Linear Associations Flashcards

1
Q

describe R: (Pearson’s) correlation coefficient

A
  • 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
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2
Q

describe R2 : the square of the correlation

A

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)
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3
Q

describe the general rule of R2 and strength of association

A
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4
Q

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.

A

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.

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5
Q

name the assumptions of the Pearson correlation

A
  • 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
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6
Q

describe rank correlations

A
  • 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
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7
Q

describe advantages and disadvantages for Pearson vs. Spearman

A
  • 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
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8
Q

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

A
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