STATISTICS PROJECT

Topic: Is a person’s BMI related to his height?

Identification of variables
--> height (scale)
--> BMI (scale)

Introduction
Body Mass Index (BMI) is a statistical measure of the weight of a person scaled according to height. The formula to calculate a person’s BMI is by taking the weight in kilograms diving by the square of the person’s height in metres. It is a reliable indicator of body fatness for most people. BMI does not measure body fat directly, but research has shown that BMI correlates to direct measures of body fat. However, because BMI is dependent only upon weight and height, it makes simplistic assumptions about the distribution of muscle and bone mass. Due to its measurement and calculation, it is the most widely used diagnostic tool to identify weight problem within a population (underweight, overweight, obesity).

For a given height, BMI is proportional to weight. For example, if body weight increases by 50%, BMI increases by 50%. For a given body shape and density, the BMI is proportional to height. For example, if all body dimensions increase by 50%, the BMI increases by 50%.However, for a given weight, BMI is inversely proportional to the square of height. This tendency for taller people to have higher BMIs is partially offset by the fact that many taller people rather tend to have narrower frames in proportion to their height.

Now, we would like to test if a person’s BMI is of any relation to his/her height.

Null hypothesis: There is no relation in a person’s BMI to his height.
Hypothesis: There is a relation in a person’s BMI to his height.

Method in going about gathering the data recordings
Data collection was done in the school gym, where the equipment of the weight & height machine is kept. We took the height and weight of our classmates and friends who were having attachment at the gym.



Our targeted group of people was both genders comprising students aged 18-21. All measurements were taken before a meal is taken. We made sure that food is not affecting the weight as it will lead to inaccurate readings.



Measurement for height starts from the ruler of the machine to the base of the machine as seen in the 2nd photo.

We took one reading of height and weight from each subject.




The BMI is calculated using the formula: weight (kg) / (height x height) (cm)

To make sure that they have not eaten for at least 2hrs, we asked if they had eaten, and rejected those who had a meal within the last 2hrs. As for the age, majority of classmates are within the range we are looking for, so it was relatively easy to gather. For the friends in the gym, we had to ask those who knew of their classmates who were between ages18-21 to get the readings.

Raw Data



SPSS Findings




When the variables are measured on the scale, the correlation coefficients measure the strength of the linear association between the BMI of respondents and height of respondents. As r=0.1, which is closer to 0, the graph shows a weak relationship.



From the table above, a Pearson’s correlation coefficient of 0.107 indicates a very weak relationship between the BMI and height of respondents.

However, p= 0.575 (p>0.05), the null hypothesis is acceptable.

Thus, there is no significant association between a person’s BMI and his height.

Regression




Linear regression quantifies the relationship by having an equation predicting a person’s height and BMI index.

Based on the table below, the linear equation is:
BMI = 3.399 * (height) + 14.977

However, it does not work efficiently in our research.

One of our example cases: A person with 1.74m in height has a BMI index of 24.8.
When we use the linear equation to prove it, the outcome BMI is 20.9.

As a conclusion, the linear equation is rejected.


Is this relationship the same for males and females?



1.0=male
2.0=female

As r=0.1, which is closer to 0, the graph shows a weak relationship.




The association for male is r= 0.468, p= 0.125, N= 12.
It shows that there is a very weak relationship and the null hypothesis is accepted.

The association for female is r= 0.123, p=0.626, N= 18.
It shows that the relationship between BMI index and their height is relatively weak. The null hypothesis is accepted as well.

As a conclusion, results have proven that there is no difference between the BMI index and height of a person.


Conclusion
In conclusion, we reject the hypothesis as Body Mass Index is not related to the person’s height. As shown in the graph above, both BMI and height have a weak correlation to each other. Instead, BMI is related to both height and weight as height is strongly related to weight. As mentioned earlier, BMI is the measure of the weight of a person scaled according to height. Therefore, it is inaccurate to say that BMI is related only to height.




Reflections
Having to do this statistic in groups of six, we divided the workload; with some of us taking the data and photos, while the others look up for necessary and relevant documents online on the net. More so, we tabulated the results together using SPSS. Through this, we were able to grasp the knowledge and technique in statistics classes every Friday. Hopefully the skills acquired would be useful in our career life after we graduate!
There were difficulties especially in meeting up due to the different commitments we have, but we have tried to accommodate t each other. This is done so by chatting online. We also send updated information and Microsoft words via email and remind each other to check their inboxes and update themselves with the recent reports.


(*Click on the pictures to see the full picture)