- Height of respondents (cm) – Scale Data
- Weight of respondents (kg) – Scale Data
- BMI of respondents – calculated manually using the formula
BMI and Height
Null Hypothesis
There is no relationship between a person’s BMI and height
Alternative Hypothesis
There is a relationship between a person's BMI and height
Dependent Variable
Respondent’s BMI
Independent Variable
Respondent’s height
Appropriate statistical technique
The proposed test is the Pearson’s correlation coefficient. We chose this method as it displays a measure of association for interval level variables. Pearson’s correlation coefficient range from -1.0 to +1.0.
However, we have to make certain assumptions before proceeding with the test:
- All observations must be independent of each other
- The dependent variable should be normally distributed at each value of the independent variable
- The dependent variable should have the same variability at each of the independent variable
- The relationship between the dependent and the independent variable should be linear
Raw Data
- Each line of data refers to an individual respondent
- The data was entered into a SPSS data file
The scatter appears to follow a general positive linear trend. There is no violation of the linearity assumption. We will then proceed to do the Pearson’s R to obtain the correlation coefficient which will indicate the strength of the relationship between BMI and height.
From the above table, it shows that (r=0.298, p=0.092, N=33). Firstly, since p > 0.05, we do not reject the null hypotheses. There is not enough significant evidence to prove otherwise. The Pearson’s correlation coefficient of 0.298 indicates a weak relationship between BMI and height.
Thus, we concluded that there is no relationship between a person’s BMI and his/her height.
Knowing that somehow there is a linear, but weak relationship between a person’s BMI and height, we decided to plot a linear regression line.
Linear Regression Line
BMI=0.133 (height) -1.458
We have already seen how a person’s BMI is not related to his/ her height. Hence, we would like to find out if a person’s BMI is related to a person’s weight.
BMI and Weight
Null Hypothesis
There is no relationship between a person’s BMI and weight
Alternative Hypothesis
There is a relationship between a person's BMI and weight
Dependent Variable
Respondent’s BMI
Independent Variable
Respondent’s weight
Appropriate statistical technique
The proposed test is the Pearson’s correlation coefficient. We chose this method as it displays a measure of association for interval level variables. Pearson’s correlation coefficient range from -1.0 to +1.0.
However, we have to make certain assumptions before proceeding with the test:
- All observations must be independent of each other
- The dependent variable should be normally distributed at each value of the independent variable
- The dependent variable should have the same variability at each of the independent variable
- The relationship between the dependent and the independent variable should be linear
The scatter appears to follow a general positive linear trend. There is no violation of the linearity assumption. We will then proceed to do the Pearson’s R to obtain the correlation coefficient which will indicate the strength of the relationship between BMI and weight.
From the above table, it shows that (r=0.918, p=0.000, N=33). Firstly, since p < 0.05, we reject the null hypothesis. There is significant evidence to prove otherwise. The Pearson’s correlation coefficient of 0.918 indicates a very strong positive relationship between BMI and weight.
Thus, we concluded that there is a relationship between a person’s BMI and his/her weight.
Knowing that somehow there is a linear strong relationship between a person’s BMI and weight, we decided to plot a linear regression line.
Linear Regression Line
BMI= 0.245 (weight) + 6.388
In short, an individual's BMI is related to his/her weight.
