Wednesday, July 7, 2010
Statistics project
On our first meeting for our statistics project, we have to decide on which topic to do. After much discussion, we finally settled with question 4, regarding Leonardo's work on how the size of one body part is related to that of another body part.
Next, we have to decide on which parts of the body do we want to compare with as there are quite a number of choices for us to choose. Suddenly, one of us suggested we can compare the height and the arm span of a person and the other four members agreed to the idea as many of us find it interesting as we never thought that how is it possible the height and the arm span of a person will be the same.
1. Introduction
Our main objective for this research is to find out the size of one body part is related to that of another body part for the purpose of instructing painters on how to paint the human body according to Leonardo’s work. For example, our group is doing on whether the distance from fingertip to fingertip (arm span) should be equal to the distance from head to heel (height).
Leonardo da Vinci (1452-1519) was a scientist and an artist, one of the greatest painters of the Italian Renaissance. In 1492 he drew the picture of a man standing inside a circle and a square.
This is known as the ‘Vitruvian Man’. The ‘Vitruvian Man’ is commonly associated with health/fitness, and with the practice of medicine till today. In some cases, the ‘Vitruvian Man’ is himself taken as an embodishment of health. In other cases he seems to be used more symbolically, as an image of science, art and proportion enmeshed to embody the practice of medicine. In some cases, the ‘Vitruvian Man’ may be taken, more or less, at face value as an image of a balanced, healthy man.
Leonardo believed that arm span was equal to height in a perfectly proportioned body. Whenever there are assumptions, there would be doubts. Hence, here we are trying to prove whether the Vitruvius’ theory is true or not. In order to prove whether this theory is reliable or not, we are testing the relationship between the arm span and the height of a person.
On our first meeting for our statistics project, we have to decide on which topic to do. After much discussion, we finally settled with question 4, regarding Leonardo's work on how the size of one body part is related to that of another body part.
Next, we have to decide on which parts of the body do we want to compare with as there are quite a number of choices for us to choose. Suddenly, one of us suggested we can compare the height and the arm span of a person and the other four members agreed to the idea as many of us find it interesting as we never thought that how is it possible the height and the arm span of a person will be the same.
1. Introduction
Our main objective for this research is to find out the size of one body part is related to that of another body part for the purpose of instructing painters on how to paint the human body according to Leonardo’s work. For example, our group is doing on whether the distance from fingertip to fingertip (arm span) should be equal to the distance from head to heel (height).
This is known as the ‘Vitruvian Man’. The ‘Vitruvian Man’ is commonly associated with health/fitness, and with the practice of medicine till today. In some cases, the ‘Vitruvian Man’ is himself taken as an embodishment of health. In other cases he seems to be used more symbolically, as an image of science, art and proportion enmeshed to embody the practice of medicine. In some cases, the ‘Vitruvian Man’ may be taken, more or less, at face value as an image of a balanced, healthy man.
Leonardo believed that arm span was equal to height in a perfectly proportioned body. Whenever there are assumptions, there would be doubts. Hence, here we are trying to prove whether the Vitruvius’ theory is true or not. In order to prove whether this theory is reliable or not, we are testing the relationship between the arm span and the height of a person.
"Somewhere, something incredible is waiting to be known"10:00 AM.
2. Research Questions
1) Is there an association between a person’s arm span and his height?
2) Is the relationship between arm span and height the same for men and women (gender)?
3) Is the relationship between arm span and height the same for the different races (Chinese, Malay and Indian)?
3. Testable Hypothesis
3.1. Hypothesis:
1) There is a relationship between a person’s arm span and the height.
2) The relationship between arm span and height is the same for men and women.
3) The relationship between arm span and height is the same for the different races.
3.2. Null Hypothesis:
1) There is no relationship between a person’s arm span and the height.
2) The relationship between arm span and height is not the same for men and women.
3) The relationship between arm span and height is not the same for the different races.
1) Is there an association between a person’s arm span and his height?
2) Is the relationship between arm span and height the same for men and women (gender)?
3) Is the relationship between arm span and height the same for the different races (Chinese, Malay and Indian)?
3. Testable Hypothesis
3.1. Hypothesis:
1) There is a relationship between a person’s arm span and the height.
2) The relationship between arm span and height is the same for men and women.
3) The relationship between arm span and height is the same for the different races.
3.2. Null Hypothesis:
1) There is no relationship between a person’s arm span and the height.
2) The relationship between arm span and height is not the same for men and women.
3) The relationship between arm span and height is not the same for the different races.
"Somewhere, something incredible is waiting to be known"9:59 AM.
4. Literature Review
Leonardo da Vinci’s drawing Vitruvian Man (1487) shows how the proportions of the human body fit perfectly into a circle or a square, which is known as an illustration of Vitruvius’ theory.
Leonardo Da Vinci (1452-1519) said it best: "The outstretched arms and legs of a man form a square and a circle: the square symbolizes the solid physical world and the circle the spiritual and eternal. Man bridges the gap between these two worlds."
Also, according to Vitruvius’s theory the distance from fingertip to fingertip (arm span) should be equal to the distance from head to heel (height).
Leonardo da Vinci’s drawing Vitruvian Man (1487) shows how the proportions of the human body fit perfectly into a circle or a square, which is known as an illustration of Vitruvius’ theory.
Leonardo Da Vinci (1452-1519) said it best: "The outstretched arms and legs of a man form a square and a circle: the square symbolizes the solid physical world and the circle the spiritual and eternal. Man bridges the gap between these two worlds."-Leonardo Da Vinci (1487) “The Magical Proportions of Man”.
Vitruvius, the architect, says in his work on architecture that “the measurements of the human body are distributed by Nature as follows that is that 4 fingers make 1 palm, and 4 palms make 1 foot, 6 palms make 1 cubit; 4 cubits make a man's height. And 4 cubits make one pace and 24 palms make a man; and these measures he used in his buildings. If you open your legs so much as to decrease your height 1/14 and spread and raise your arms till your middle fingers touch the level of the top of your head you must know that the centre of the outspread limbs will be in the navel and the space between the legs will be an equilateral triangle.”
Also, according to Vitruvius’s theory the distance from fingertip to fingertip (arm span) should be equal to the distance from head to heel (height).
"Somewhere, something incredible is waiting to be known"8:53 AM.
5. Methodology
5.1. Pilot Testing
Before doing the test with the subjects, we decided to conduct a pilot test on our group members. This is to ensure that the process can run smoothly and further recognize the need for any improvement.
For our pilot test, we booked a discussion room in the library and had our equipments prepared.
Initially, we measured our height and arm span without leaning against the wall. We found that it was quite difficult in achieving balance and the data we took were not accurate. After a discussion, one of our members suggests that we could divide in measuring our arm span into 3 parts:
1) From the tip of the left middle finger to the tip of the left shoulder,
2) The tip of the left shoulder to the tip of the right shoulder,
3) From the tip of the right shoulder to the tip of the right middle finger.
After measuring the arm span in 3 parts, we sum up all the 3 data to have our complete arm span.
Even though it was easier to measure, the data were inaccurate as our hands tend to be unstable (we keep trembling as the strain is “unbearable’), due to this, there would always be an error.
Finally, we had a better idea amongst us. We moved the chairs away and tried to get some space. We measured our height and arm span by leaning against the wall. It was not only easier to measure, but also minimizes the error that could easily be made.
5.2. Data Collection
The focus of this study was primarily on Da Vinci’s Vitruvius’s man.
We started off by gathering in the library and briefly explain the planned procedure to the group members. There were total of five members, two members will be taking the measurements, another two will be in-charge of the informed consent and the last member will be the photographer. When all the group members have a full understanding about their assigned duty, the data collection starts.
The data collection was done using accidental sampling. We chose accidental sampling as it is more convenient and easier to obtain our data. However, accidental sampling is not representative of any group of people. The subjects of this study were chosen randomly in the school library.
Firstly, we would seek the consent of each subject whether they are willing to participate in our study. We informed the subject the purpose and procedure of our study and ensure their confidentiality would be assured. If they agree to participate in our study, they are required to sign a consent form which consists of their measurements to be taken for this study only and they did it out of free will and their rights would be protected through the informed consent.
(shown in Diagram 1: Section A)
5.1. Pilot Testing
Before doing the test with the subjects, we decided to conduct a pilot test on our group members. This is to ensure that the process can run smoothly and further recognize the need for any improvement.
For our pilot test, we booked a discussion room in the library and had our equipments prepared.
1) From the tip of the left middle finger to the tip of the left shoulder,
2) The tip of the left shoulder to the tip of the right shoulder,
3) From the tip of the right shoulder to the tip of the right middle finger.
After measuring the arm span in 3 parts, we sum up all the 3 data to have our complete arm span.
Even though it was easier to measure, the data were inaccurate as our hands tend to be unstable (we keep trembling as the strain is “unbearable’), due to this, there would always be an error.
Finally, we had a better idea amongst us. We moved the chairs away and tried to get some space. We measured our height and arm span by leaning against the wall. It was not only easier to measure, but also minimizes the error that could easily be made.
The focus of this study was primarily on Da Vinci’s Vitruvius’s man.
We started off by gathering in the library and briefly explain the planned procedure to the group members. There were total of five members, two members will be taking the measurements, another two will be in-charge of the informed consent and the last member will be the photographer. When all the group members have a full understanding about their assigned duty, the data collection starts.
The data collection was done using accidental sampling. We chose accidental sampling as it is more convenient and easier to obtain our data. However, accidental sampling is not representative of any group of people. The subjects of this study were chosen randomly in the school library.
Firstly, we would seek the consent of each subject whether they are willing to participate in our study. We informed the subject the purpose and procedure of our study and ensure their confidentiality would be assured. If they agree to participate in our study, they are required to sign a consent form which consists of their measurements to be taken for this study only and they did it out of free will and their rights would be protected through the informed consent.
(shown in Diagram 1: Section A)
Diagram 1: Section A
We took the measurements once for each subject.
After the subject signed the consent form, we would start measuring the subjects’ arm span and height according to the 6 steps below:
1. Measure the subject’s arm span by standing against a flat surface and spreading his/her arms out as far as possible.
3. Tell the subject to remove their shoes and stand against a flat surface before measuring the subject’s height.
4. Measure the distance from the top of the subject’s head to the floor.
6. Record the data on the second page of the consent form. (shown in Diagram 2: Section B)
Diagram 2: Section B
"Somewhere, something incredible is waiting to be known"7:19 AM.
6. Data Analysis
6.1. SPSS Data
6.2. Arm span vs. Height
p < 0.0005
n=30
a=0.05
Pearson’s R= 0.996 > 0, indicates a positive association.
Pearson’s R= 0.996 > 0.8, indicates a very strong association
Result: there is a positive, very strong association between a person's arm span and height.
6.3 Arm span vs Height vs Gender
The association for male is r = 0.986, p < 0.0005, n = 14, a = 0.05
The association for female is r = 0.960, p < 0.0005, n = 16, a = 0.05
p < a, reject the null hypothesis
Pearson’s R > 0, indicates a positive association.
Pearson’s R > 0.8, indicates a very strong association
Result: there is a positive, very strong association between a person's arm span and height for different gender with the association for male and female.
6.4 Arm span vs Height vs Race
The association for Chinese is r = 1.000, p < 0.0005, n = 13, a = 0.05
The association for Malay is r = 0.991, p < 0.0005, n = 9, a = 0.05
The association for Indian is r = 0.993, p < 0.0005, n = 8, a = 0.05
p < a, reject the null hypothesis
Pearson’s R > 0, indicates a positive association.
Pearson’s R > 0.8, indicates a very strong association
Result: there is a positive, very strong association between a person's arm span and height for different races with the association for Chinese, Malay and Indian
6.1. SPSS Data
6.2. Arm span vs. Height
n=30
a=0.05
Pearson’s R= 0.996 > 0, indicates a positive association.
Pearson’s R= 0.996 > 0.8, indicates a very strong association
Result: there is a positive, very strong association between a person's arm span and height.
6.3 Arm span vs Height vs Gender
The association for male is r = 0.986, p < 0.0005, n = 14, a = 0.05
The association for female is r = 0.960, p < 0.0005, n = 16, a = 0.05
p < a, reject the null hypothesis
Pearson’s R > 0, indicates a positive association.
Pearson’s R > 0.8, indicates a very strong association
Result: there is a positive, very strong association between a person's arm span and height for different gender with the association for male and female.
6.4 Arm span vs Height vs Race
The association for Malay is r = 0.991, p < 0.0005, n = 9, a = 0.05
The association for Indian is r = 0.993, p < 0.0005, n = 8, a = 0.05
p < a, reject the null hypothesis
Pearson’s R > 0, indicates a positive association.
Pearson’s R > 0.8, indicates a very strong association
Result: there is a positive, very strong association between a person's arm span and height for different races with the association for Chinese, Malay and Indian
"Somewhere, something incredible is waiting to be known"6:48 AM.
7. Conclusion
7.1. Implication of findings
- There is a positive and very strong association between a person’s arm span and height.
- There is a positive and very strong association between a person’s arm span and height for different gender with the association for male and female.
- There is a positive and very strong association between a person’s arm span and height for different races with the association for Chinese, Malay and Indian.
Thus, these proves our hypothesis.
7.2. Influence of findings
1. Unreliable readings – therefore cannot represent the true findings of the study
2. Inconsistency in arm span
- Did the subject spread his/her arms out as far as possible?
- Did the subject have long fingernails?
- Did the subject balance both arms symmetrically?
3. Inconsistency in height
- Did the subject wear shoes?
- Did the subject stand straight and lean against the flat wall?
- Were the measurements taken accurately from the top of the head to the bottom of the foot?
7.3. Discussion
The sample size we have collected is too small to represent the significance of the relationship between the height and the arm span. Even though our data shows a positive and strong relationship between the height and arm span, but there are still a few number of people proves otherwise. Thus, our sample size is not representative enough for the target population for the study.
7.4. Reflection
In this project, we gain experiences on how to do a research study. There are a lot of aspects required in a research study. Certain aspects required us to do things all over again till we get the right results and we also had to test and retest to check the consistency of the result.
We learned that in order to start with a research, a pilot test would be useful for us as it will give us a brief idea of how our study is going to be. As we start measuring our group members, we realized the arm span and height of each member differs a lot. We decided to use a different method to measure our group members and fortunately, we obtain a more accurate data to support our hypothesis.
Through this research study, we learn how to apply the statistical studies which we had learned and the skills to analyze and interpret finding. Even though there are a few setbacks met, but we managed to learn from our mistakes. Moreover, this project requires us to do it on a blog instead of the usual PowerPoint slides, as some of us never create a blog before. Despite we met with obstacles, but we still find it challenging and managed to overcome it.
"Somewhere, something incredible is waiting to be known"5:53 AM.
