Research & Statistics

 1. Introduction

On our first meeting for our statistics project, we had to decide on which topic to do. After much research and discussion, we finally settled on question 4, regarding Leonardo's work on how the size of one body part is related to that of another body part

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 known as the ‘Vitruvian Man’. The Vitruvian Man is a drawing that is accompanied by notes based on the work of the architect, Vitruvius The drawing and text are sometimes called the Canon of Proportions or, less often, Proportions of Man.

The ‘Vitruvian Man’ has been commonly associated with health, fitness and with the practice of medicine up till today. In some cases, the ‘Vitruvian Man’ is taken as an embodishment of health. In other cases it is used more symbolically, as an image of science, art and proportion enmeshed to embody the practice of medicine.

After much research, we had to decide on which parts of the body we want to compare as there are quite a number of choices for us to choose from. Among them were:

• the length of the outspread arms is equal to the height of a man
• from the hairline to the bottom of the chin is one-tenth of the height of a man
• from below the chin to the top of the head is one-eighth of the height of a man
• from above the chest to the top of the head is one-sixth of the height of a man
• from above the chest to the hairline is one-seventh of the height of a man.
• the maximum width of the shoulders is a quarter of the height of a man.
• from the breasts to the top of the head is a quarter of the height of a man.
• the distance from the elbow to the tip of the hand is a quarter of the height of a man.
• the distance from the elbow to the armpit is one-eighth of the height of a man.
• the length of the hand is one-tenth of the height of a man.
• the root of the penis is at half the height of a man.
• the foot is one-seventh of the height of a man.
• from below the foot to below the knee is a quarter of the height of a man.
• from below the knee to the root of the penis is a quarter of the height of a man.
• the distances from the below the chin to the nose and the eyebrows and the hairline are equal to the ears and to one-third of the face.

In the end, we decided to compare the height and the arm span of a person as many of us found it interesting for we never thought it possible that the height and the arm span of a person could be the same. Therefore our main objective will be to test this theory.

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. Hypothesis

H⁰ (null) hypothesis

1)    There is no relation between a person's height and arm span.

2)    For men and women, the relationship between arm span and height is not the same.

H¹(alternative) hypothesis

1)    This is a relationship between a person's height and arm span.

2)    For men and women, the relationship between arm span and height is the same.

4. Methodology

Variables:

Independent variable: Height (in cm)

Dependent variable: Arm span (in cm)

Conceptualization:

Height:  The distance from the bottom of the feet to the top of the head in a human body standing erect.
Arm span: Physical measurement of the length from one end of an individual's arms (measured at the fingertips) to the other when raised parallel to the ground at shoulder height at a one-hundred eighty degree angle.

Operationalization: 

Measuring tapes will be used to measure both height and arm span.

     

Our subjects were mostly our juniors from Year 1, Social Work course and also our own family members to get a variety of results. Consent was through verbal means and we only carried out the measurements upon consent of the other party.

Data collection:

Upon consent, we first measured the subject’s arms span by having him/her stand against a wall and spreading his/her arms as wide as possible and as straight as possible. We then used a measuring tape to measure the arm span.

After keying in the data in SPSS, we followed by having the subject remove his/her shoes and stand erect against the wall and measuring the subject’s height using the same measuring tape and a book to determine the height.

This method was repeated throughout the whole data collection process which spanned throughout 3 days depending on the availability of the subjects.

All the data was collected and recorded on the spot using SPSS.

5. Choosing an appropriate statistical test

Thus we have decided to use Pearson's R to prove the relationship.

6. Data analysis

6.1 SPSS Data

6.2 Arms span vs Height

P < 0.05 

n=35

P < α, reject the null hypothesis, means there is a association between the length of arm span and height.

Pearson’s R= 0.949 > 0, indicates a positive relationship.

Pearson’s R= 0.949 > 0.8, indicates a very strong relationship.

Result: there is a very strong, significant and positive relationship between a person's arm span and height.

6.3 Arms span vs Height vs Gender

P < α, reject the null hypothesis, means there is a association between the length of arm span and height, regardless of gender

The association for female is r = 0.953, p < 0.0005, n = 18, a = 0.05

The association for male is r = 0.814, p < 0.0005, n = 17, a = 0.05

Result: there is a very strong, positive association between a person's arm span and height for different gender with the association for both male and female.

7. Conclusion

7.1 Results

1)    There is a very strong, significant and positive relationship between a person's arm span and height.

2)    There is a very strong, positive association between a person's arm span and height for different gender with the association for both male and female.

7.2 Factors that might affect results

-       Symmetry of subjects’ arms

-       Inaccurate readings

-       Inconsistency of measuring instruments used

-       Erectness of how the subjects stood

7.3 Reflections

To be very honest, we started off the project with some worries and insecurities as this was something that we had never done before and it is also very different from what we normally do in our social science (social work) course. So we were kind of unsure what to expect from it. To make matters worse, we always thought that research is something very complicated and beyond what we can do.

When we started to collect sample data from people, we actually kept modifying the method of collection from what was discussed previously. Eventually we finally settled down with the most uniform and accurate method. So, we really had to be quick thinkers and react accordingly to the situation.

After completing this project, we got to experience how an actual research is done by applying all the skills and knowledge that we learned during the Statistics and Research Method class. Now, we are more confident to say that doing research is not that complicated anymore.