golden ratio phase 2

7/31/2019 Golden Ratio Phase 2

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2012

Carrie Meserole

Statistic 1510

5/11/2012

The Golden Ratio- Research project


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1The Golden Ratio Research Project

Abstract

The goal of this paper and analysis is to obtain data that will support or refute the

hypotheses that the Golden Ratio is a core element in the creation of all nature in general. The

human body was the subject in this analysis; measuring from the height/ navel to foot, the navel

to foot/ shoulder to the top of the head, navel to knee/ knee to foot, and length of face/ width of

face. TC-Stats was used to construct graphical displays, and summary statistics tables in order to

assist me in determining if the Golden Ratio is a core element in the creation of all nature in

general. After determining the data sets were not normally distributed I chose to use the

Kruskal-Wallis technique to determine if there was any difference. The technique concluded

that there was no evidence to support the Golden Ratio is a core element in the creation of all

nature in general.

Introduction

The research conducted in this research paper consists of obtaining measurements from

random people located in my town Bakersfield, Ca. The reason for this study is to demonstrate

that the idea that nature is constructed with the Golden Ratio as a core element is not true or is

true. The Golden Ratio is a value known as Phi or 1.6180 and many believe that the proportion

is found in architecture, nature, and the human body.

Method

In order to obtain the information need I handed out surveys to my family and friends.

On the survey it stated the purpose of colleting the measurements and that it was for a statistical

research project. In order to insure proper input I handed out the surveys and explained how to

do the measurements correctly. I had everyone complete their own measurements. This also

helped to ensure that all of the measurements were done the same way. I also posted an event on

Facebook.com. I explained that I am doing a research project for my statistics class at Taft

College. I explained how to do the measurements and this again helped to also ensure that they


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were done the same way. I then took a random sample of 35 of the 50 people to ensure that the

sample is representative of the population.

While conducting this experiment I wanted to find out if the Golden Ratio is a core element in

the creation of all nature in general. In order to find the answer, I used the Kruskal-Wallis

technique. The Kruskal-Wallis technique is used when you have multiple sets of data which are

not normally distributed and you want to determine if one set of data is different from the others.

While the Kruskal-Wall does not tell us which measurement is different, it does tell me if there is

a difference giving us the ability to reference back to the median of each measurement to

conclude which measurement is different from the others.

Participants

The participants were 27 females and 23 males.

Of the participants there were 31 adults and 19

children. I explained to the participants that this

was a statistical research project for my statistics

class at Taft College and it was to prove that the

Golden Ratio does appear in everyone.

Results

Before conducting this experiment my hypothesis was that nature is constructed with the Golden

Ratio as a core element. Using the Kruskal- Wallace technique with an alpha level of .05 I

found significant evidence (P-Value= 1.152E-35 which is approximate 0) that we are to reject

our null hypothesis.


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Figure 1- Box and whisker plot-

Figure 2- Summary Statistics

Hgt/N-footHeight/ Navel to foot

N-F/ S-head- Navel to foot/ Shoulder to top of the head

N-K/ K-F- Navel to knee/ knee to foot

L-Face/ W-face- Length of face/ Width of face


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Figure 3- Histogram

The navel to knee/ knee to foot histogram is skewed right somewhat. 78% of the population

that is represented in this data is between 1.0000-1.2500 which does not meet the Golden

Ratio of 1.618. There is nobody that even represents the Golden Ratio for this

measurement. The length of face/ width of face there is 34% that meet the Golden Ratio,

which means this measurement does not meet the Golden Ratio as well. This histogram is

bell shaped symmetric.


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The navel to foot and shoulder to the top of the head histogram is skewed left. Thisproves for this measurement that the nature is constructed with the Golden Ratio as a

core element in fact is not true. Now, the height/navel-foot there is 84% that do in

fact fulfill the Golden Ratio of 1.618. This histogram is skewed right.


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Figure 4- Age Histograms

Figure 5- Summary Statistics

The age histogram represents the different ages that I surveyed. The ages that were measured

from my research project ranged from 1 years old to 61 years old. The average age is 25.34


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Figure 6- Norm Plot

Height/ Navel to foot Navel - foot/ Shoulder top head

Navel-Knee/ Knee-Foot Length of face/Width of face

Normal plots were used to determine whether to use the ANOVA or the Kruskal-Wallis

technique. If the data is normal you use ANOVA, if it is not normal you would use the Kruskal-

Wallis. As you can see, all of the norm plots have some abnormalities.


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Conclusion

In concluding and looking the 50 people measured from a source of 4 different

measurements the Golden Ratio does not exists. Many of the variables that I initially felt would

have represented the Golden Ratio of 1.618 did not. While using the Kruskal-Wallace technique

with the alpha level of .05, I found a significant evidence that the p-value is 1.152E-35 which is

approximately 0, and that it would reject the null hypothesis (Ho:n) and H At

least one +.

There were a few limitations when dealing with this data set. The sample size could have

been bigger; a bigger sample size would have made the data more reliable and given more

statistical significance.


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Appendix

Please fill out this survey with the appropriate data for each member of your family. Please give all

measurements in the number of inches. Make sure that you do not include your name when returning

this survey. All data will be used in a statistical report for my college statistics class. If you have any

questions, comments or concerns please just ask.

1. Male or Female2. Age-3. Height-4. Shoulder line to the top of the head-5. Navel to foot-6. Navel to the top of the head-7. Navel to the knee-8. Knee to the end of the foot-9. Width of face-10.Length of face-


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Raw Data

F/M AGE HIEGHT

NAVEL-

FOOT

SHOULDER-

TOP HEAD

NAVEL-

TOP

HEAD

NAVEL

-

KNEE

KNEE-

FOOT

LENGTH

FACE

WIDTH

FACE

HIEGHT

/

NAVEL-

FOOT

NAVEL-

FOOT /

SHOULDER-

TOP HEAD

NAVEL -

KNEE /

KNEE-

FOOT

LENGTH

FACE /

WIDTH

FACE

F 26 66.25 37 11 26.5 21 18 7.75 4.5 1.7905 3.3636 1.1667 1.7222

M 32 69 41 12 29 23 18 7 6 1.6829 3.4167 1.2778 1.1667

F 52 65 37 11 29 19 16 9 4.75 1.7568 3.3636 1.1875 1.8947

M 7 48.5 28 9 20.5 14 13.5 7 4.75 1.7321 3.1111 1.037 1.4737

M 8 56 34 10 22 17.5 17 8 6 1.6471 3.4 1.0294 1.3333

M 32 69 42 10.5 27 22 19 8 6 1.6429 4 1.1579 1.3333

F 27 65 39.5 11.5 26.5 22 19 8 5.75 1.6456 3.4348 1.1579 1.3913

M 32 74.5 44.5 11 29.5 23 22 5.5 6.5 1.6742 4.0455 1.0455 1.1818

F 59 63.5 38.5 11.5 25 19.5 20.5 7.75 5.5 1.6494 3.3478 0.9512 1.4091

M 60 64.5 39 10 25.5 20 18.5 9 5.5 1.6538 3.9 1.0811 1.6364

M 60 73.75 46 11.5 32 22.5 23.5 9.5 7.5 1.6033 4 0.9574 1.2667

M 31 71.75 44.5 10.5 27.5 23 21 9.5 7.5 1.6124 4.2381 1.0952 1.2667

F 30 63.5 38.5 9.5 24 20.5 19 9.5 5.5 1.6494 4.0526 1.0789 1.7273

F 7 48.5 29 10 19.5 16 13.5 6.5 5 1.6724 2.9 1.1852 1.3

F 53 61 35 9.5 27 17.5 19 8 6 1.7429 3.6842 0.9211 1.3333

F 27 66.5 40 9.5 26.5 20 19.5 8 5.5 1.6625 4.2105 1.0256 1.4545

F 28 62 35.5 10 25 20 19.5 7 4.5 1.7465 3.55 1.0256 1.5556

M 32 73 44 11 29 23 19.5 9.5 7 1.6591 4 1.1795 1.3571

F 30 63 39.5 9 26 21 17 8.5 6 1.5949 4.3889 1.2353 1.4167

M 7 48.5 30 8.5 19 15 14.5 6 4.5 1.6167 3.5294 1.0345 1.3333

M 9 55 33.5 10.5 21.5 19 16.5 8 5 1.6418 3.1905 1.1515 1.6

M 9 56.5 35 8.75 21.5 34.5 17 6.75 4.75 1.6143 4 2.0294 1.4211

F 11 57 35.5 9 20.5 19 16 7 5.5 1.6056 3.9444 1.1875 1.2727

F 7 52.5 31 9 21 18 14 7 5 1.6935 3.4444 1.2857 1.4

M 3 36.5 20.5 8 17 11 10 6 4 1.7805 2.5625 1.1 1.5

F 28 62 34 10.5 23 20 16 9 4.5 1.8235 3.2381 1.25 2

M 40 67.5 31 11 27 21 21 8.5 6 2.1774 2.8182 1 1.4167

F 28 62 38 11.5 26 18 18 8 6 1.6316 3.3043 1 1.3333

M 6 47 28 9 20 14.5 16 8 4.5 1.6786 3.1111 0.9062 1.7778

F 59 63 39 11 26 19 19 8 5 1.6154 3.5455 1 1.6

M 33 70.5 43.5 11 26 22 21.5 9.5 5.5 1.6207 3.9545 1.0233 1.7273

F 30 64.5 39.5 11.5 26 21 19.5 8.5 5.5 1.6329 3.4348 1.0769 1.5455

F 5 47 27 8 18.5 13 13 7.5 5 1.7407 3.375 1 1.5


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F 5 44.5 26.5 8 18.5 15 12.5 7 4.5 1.6792 3.3125 1.2 1.5556

M 8 54.5 32.5 10.5 22 18.5 16 7.5 5 1.6769 3.0952 1.1562 1.5

M 34 69 42 11 29 23 20 9 5 1.6429 3.8182 1.15 1.8

M 41 70.5 42.5 28 23 20 20 9 5.25 1.6588 1.5179 1 1.7143

M 35 67.5 41 11 25 18 21.5 8 6 1.6463 3.7273 0.8372 1.3333

F 1 31.5 17.5 7 15 9.5 8 6.5 4 1.8 2.5 1.1875 1.625

M 1 30.75 17 7 14.75 9 8 6.75 4.25 1.8088 2.4286 1.125 1.5882

F 6 44.5 26.5 7.75 18.5 14 13 6.5 4.5 1.6792 3.4194 1.0769 1.4444

F 27 62.5 38 10.5 26 21 17 7.5 5.25 1.6447 3.619 1.2353 1.4286

F 8 50 31.5 9 20 16 14.5 6 4.5 1.5873 3.5 1.1034 1.3333

F 34 64.5 38.5 11 25.5 20.5 19 8 5 1.6753 3.5 1.0789 1.6

F 60 64.5 39 9 28 19.5 19 8 5.5 1.6538 4.3333 1.0263 1.4545

M 8 57.5 35 10.5 23.5 18 15.5 7.5 5 1.6429 3.3333 1.1613 1.5

F 8 25 32 9.5 20 17 15 6.5 4.75 0.7812 3.3684 1.1333 1.3684

F 10 57.5 34.5 10 22.5 17 17 7 5 1.6667 3.45 1 1.4

M 34 71 44 11.5 27 22.5 23 8 6.5 1.6136 3.8261 0.9783 1.2308

M 39 68 39.5 11 28.5 19 20 8 6 1.7215 3.5909 0.95 1.3333

There will also be raw data turned in at the time of the final.


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Bibliography

1. http://qt--server.taftcollege.edu/podcasts/stat1510/youtube/Golden_Ratio_Human_Body.mp4

2. http://qt-server.taftcollege.edu/podcasts/stat1510/youtube/The_Golden_Mean.mp4 3. Bourne. M, What has mathematics got to do with beauty? Actually, a lot. Physical

attraction depends on ratio. Intmath.com July 24,2011

4. Unknown. The Human Body. GOLDENNUMBER.NET. 3/2/12. 2011.

5. Filipovic, D. The Golden Section and the human body. Golden Section. Radoslav Jovanovic.January 2003
http://qt-server.taftcollege.edu/podcasts/stat1510/youtube/Golden_Ratio_Human_Body.mp4http://qt-server.taftcollege.edu/podcasts/stat1510/youtube/Golden_Ratio_Human_Body.mp4http://qt-server.taftcollege.edu/podcasts/stat1510/youtube/Golden_Ratio_Human_Body.mp4http://qt-server.taftcollege.edu/podcasts/stat1510/youtube/Golden_Ratio_Human_Body.mp4http://qt-server.taftcollege.edu/podcasts/stat1510/youtube/Golden_Ratio_Human_Body.mp4http://qt-server.taftcollege.edu/podcasts/stat1510/youtube/The_Golden_Mean.mp4http://qt-server.taftcollege.edu/podcasts/stat1510/youtube/The_Golden_Mean.mp4http://www.intmath.com/numbers/math-of-beauty.phphttp://www.goldennumber.net/body.htmhttp://milan.milanovic.org/math/english/golden/golden2.htmlhttp://milan.milanovic.org/math/english/golden/golden2.htmlhttp://milan.milanovic.org/math/english/golden/golden2.htmlhttp://www.goldennumber.net/body.htmhttp://www.intmath.com/numbers/math-of-beauty.phphttp://qt-server.taftcollege.edu/podcasts/stat1510/youtube/The_Golden_Mean.mp4http://qt-server.taftcollege.edu/podcasts/stat1510/youtube/Golden_Ratio_Human_Body.mp4http://qt-server.taftcollege.edu/podcasts/stat1510/youtube/Golden_Ratio_Human_Body.mp4


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