devin capela golden ratio project (phase two) stats 1510 freshman year tc 5-4-12
TRANSCRIPT
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
1/22
Golden Ratio Project Phase Two
Devin Capela
Golden Ratio Project (Phase Two)
Stats 1510
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
2/22
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.
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
3/22
Golden Ratio Project Phase Two 3
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 -
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
4/22
Golden Ratio Project Phase Two 4
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.)
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
5/22
Golden Ratio Project Phase Two 5
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
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
6/22
Golden Ratio Project Phase Two 6
Figure 1.1 (Female Summary Statistics)
Figure 1.2 (Male Summary Statistics)
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
7/22
Golden Ratio Project Phase Two 7
Figure 1.3 (Female Box and Whisker Plot)
Figure 1.4 (Male Box and Whisker Plot)
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
8/22
Golden Ratio Project Phase Two 8
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.
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
9/22
Golden Ratio Project Phase Two 9
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.
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
10/22
Golden Ratio Project Phase Two 10
Figure 1.5 (Normal Plot of Ratio #1)
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
11/22
Golden Ratio Project Phase Two 11
Figure 1.6 (Normal Plot of Ratio #2)
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
12/22
Golden Ratio Project Phase Two 12
Figure 1.7 (Normal Plot of Ratio #3)
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
13/22
Golden Ratio Project Phase Two 13
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
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
14/22
Golden Ratio Project Phase Two 14
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.
.
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
15/22
Golden Ratio Project Phase Two 15
Phase One of this Project
Devin Capela
Golden Ratio Project (Phase One)
Stats 1510
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
16/22
Golden Ratio Project Phase Two 16
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 -
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
17/22
Golden Ratio Project Phase Two 17
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.
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
18/22
Golden Ratio Project Phase Two 18
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.
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
19/22
Golden Ratio Project Phase Two 19
Figure 1.1 (Female Summary Statistics)
Figure 1.2 (Male Summary Statistics)
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
20/22
Golden Ratio Project Phase Two 20
Figure 1.3 (Female Box and Whisker Plot)
Figure 1.4 (Male Box and Whisker Plot)
Appendix (Next Page)
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
21/22
Golden Ratio Project Phase Two 21
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
-
7/31/2019 Devin Capela Golden Ratio Project (Phase Two) Stats 1510 Freshman Year TC 5-4-12
22/22
Golden Ratio Project Phase Two 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.
.