LSP 121

1
LSP 121

• Introduction to Correlation

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Correlation

• Correlation when a relationship exists between
  two sets of data
• The news is filled with examples of correlation
• If you eat so many helpings of tomatoes
• One alcoholic beverage a day
• Driving faster than the speed limit
• Women who smoke during pregnancy
• If you eat only fast food for 30 days
• If your parents did not have offspring, then you
  wont either (huh?)

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How Do You Calculate Correlation in Excel?

• Make an XY scatterplot of the data, putting one
  variable on the x-axis and one variable on the
  y-axis.
• Insert a linear trendline on the graph and
  include the R2 value
• Interpret the results

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Interpreting the Results

• The higher the R2 value, the better
• If you only have a few data points, then you need
  a higher R2 value in order to conclude there is a
  correlation
• Crude estimate R2 gt 0.5, most people say there
  is a correlation R2 lt 0.3, the correlation is
  essentially non-existent
• R2 between 0.3 and 0.5?? Gray area!

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Examples

• Look at
• CigarettesBirthweight.xls
• SpeedLimits.xls
• HeightWeight.xls
• Grades.xls
• WineConsumption.xls
• BreastCancerTemperature.xls

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How Do We Calculate Correlation in SPSS/PASW?

• In SPSS, click on Analyze -gt Correlate -gt
  Bivariate
• Select the two columns of data you want to
  analyze (move them from the left box to the right
  box)
• You can actually pick more than two columns, but
  well keep it simple for now

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How Do We Calculate Correlation in SPSS/PASW?

• Make sure the checkbox for Pearson Correlation
  Coefficients is checked
• Click OK to run the correlation
• You should get an output window something like
  the following slide

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The correlation between height and weight is 0.861
The Pearson Correlation value is not the same as
Excels R-squared value it can be positive or
negative
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Positive and Negative Correlation

• Positive correlation as the values of one
  variable increase, the values of a second
  variable increase (values from 0 to 1.0)
• Negative correlation as the values of one
  variable increase, the values of a second
  variable decrease (values from 0 to -1.0)
• Note The SPSS R value will be greater than
  Excels R2 value! R.5 equivalent to R2.25

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Positive and Negative Correlation

• There is a negative correlation between TV
  viewing and class gradesstudents who spend more
  time watching TV tend to have lower grades (or,
  students with higher grades tend to spend less
  time watching TV).

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Positive and Negative Correlation
Positive correlation
Negative correlation
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Positive and Negative Correlation

• When looking for correlation, positive
  correlation is not necessarily greater than
  negative correlation
• Which correlation is the greatest?
• -.34 .72 -.81 .40 -.12

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What Can We Conclude?

• If two variables are correlated, then we can
  predict one based on the other
• But correlation does NOT imply cause!
• It might be the case that having more education
  causes a person to earn a higher income. It might
  be the case that having higher income allows a
  person to go to school more. There could also be
  a third variable. Or a fourth. Or a fifth

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What Can We Conclude?

• Causality one variable, say A, actually causes
  the change in B. In the absence of any other
  evidence, data from observational studies simply
  cannot be used to establish causation.

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What Can We Conclude?

• Common underlying cause or causes most
  important one A is correlated to B, but there
  is a third factor C (the common underlying cause)
  that causes the changes in both A and B.
• Example as ice cream sales go up, so do crime
  rates.

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What Can We Conclude?

• Sheer coincidence the two variables have
  nothing in common, but they create a strong R or
  R2 value
• Both variables are changing over time divorce
  rates are going up and so are drug-offenses. Is
  an increase in divorce causing more people to use
  drugs (and get caught)?