1. Correlation and its Applications
9/21/2018
HK Dr. Sasho MacKenzie

2. You need to determine %Fat
What’s the most accurate way to determine % body fat?
Sacrifice the individual, separate the fat from the rest of the system and weight it.
This wouldn’t fly with the Ethics Board.
How else could we determine % body fat?
9/21/2018
HK Dr. Sasho MacKenzie

3. Indirect Measurement
BMI is an indirect measurement that could estimate % body fat.
We could do an a initial study that determines the relationship between BMI and %fat.
In all future studies, we could measure BMI (no sacrifice necessary), and apply the relationship found in the initial study.
9/21/2018
HK Dr. Sasho MacKenzie

4. Initial Study
Both BMI and %body fat were directly measured from the cadavers of male gun shot victims in NYC from
See Correlation.xls for data.
A statistical technique called correlation was applied to determine the association between BMI and % body fat.
A closely related method, linear regression, was used to determine a linear mathematical relationship between BMI and %body fat.
9/21/2018
HK Dr. Sasho MacKenzie

5. Scatter plot: Body fat % vs. BMI
Best fit line
9/21/2018
HK Dr. Sasho MacKenzie

6. Visual Assessment
From the scatter plot we can see that the two variables are related.
With the use of correlation and regression, we can quantify the relationship.
9/21/2018
HK Dr. Sasho MacKenzie

7. Correlation Coefficient
The coefficient ranges from -1 to 1
A correlation of 1 means a perfect relationship.
Take-off velocity and jump height.
A correlation of -1 also means a perfect relationship.
100 m sprint speed and 100 m race time.
A correlation of 0 means no relationship.
9/21/2018
HK Dr. Sasho MacKenzie

8. Positive Correlation Best fit line 9/21/2018
HK Dr. Sasho MacKenzie

9. Negative Correlation Best fit line 9/21/2018
HK Dr. Sasho MacKenzie

10. Zero Correlation
Best fit line
9/21/2018
HK Dr. Sasho MacKenzie

11. The Equation zx = z-score of variable X zy = z-score of variable Y
N = number of pairs of scores
This is the Pearson’s Correlation Coefficient
9/21/2018
HK Dr. Sasho MacKenzie

12. Excel Spreadsheet
At this point in the lecture I opened the spreadsheet Correlation.xls to show the calculation.
9/21/2018
HK Dr. Sasho MacKenzie

13. Evaluating the size of r
The following are general guidelines for absolute values of r.
0.5 to Low
0.7 to Moderate
0.9 to High
9/21/2018
HK Dr. Sasho MacKenzie

14. Significance of r
The size of r is only part of performing a calculation of correlation.
The next step is calculating its level of significance.
Determines if r is reliably different from zero. Did the r value result from sheer chance?
9/21/2018
HK Dr. Sasho MacKenzie

15. Size ≠ Significance
The size of the r value does not completely determine the significance.
The number of scores (N) in the data set also has a very strong influence on the level of significance.
The significance tells us the probability that we would find the same level of association due to chance alone.
9/21/2018
HK Dr. Sasho MacKenzie

16. Calculating Significance of r
We will use a computer program such as Excel or SPSS to calculate significance.
There are 2 steps required in Excel.
Calculate a t-stat
Determine the p-value for that t-stat
9/21/2018
HK Dr. Sasho MacKenzie

17. The t-statistic equation for r
(Warner, 2008)
r = Pearson’s correlation coefficient
N = number of pairs of scores
At this point all the equations may seem overwhelming. Don’t panic clarity will arrive.
9/21/2018
HK Dr. Sasho MacKenzie

18. P-value
To determine the p-value for a t-statistic in Excel, we use the function TDIST().
It requires the t-statistic and the degrees of freedom (N-2) as input.
The p-value quantifies the level of significance of r.
For example, a p-value of .01 means the calculated r value (or a greater value) would occur, by chance alone, only 1 time out of 100.
9/21/2018
HK Dr. Sasho MacKenzie

19. Correlation ≠ Cause and Effect
Correlation does not reveal cause and effect.
For example, BMI is related to, and can predict % body fat, but an increase in BMI does not mean an increase in body fat.
BMI could increase due to increases in muscle mass.
9/21/2018
HK Dr. Sasho MacKenzie

20. Applications of Correlation
9/21/2018
HK Dr. Sasho MacKenzie