there was a relationship

between handedness and water drank. The hypothesis was that there was no difference

between handedness. The ambidextrous people were not considered because there were only 2

in the sample, which did not represent them properly. A rank-sum test resulted in a p-value of

0.5375 which supported the hypothesis.


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Water drank b left-handed people histogram and summar statistics

Mean S Min Q1

M Q3

Ma

55.4000 39.1127 8 16 60 92.5 100


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Water drank by right-handed people histogram and summary statistics

Mean S Min Q1 M Q3 Max

76.9767 60.5941 1.0000 32.0000 60.0000 120.0000 256.0000

The next question was, what party were people in the Tea Party most likely to come

from. My hypothesis was that most of the members of the Tea Party would come from the

Republican party. The former party membership is show in the bar graph bellow.

This question was slightly tricky. I wanted to perform a goodness of fit test but for that I

needed to find the true proportions, which I didnt have. So I decided to use the proportion of each

partys membership as a replacement since it seems reasonable to test against these values.

The Independent and Other category were grouped together and the test was performed

resulting in a p-value=0.8453 that had no meaning due to a violation of assumptions. This test

was inconclusive.


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Democrats Republicans Other

members 22 19 9

Proportion of sample 44% 38% 18%

Former part association of Tea Part member

Our last question was whether students are less likel to work 30 hours or more than

non-students. I predicted that students would me more likel to work less than 30 hours a week.

This data was then put into a table and a test of independence was performed. The X 2 was

13.1335 and the p-value was 0.0003. This supports the hpothesis.


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S D A 16

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of this, however, a rank-sum test proved my hypothesis that handedness has nothing to do with

how much water somebody drinks.

The results of the following question should be taken lightly since estimates were used in

liue of true proportions. The question was whether individuals from one party were more likely to

switch to the tea party. My hypothesis that members of one party were more likely to join the tea

party could not be proved or discredited because the assumptions for the test failed so the

p-value was practically useless.

The last question was answered using a test of independence that showed being a

student and working more that 30 hours a week were linked.

Shortly after beginning the analysis it became clear that 50 was not a big enough sample

size to reliably answer all of the questions proposed in the introduction. This sample size was

selected because it appeared to be a manageable size. However, it turned out to be too small to

the point that some statistical tests could not be performed. A better sample size would have

been 75 or 100. This would have substantially increased the effort needed to analyse the data

but at the same time produced better results.

The main purpose of this project was to be a learning experience and provide a

meaningful way to practice the techniques learned in the course.

Appendi

The raw data is available upon request. Here are the assumptions and work for each test

performed on the data. All of the following p-values were compared against alpha=0.05.

2: For the second question I performed a t-test with

Ho:M=F HA:M>F Alpha= 0.05

Then we begin to check the assumptions which are violated by normal plots. This causes us to

switch to a non-parametric test, the wilcoxon rank-sum. This results in a p-value of 0.7604.


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Ho:M=F HA:M>F Alpha= 0.05

There was not enough evidence to suggest median female income was less than median male

income.

Female Income Male Income

3a: For the next section I did a test of independence for each of the tables. The first one, which

was between party and opinion about Obamas reelection.

HA: Party and belief that Obama will be reelected are independent.

HO: Party and belief that Obama will be reelected are dependent.

This first test of independence returned X2 =12.7055 and p-value=0.0053. However the

assumptions were violated because half of the expected values were bellow 5.

8.74 10.12 1.38 2.76

10.26 11.88 1.62 3.24

Even when the table was collapsed to have the Other and Independent columns together the

assumptions were still violated by the expected values since a third were bellow 5. This


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Se Daa Aai 19

eeed a cci f beig eached.

8.74 10.12 4.14

10.26 11.88 4.86

3b: The e e a beee a ad aa f he heah cae bi.

HA: Pa ad aa f he heah cae bi ae ideede.

HO: Pa ad aa f he heah cae bi ae deede.

The eeced ae ae ied be ad ee ai ice a ih ae be 5.

6.84 7.92 3.24

12.16 14.08 5.76

3c: The e efed he ae e he a abe.

HA: Pa ad ace he deah ea ae ideede.

HO: Pa ad ace he deah ea ae deede.

The eeced ae ffi he ai -ae f 0.9483 i aid. Thee i egh

eidece gge a ad ace he deah ea ae deede.

12.54 14.52 5.94

6.46 7.48 3.06

4a: F he e ei, he fi a ied a e f ideedece beee hadede ad

ii he deah ea.

HA: Hadede ad ace he deah ea ae ideede.

HO: Hadede ad ace he deah ea ae deede.


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The expected values clearly show that the assumptions are violated so the p-value has no

meaning. This test was inconclusive.

19.78 2.3 0.92

23.22 2.7 1.08

4b: The next part was finding a relationship between handedness and the amount of water drank.

I decided to only compare left and right handed people because there were only two

ambidextrous people in the sample. I was unable to perform a t-test because the normality

assumption was violated by normal plots.

Ho:R=L HA:R=/=L Alpha= 0.05

Left handed Right handed

This forced me to switch to a rank-sum test which required no assumptions and returned a

p-value of 0.5375. This meant the null hypothesis was not rejected. There is enough evidence to

suggest right handed people drink different amounts of water than left handed people.

Ho:R=L HA:R=/=L Alpha= 0.05

6: For the sixth and final question I performed a test of independence.

HA: Being a student and working more than 30 hours are independent.


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HO: Being a student and working more than 30 hours are dependent.

The test resulted in X2 =13.1335 and the p-value was 0.0003 and the assumptions are met by

the expected values. There is not enough evidence to suggest being a student and working are

independent.

11.245 14.655

12.655 16.345

Questions contained in the survey

1. Gender: Male Female

2. Ethnicity: White Black Hispanic Other

3. Age (years):

4. Height (in inches, so 5 ft 7 inches would be 67):

5. Weight (pounds):

6. Hours worked per week:

7. Are you currently a Student? Yes No

8. Education Level (completed, not in progress):

(High School Grad = 12, Associate Degree = 14,

BA/BS = 16, MA/MS = 18, PhD = 20)

9. Annual Gross Income (numbers only, $39000 is 39000, not 39,000 or $39K):

10. Eye color: Brown Black Blue Hazel Each eye is a different color Other

11. Natural hair color. Black Blond Brown or Brunette Grey Red Silver

Other

12. Number of ounces of water you drank for the two days prior to submitting this survey.

One cup of water is 8 ounces whereas most glasses are 12 or 16 ounces.


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13. Are you in favor of the death penalty? Yes No

In this context in favor means you are for the death penalty for at least one,

but not necessarily all, crimes that are currently punishable by death.7

14. What political party do you most closely associate yourself with? By associate, I mean

what party are you registered to vote with or if you are not registered, which party

would you register with if you had to chose. Democrat Republican Independent

Other

15. Are you registered to vote? Yes No

16. Do you personally know anyone that has been infected with the HIV virus?

Yes No

By personally know, I mean a personal knowledge of that person. As an example, we all

probably know Magic Johnson, but I doubt any of us have actually met him or are

friends with him. If Magic is the only person you know who has been infected with

HIV, then your answer to this question would be no.HIV, then your answer to this question would

be no.

17. Are you in favor of the health care bill as passed? Yes No Undecided

18. Are you leftRhanded, rightRhanded, or ambidextrous?

19. Do you believe President Obama will be reelected? Yes No Uncertain

20. Change of Party Affiliation

I considered myself a Democrat or Liberal and now associate myself with the Tea

Party.

I considered myself a Republican or Conservative and now associate myself with the

Tea Party.

I considered myself other than Democrat or Republican and now associate myself

with the Tea Party.


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Not applicable to me.

21. Consider Proposition 8, the 2008 proposition regarding marriage for same sex couples. The

proposition defined marriage as between a man and a woman and prohibits same sex couples

from marrying. Do you agree with Proposition 8? Yes No

22. What is your shoe size?

23. What is your ring size?

6. Hours worked per week:

7. Are you currently a Student? Yes No

8. Education Level (completed, not in progress):

(High School Grad = 12, Associate Degree = 14,

BA/BS = 16, MA/MS = 18, PhD = 20)

9. Annual Gross Income (numbers only, $39000 is 39000, not 39,000 or $39K):

10. Eye color: Brown Black Blue Hazel Each eye is a different color Other

11. Natural hair color. Black Blond Brown or Brunette Grey Red Silver

Other

12. Number of ounces of water you drank for the two days prior to submitting this survey.

One cup of water is 8 ounces whereas most glasses are 12 or 16 ounces.

13. Are you in favor of the death penalty? Yes No

In this context in favor means you are for the death penalty for at least one,

but not necessarily all, crimes that are currently punishable by death.7

14. What political party do you most closely associate yourself with? By associate, I mean

what party are you registered to vote with or if you are not registered, which party

would you register with if you had to chose. Democrat Republican Independent

Other

15. Are you registered to vote? Yes No


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16. Do you personally know anyone that has been infected with the HIV virus?

Yes No

By personally know, I mean a personal knowledge of that person. As an example, we all

probably know Magic Johnson, but I doubt any of us have actually met him or are

friends with him. If Magic is the only person you know who has been infected with

HIV, then your answer to this question would be no.

17. Are you in favor of the health care bill as passed? Yes No Undecided

18. Are you leftRhanded, rightRhanded, or ambidextrous?

19. Do you believe President Obama will be reelected? Yes No Uncertain

20. Change of Party Affiliation

I considered myself a Democrat or Liberal and now associate myself with the Tea

Party.

I considered myself a Republican or Conservative and now associate myself with the

Tea Party.

I considered myself other than Democrat or Republican and now associate myself

with the Tea Party.

Not applicable to me.

21. Consider Proposition 8, the 2008 proposition regarding marriage for same sex couples. The

proposition defined marriage as between a man and a woman and prohibits same sex couples

from marrying. Do you agree with Proposition 8? Yes No

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