Linear Associations

Question 1

describe R: (Pearson’s) correlation coefficient

Answer 1

• indicates the strength and direction of a linear association
• ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation)
• based on creating a “line of best fit” that minimizes the total squared distance from the line
  
  • thus the direction of the distance doesn’t matter, but extreme points affect the line more

Question 2

describe R² : the square of the correlation

Answer 2

coefficient of determination

• answers the question, “how much of the variance in the outcome variable is explained by variance in the predictor variable?”
• R² ranges from 0 if there is no correlation, to 1 if the correlation is perfect (either positive or negative)

Question 3

describe the general rule of R² and strength of association

Answer 3

Question 4

Pearson correlation is based on the _____; it makes certain assumptions. If the assumptions are not met, the model will still run but the conclusions may be invalid.

Answer 4

Pearson correlation is based on the normal distribution; it makes certain assumptions. If the assumptions are not met, the model will still run but the conclusions may be invalid.

Question 5

name the assumptions of the Pearson correlation

Answer 5

• Normality of variables
  
  • data must be interval: non-interval data cannot be normal
  • data must be centrally and symmetrically distributed with a single mode and neither too few or too many extreme values
• linearity of association
  
  • associations must be monotome (not changing direction)
  • the line of best fit through the scatterplot should be a nearly straight line and not a curve
• oval scatterplot
  
  • the scatterplot should form an oval, not a triangle

Question 6

describe rank correlations

Answer 6

• Pearson correlation minimizes the total squared distance from the line
• in contrast, Spearman’s rank ignore the size of differences:
  
  • it doesn’t matter if one subject is a lot taller and heavier than another, or only a little bit

Question 7

describe advantages and disadvantages for Pearson vs. Spearman

Answer 7

• Spearman’s rank is less statistically powerful than Pearson correlation
• statistical models (e.g. regression) use Pearson rather than Spearman
• S for Spearman for Safe
• P for Pearson for Powerful

Question 8

summarize the difference between Pearson’s correlation and Spearman’s rank

Answer 8