devin capela golden ratio project (phase two) stats 1510 freshman year tc 5-4-12

7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12

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Golden Ratio Project Phase Two

Devin Capela

Golden Ratio Project (Phase Two)

Stats 1510


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Golden Ratio Project Phase Two 2

Abstract

This project compares males and females in regards to The Golden Ratio. Each person that

was measured for this project was selected from the same population of interest (high

school students) and was selected in the same manner (SRS). A Kruskal Wallis test was

used to compare the data sets to one another and to see if the Golden Ratio was present in

each of the ratios derived from our data sets. This project comes to the conclusion that the

Golden Ratio is not preserved in the data and that the three recorded ratios differed from

each other very significantly.


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Introduction

In this experiment, males and females were compared to one another in regards to The

Golden Ratio.The Golden Ratio, refers to the length to width ratio of rectangles that is

most pleasing to the eye. (http://www.geom.uiuc.edu/~demo5337/s97b/art.htm) The

Golden Ratio is also thought by many to be found in infinite aspects of nature, such as

sunflower patterns, snails, pinecones, seashells, and even the human body in many

different variations and measurements. (http://www.youtube.com/watch?v=085KSyQVb-

U&feature=fvst) The Golden Ratio was originally traced back to Ancient Greece, where a

man named Leonardo Fibonacci devised a geometric sequence of numbers that was

believed to be correlated to many, if not all things in the universe, and that somehow all of

these things are derived from this sequence of numbers.

(http://www.youtube.com/watch?v=2zWivbG0Rio) This experiment was carried out in

order to observe and analyze the validity of The Golden Ratio, and to see if both men and

women fall into the categorizations of The Golden Ratio, or to what degree of this ratio

males and females differ from one another. It was hypothesized that The Golden Ratio

would not be held completely intact upon examination of the data of this experiment; the

ratios derived from the separate samples will be somewhat close to The Golden Ratio, but

the exact ratio of 1.618 will not be found within the data.
http://www.youtube.com/watch?v=085KSyQVb-U&feature=fvsthttp://www.youtube.com/watch?v=085KSyQVb-U&feature=fvsthttp://www.youtube.com/watch?v=085KSyQVb-U&feature=fvsthttp://www.youtube.com/watch?v=085KSyQVb-U&feature=fvsthttp://www.youtube.com/watch?v=085KSyQVb-U&feature=fvsthttp://www.youtube.com/watch?v=085KSyQVb-U&feature=fvst


4/22


Methods

In order to conduct this experiment, two samples of 20 people each (20 males and 20

females) were taken from the population of interest (High School students). This sampling

method resembles a stratified random sample, yet since the people that were selected to be

measured in the experiment werent necessarily randomly selected via random number

generation, this type of sampling method doesnt quite fall under the category of a true

stratified random sample. Twenty high school females and twenty high school males were

selected by way of randomly stopping by classrooms and asking if a few willing students

would like to be measured for a college statistics project. These two samples (one sample of

twenty males and one sample of twenty females) are representative of the population; all

individuals measured in this experiment were selected in the same manner, measured with

the same measuring tape, and do not deviate from the population of interest, high school

students, in any way. Six total measurements (in inches) were taken with the one

measuring tape from each individual to the nearest half-inch, and three ratios were derived

from the data: Total Height and Belly Button to Foot (ratio 1), Finger to Elbow and Wrist to

Elbow (ratio 2), and Length of face by Width of Face (ratio 3). TC Stats was used to record

the measurements of each individual and to derive the summary statistics, perform a

Kruskal Wallis test, as well as graphical displays for both males and females in regards to

the three ratios observed. (Normal Plots, Box and Whisker Plots, etc.)


5/22


Results

Upon completion of the experiment, the data that was collected was analyzed by way of

graphical display, comparison of five number summaries, and a Kruskal Wallis test. Figure

1.1, which is the summary statistics of the females measured in this experiment, and Figure

1.2, which is the summary statistics of the males measured in this experiment, illustrate the

five number summaries of both samples side-by-side so that they may be easily compared

to one another in each aspect of the five number summaries. The sample sizes, mean, and

standard deviation are also presented in the summary statistics, and allow for the viewer to

easily make comparisons between each simple random sample. Figure 1.3 and 1.4 show

graphical displays of the five number summaries for both samples presented as box and

whisker plots. A box and whisker plot is a type of graph that displays the five number

summaries for each desired group on a number line. A box and whisker plot can be very

helpful in many cases, and was used in this report to visually show how both samples

differed from one another in regards to their three ratios. A Kruskal Wallis test was

performed on the three observed ratios to determine if the ratios were equal to one

another; the ratios were significantly different from one another. (p


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Figure 1.1 (Female Summary Statistics)

Figure 1.2 (Male Summary Statistics)


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Figure 1.3 (Female Box and Whisker Plot)

Figure 1.4 (Male Box and Whisker Plot)


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Discussion

In the introduction, it was hypothesized that The Golden Ratio would not be held

completely intact upon examination of the data of this experiment; the ratios derived from

the separate samples will be somewhat close to The Golden Ratio, but the exact ratio of

1.618 will not be found within the data. This hypothesis was supported by the data when

using a Kruskal Wallis test. It is likely that many people searching for the Golden Ratio in

nature, often find the ratio because they are looking for it with a very fixated point of view;

it is very easy to see reoccurring themes and patterns in just about anything you study, but

that doesnt mean that the subject is based solely on the specific pattern that was observed.

The Golden Ratio is claimed to be in every aspect of nature, but this project does not

support this claim when pertaining to several measurements of the human body. The

Golden Ratio tries to explain why and how nature is the way it is, but it is best not to force

an idea somewhere it does not belong; the Golden Ratio isnt the only ratio found within

nature, it is only the most talked about ratio observed in nature. (See: Fibonacci Flim-

Flam in Appendix) Although not a confounding factor, it would have been an improvement

if a greater number of subjects were measured for this project. Another idea that would

have added a nice component to this project would have been to sample from several

different geographical locations to encompass a greater diversity of people. One more good

idea would have been to measure non-human subjects, such as sunflowers, seashells and

pinecones to add another dimension to the study of the Golden Ratio.


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Appendix

In TC Stats, a Kruskal Wallis test was performed because the recorded ratios were not

normal and we had more than two samples to compare. (See normal plots 1.5, 1.6, and 1.7)

Independence was justified because none of the ratios affect each other in any way. All

three ratios were selected in TC Stats in our Kruskal Wallis test, which yielded a test

statistic of 89.8983, and a p-value of 6.05E- 19 (approximately 0.0000). This p-value is less

than our significance level (alpha) of 0.05, which means that we reject the null hypothesis.

For our Kruskal Wallis test, Ho: Theta (ratio one) = Theta (ratio two) = Theta (ratio three),

and Ha: At least one of these values is not equal to the others.

Since we reject Ho based on our p-value, we can confirm that at least one of our ratios is not

equal to the others. When we take a look at the medians of the three ratios and compare

them, we can easily see that all three are different from each other, and that ratio three is

significantly different than the other two. (See Summary Statistics)

These results lead us to conclude that there is sufficient evidence to suggest that the Golden

Ratio does not exist within our data.

Fibonacci Flim-Flam

This article (http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm) offers a very

detailed explanation, complete with research and several test results, as to why the Golden

Ratio is not a reality in nature, and provides an interesting change-of-pace counter-

argument to the other research offered within this project.


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Figure 1.5 (Normal Plot of Ratio #1)


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Gender

Total

Height

(inches)

BellyButton to

Foot

(inches)

Finger to

Elbow

(inches)

Wrist to

Elbow

(inches)

Length of

Face

(inches)

Width of

Face

(inches)

Ratio

#1

Ratio

#2 Ratio

Female 66.5 42 16.5 10 7 5.5 1.5833 1.65 1.27

Female 65.5 39 15 9 7 5 1.6795 1.6667

Female 69 42 17 10 7 5 1.6429 1.7

Female 68 43 18 11 7 5 1.5814 1.6364

Female 66.5 42 17 10 6.5 4.5 1.5833 1.7 1.44

Female 64 40 17 10.5 6 5 1.6 1.619

Female 66 39 16 9 7 5 1.6923 1.7778

Female 67 43 17 10 8 4.5 1.5581 1.7 1.77

Female 63 39 16.5 10 7 5 1.6154 1.65

Female 68 43 17.5 11 7 5 1.5814 1.5909

Female 61 39 15 9 6 4.5 1.5641 1.6667 1.33

Female 65.5 40 17 10 6 5 1.6375 1.7

Female 64 41 17 10.5 6 5 1.561 1.619

Female 65 40 16 10 6 4.5 1.625 1.6 1.33

Female 59 37 15.5 9 6 4.5 1.5946 1.7222 1.33

Female 66.5 41 17 10 7 5 1.622 1.7

Female 65 40 16 9.5 7 5 1.625 1.6842

Female 65 41 17 10 6.5 5 1.5854 1.7

Female 63 40 15 9 7 5 1.575 1.6667

Female 67 41 16.5 9.5 7 5 1.6341 1.7368

Male 67 42 17 10 7 6 1.5952 1.7 1.16

Male 71 46 19 11 7 5 1.5435 1.7273

Male 70 43 19 11.5 7 5 1.6279 1.6522

Male 72 46 18 11 7.5 6 1.5652 1.6364 1

Male 66 40 17 10 6 4.5 1.65 1.7 1.33

Male 65 40 17 10 6 5 1.625 1.7

Male 70 44 18 11 7 5 1.5909 1.6364

Male 69 41 17 10 7 5 1.6829 1.7

Male 68 42 18 11 6.5 5 1.619 1.6364

Male 71 43 18.5 11 7 5 1.6512 1.6818

Male 68 42 18 11 7 5.5 1.619 1.6364 1.27

Male 69.5 43 17.5 11 7 5 1.6163 1.5909

Male 70 43 18.5 11 7 5 1.6279 1.6818

Male 72 46 19 11 6.5 4.5 1.5652 1.7273 1.44

Male 71 44 18 11 7 4.5 1.6136 1.6364 1.55

Male 69.5 44 18 11 7 5 1.5795 1.6364

Male 68 42 18 11 7 5 1.619 1.6364

Male 66 41 17 10.5 7 5.5 1.6098 1.619 1.27

Male 71 43 21 13 7 5 1.6512 1.6154

Male 71 44 19 12 7 5 1.6136 1.5833


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Works Cited

Blacker, Steve, Jeanette Polanski, and Marc Schwach. "The Golden Ratio." The Geometry

Center Welcome Page. Web. 11 Mar. 2012.

.

HighFlyingDutchman. "Golden Ratio in Human Body." YouTube. YouTube, 18 Sept. 2008.

Web. 12 Mar. 2012. .

Angiegreek. "The Golden Mean." YouTube. YouTube, 23 Nov. 2007. Web. 12 Mar. 2012.

.

Simanek, Donald E. "Fibonacci Flim-Flam." Fibonacci Flim-Flam. Web. 14 May 2012.

.


15/22


Phase One of this Project

Devin Capela

Golden Ratio Project (Phase One)

Stats 1510


16/22


Introduction

In this experiment, males and females were compared to one another in regards to The

Golden Ratio. The Golden Ratio, refers to the length to width ratio ofrectangles that is

most pleasing to the eye. (http://www.geom.uiuc.edu/~demo5337/s97b/art.htm) The

Golden Ratio is also thought by many to be found in infinite aspects of nature, such as

sunflower patterns, snails, pinecones, seashells, and even the human body in many

different variations and measurements. (http://www.youtube.com/watch?v=085KSyQVb-

U&feature=fvst) The Golden Ratio was originally traced back to Ancient Greece, where a

man named Leonardo Fibonacci devised a geometric sequence of numbers that was

believed to be correlated to many, if not all things in the universe, and that somehow all of

these things are derived from this sequence of numbers.

(http://www.youtube.com/watch?v=2zWivbG0Rio) This experiment was carried out in

order to observe and analyze the validity of The Golden Ratio, and to see if both men and

women fall into the categorizations of The Golden Ratio, or to what degree of this ratio

males and females differ from one another. It was hypothesized that The Golden Ratio

would not be held completely intact upon examination of the data of this experiment; the

ratios derived from the separate samples will be somewhat close to The Golden Ratio, but

the exact ratio of 1.618 will not be found within the data.
http://www.youtube.com/watch?v=085KSyQVb-U&feature=fvsthttp://www.youtube.com/watch?v=085KSyQVb-U&feature=fvsthttp://www.youtube.com/watch?v=085KSyQVb-U&feature=fvsthttp://www.youtube.com/watch?v=085KSyQVb-U&feature=fvsthttp://www.youtube.com/watch?v=085KSyQVb-U&feature=fvsthttp://www.youtube.com/watch?v=085KSyQVb-U&feature=fvst


17/22


Methods

In order to conduct this experiment, two samples of 20 people each (20 males and 20

females) were taken from the population of interest (High School students). This sampling

method resembles a stratified random sample, yet since the people that were selected to be

measured in the experiment werent necessarily randomly selected via random number

generation, this type of sampling method doesnt quite fall under the category of a true

stratified random sample. Twenty high school females and twenty high school males were

selected by way of randomly stopping by classrooms and asking if a few willing students

would like to be measured for a college statistics project. These two samples (one sample of

twenty males and one sample of females) are representative of the population; all

individuals measured in this experiment were selected in the same manner, measured with

the same measuring tape, and do not deviate from the population of interest, high school

students, in any way. Six total measurements (in inches) were taken with the one

measuring tape from each individual to the nearest half-inch, and three ratios were derived

from the data: Total Height and Belly Button to Foot (ratio 1), Finger to Elbow and Wrist to

Elbow (ratio 2), and Length of face by Width of Face (ratio 3). TC Stats was used to record

the measurements of each individual and to derive the summary statistics as well as

graphical displays for both males and females in regards to the three ratios observed.


18/22


Results

Upon completion of the experiment, the data that was collected was analyzed by way of

graphical display and comparison of five number summaries. Figure 1.1, which is the

summary statistics of the females measured in this experiment, and Figure 1.2, which is the

summary statistics of the males measured in this experiment, illustrate the five number

summaries of both samples side-by-side so that they may be easily compared to one

another in each aspect of the five number summaries. The sample sizes, mean, and

standard deviation are also presented in the summary statistics, and allow for the viewer to

easily make comparisons between each simple random sample. Figure 1.3 and 1.4 show

graphical displays of the five number summaries for both samples presented as box and

whisker plots. A box and whisker plot is a type of graph that displays the five number

summaries for each desired group on a number line. A box and whisker plot can be very

helpful in many cases, and was used in this report to visually show how both samples

differed from one another in regards to their three ratios.


19/22


Figure 1.1 (Female Summary Statistics)

Figure 1.2 (Male Summary Statistics)


20/22


Figure 1.3 (Female Box and Whisker Plot)

Figure 1.4 (Male Box and Whisker Plot)

Appendix (Next Page)


21/22


Gender

Total

Height

(inches)

BellyButton to

Foot

(inches)

Finger to

Elbow

(inches)

Wrist to

Elbow

(inches)

Length of

Face

(inches)

Width of

Face

(inches)

Ratio

#1

Ratio

#2 Ratio

Female 66.5 42 16.5 10 7 5.5 1.5833 1.65 1.27

Female 65.5 39 15 9 7 5 1.6795 1.6667

Female 69 42 17 10 7 5 1.6429 1.7

Female 68 43 18 11 7 5 1.5814 1.6364

Female 66.5 42 17 10 6.5 4.5 1.5833 1.7 1.44

Female 64 40 17 10.5 6 5 1.6 1.619

Female 66 39 16 9 7 5 1.6923 1.7778

Female 67 43 17 10 8 4.5 1.5581 1.7 1.77

Female 63 39 16.5 10 7 5 1.6154 1.65

Female 68 43 17.5 11 7 5 1.5814 1.5909

Female 61 39 15 9 6 4.5 1.5641 1.6667 1.33

Female 65.5 40 17 10 6 5 1.6375 1.7

Female 64 41 17 10.5 6 5 1.561 1.619

Female 65 40 16 10 6 4.5 1.625 1.6 1.33

Female 59 37 15.5 9 6 4.5 1.5946 1.7222 1.33

Female 66.5 41 17 10 7 5 1.622 1.7

Female 65 40 16 9.5 7 5 1.625 1.6842

Female 65 41 17 10 6.5 5 1.5854 1.7

Female 63 40 15 9 7 5 1.575 1.6667

Female 67 41 16.5 9.5 7 5 1.6341 1.7368

Male 67 42 17 10 7 6 1.5952 1.7 1.16

Male 71 46 19 11 7 5 1.5435 1.7273

Male 70 43 19 11.5 7 5 1.6279 1.6522

Male 72 46 18 11 7.5 6 1.5652 1.6364 1

Male 66 40 17 10 6 4.5 1.65 1.7 1.33

Male 65 40 17 10 6 5 1.625 1.7

Male 70 44 18 11 7 5 1.5909 1.6364

Male 69 41 17 10 7 5 1.6829 1.7

Male 68 42 18 11 6.5 5 1.619 1.6364

Male 71 43 18.5 11 7 5 1.6512 1.6818

Male 68 42 18 11 7 5.5 1.619 1.6364 1.27

Male 69.5 43 17.5 11 7 5 1.6163 1.5909

Male 70 43 18.5 11 7 5 1.6279 1.6818

Male 72 46 19 11 6.5 4.5 1.5652 1.7273 1.44

Male 71 44 18 11 7 4.5 1.6136 1.6364 1.55

Male 69.5 44 18 11 7 5 1.5795 1.6364

Male 68 42 18 11 7 5 1.619 1.6364

Male 66 41 17 10.5 7 5.5 1.6098 1.619 1.27

Male 71 43 21 13 7 5 1.6512 1.6154

Male 71 44 19 12 7 5 1.6136 1.5833


22/22


Works Cited

Blacker, Steve, Jeanette Polanski, and Marc Schwach. "The Golden Ratio." The Geometry

Center Welcome Page. Web. 11 Mar. 2012.

.

HighFlyingDutchman. "Golden Ratio in Human Body." YouTube. YouTube, 18 Sept. 2008.

Web. 12 Mar. 2012. .

Angiegreek. "The Golden Mean." YouTube. YouTube, 23 Nov. 2007. Web. 12 Mar. 2012.

.

devin capela golden ratio project (phase two) stats 1510 freshman year tc 5-4-12

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