Correlation and its Applications 2282021 HK 396 Dr

Correlation and its Applications 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 1

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 weigh it. • This wouldn’t fly with the Ethics Board. • How else could we determine % body fat? 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 2

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. 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 3

Initial Study • Both BMI and %body fat were directly measured from the cadavers of male gun shot victims in NYC from 1993 -2006. • 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. 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 4

Scatter plot: Body fat % vs. BMI Best fit line 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 5

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. 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 6

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. 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 7

Positive Correlation Best fit line 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 8

Negative Correlation Best fit line 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 9

Zero Correlation Best fit line 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 10

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 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 11

Excel Spreadsheet • At this point in the lecture I opened the spreadsheet Correlation. xls to show the calculation. 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 12

Evaluating the size of r • The following are general guidelines for absolute values of r. • 0. 5 to 0. 7 - Low • 0. 7 to 0. 8 - Moderate • 0. 9 to 1. 0 - High 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 13

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? 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 14

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. 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 15

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. 1) Calculate a t-stat 2) Determine the p-value for that t-stat 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 16

The t-statistic equation for r (Warner, 2008) • r = Pearson’s correlation coefficient • N = number of pairs of scores 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 17

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. 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 18

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. 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 19

Applications of Correlation 2/28/2021 HK 396 - Dr. Sasho Mac. Kenzie 20