Correlation

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Correlation
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In this lesson you will cover

• How to measure and interpret correlation
• About the effects of scaling data on correlation

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When two sets of random variables (bivariate
data) are displayed on a scatter graph we are
used to describing the correlation but how do you
measure it?
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Two sets of random variables (bivariate data) we
can describe correlation but how do you measure
it?
x - - y - - x
x - y - x
x - - y - - - x -
x - y - - x -
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• Covariance how do you interpret it?
• When the covariance is positive it suggests
  positive correlation
• When covariance is negative it suggests negative
  correlation
• When the covariance is close to zero it suggests
  no correlation.

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• Covariance can you see any potential problems
  with this method alone?
• When the covariance is positive it suggest
  positive correlation
• When covariance is negative it suggest negative
  correlation
• When the covariance is close to zero it suggests
  no correlation.
• You guessed it
• (you dont know the range)

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Pearson Moment Correlation Coefficient

• Is to standardise the covariance so that it can
  interpreted easily. It converts the covariance to
  a number between -1 to 1, where
• -1 is a perfect negative correlation
• 1 is a perfect positive correlation
• 0 is no correlation

Karl Pearson 1857 - 1936
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Pearson Moment Correlation Coefficient can be
simplified to
This is the covariance
This is the standard deviation of y
This is the standard deviation of x
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The effect of scaling

• If you work out the correlation coefficient for
  sales of ice-cream temperature (t) in
  Fahrenheit. Would you expect the correlation to
  change if you worked on the same data but in
  Celsius?
• No scaling has no effect on correlation.

10
Be aware of correlation claims

• Some things may look like they are connected but
  they are not
• General knowledge and height
• Children in a school from year 7 to year 13 are
  asked general knowledge questions. The
  correlation is worked out using height and their
  score. In your opinion does height have any
  effect on their score? If not can you suggest
  what is the explanatory factor that is connected
  to both?
• Outliners
• As all data items are used outliners will effect
  the correlation coefficient. When outliners are
  obvious it is worth ignoring them altogether.
• Non-linear relationships.
• Pearson's p.m.c.c. is only suitable for linear
  relationships