Is the length of your arm related to your height?

Introduction
We have chosen to do our statistic topic on "Is a person's arm span related to his/her height?"
Objectives
Upon proceeding to this project we must:

• Specify research goals
• Formulate research question hypothesis
• Identify the variables
• Use appropriate method to collect data
• Analyze the data
• Test hypothesis
• Propose an appropriate statistical technique to test Ho -- Pearson's R
• Draw a scatter plot to check for linearity and homogenous  variance 
• Compute Pearson's correlation coefficient
• Compute Regression Equation
• Draw conclusion

Specify research goals
Our research question: Is there a relationship between a person's arm span and his/her height?


Formulate research question hypotheses
Null hypothesis: 
There is no relationship between a person's arm span (cm) and his/her height (cm).

Research hypothesis: 
There is a relationship between a person's arm span (cm) and his/her height (cm).


Identify the variables

Measure and record

Measure method

Measuring Standing Height

Human height is the distance from the bottom of the feet to the top of the head in a human body standing erect. 

According to the Center for Disease Control, height is measured by: 

• Remove bulky clothing, including thick-soled shoes and hair ornaments.
• Stand against a wall facing outwards and look straight ahead. 
• Make sure the head, shoulders, rear end and heels should touch the wall. 
• Gently press a ruler or any flat stick down on the top of the head.
• Mark the spot where the ruler touches the wall with a pencil.
• Ask the subject step away from the wall.
• Use a tape measure to record the distance from the floor to the mark, without rounding up fractions of centimeters.

Measuring Arm Span

Arm span is the length from one end of an individual's arm (measured at the middle fingertips) to the other when raised parallel to the ground at shoulder height at a one-hundred eighty degree angle.

Arm span is measured by:

• Stand against a wall facing outwards and look straight ahead. 
• Make sure the head, shoulders, rear end and heels should touch the wall. 
• Place the stretching arm 90 degrees perpendicular to the body.
• Mark spots where the middle fingertips touches the wall with a pencil.
• Ask the subject step away from the wall.
• Using a measuring tape measure the distance from the two spots, without rounding up fractions of centimeters.
• Ensure the measuring tape is straight and read the reading at eye level. 
  

Repeat this procedure three times and calculate the mean score.

Location & subject
Data collection was done on Friday, 19/01/11, beside NYP's Mc Donald open area.
our targeted subject comprise of 60 NYP students whereas 24 are male and 36 are female.

Our raw data:

• Sex: 1-Male, 2-Female
• H1: Height reading at the first time
• H2: Height reading at the second time
• H3: Height reading at the thrid time
• meanH: mean height
• AS1: Arm span reading at the first time
• AS2: Arm span reading at the second time
• AS3: Arm span reading at the thrid time
• meanAS: mean arm span

Analyze the data
Hypotheses testing
Propose an appropriate statistical technique to test Hypotheses:

• → Pearson's product moment correlation coefficient.

• However, Pearson's product monent correlation coeffcient is a symmetric measure of association for interval level variables. The variables must comply with the assumptions:
• Assumption 1: all observations must be independent of each other
• Assumption 2: the dependent variable should be normally distributed at each value of the independent variable
• Assumption 3: the dependent variable should have the same variability at each value of the independent variable
• Assumption 4: the relationship between the dependent and independent variables should be linear
• So we will first examine the scatter plot to ascertain if the arm span and height have the same variability and if their relationship is linear.

Draw a scatter plot

Figure1: Scatter diagram and regression line showing relationship between arm span and height

Result: 
The scatter appears to follow a general positive linear trend. There is no violation of the linearity assumption. The variables comply with the assumptions, so we can use Pearson's R to test the hypotheses.

Computer Pearson's correlation coefficient

Result: 

There is a positive, very strong relationship between a person's arm span and the person's height. (Pearson's R=0.927, p<0.0005, N=60)

Is this relationship the same for male and female?
Draw scatter plot by gender

Figure2: Scatter diagram and regression line showing relationship between arm span and height in both male anf female

Result: 
The scatter appears to follow a general positive linear trend for both male and female. There is no violation of the linearity assumption. The variables comply with the assumptions, so we can use Pearson's R to test the hypotheses.


Computer Pearson's correlation coefficient

Result:
There is a positive, very strong relationship between a person's arm span and the height in male. (r=0.898, p<0.0005, N=24) 
In females, there is a positive, strong relationship between the two variables. (r=0.725, p<0.0005, N=36)


Compute regression equation
After knowing that there is a relationship between a person's arm span and his/her height exists, we can use linear regression quantifies the relationship.

Whole subject

Based on the table above, the linear equation is:
Arm span=1.123*(height)-21.232
In one of our example case: A person's height: 170cm
                                             Subsidize into the equation: arm span=1.123*(170)-21.232=169.678cm
                                             Actual arm span: 170cm

Male

Based on the table above, the linear equation for male is:
Arm span=1.014*(height)-1.456

Female

Based on the table above, the linear equation for female is:
Arm span=0.803*(height)+28.929

 Conclusion
There is a positive, very strong relationship between a person's arm span and his/her height.

The linear equation is:

Arm span=1.123*(height)-21.232


Reflections
Individual reflections

Group reflection

Statistics refer to the methods and rules used for organizing, summarizing and interpreting information. We had no idea on how to start our project at first. Thankfully, we had our good friends who have already done this module helped us though the jungles. We would like to thank Ms Chia for giving us support and assurance on our work.

In our project we have proven that there is a strong relationship between a person's arm span and their height. The linear equation is: Arm span=1.123*(height)-21.232

By doing this research, it has managed to change our perception of statistics. We have never thought statistic could be used to interpret such common part in everyday life.

Last but not least, we would like to especially thank our models to give us their warmest support, without them we could never have done our job!