LSP%20121

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LSP 121

• Introduction to Correlation

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Correlation

• 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
• Often, we can quantify correlation

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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.
• Select the two columns you wish to graph
• Choose Insert ? Scatter
• Insert a linear trendline on the graph and
  include the R2 value
• Click one of the data points on the chart
• Right-click, choose Add Trendline,
• Check boxes/buttons for Linear, Display
  Equation, Display R2
• Interpret the results
• Try it with CigarettesBirthweight.xls

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Smokes/day and Birth Weight
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Interpreting the Results

• The higher the R2 value, the greater the
  likelihood that there is correlation
• Crude estimate R2 gt 0.5
• Most people say there is a correlation
• R2 lt 0.3
• Most say correlation is essentially non-existent
• R2 between 0.3 and 0.5?
• Gray area further analysis is needed
• If you only have a few data points, then you need
  a higher R2 value in order to make a decision
  whether there is or is not a correlation

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Examples Are they correlated?

• Look at
• CigarettesBirthweight.xls
• SpeedLimits.xls (under Older Data)
• HeightWeight.xls
• Grades.xls (under Older Data)
• WineConsumption.xls (under Older Data)
• 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)

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Positive v.s. 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).
• There is a negative correlation between exercise
  and heart disease
• There is a positive correlation between exercise
  and self-esteem

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Positive and Negative Correlation on a graph
Positive correlation
Negative correlation
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How would you classify these correlations?
Negative correlation
Positive correlation
NO 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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Correlation vs Causation

• Correlation Two concepts are related in some
  way.
• Causation Changing one of the factors also
  causes a change in the other factor.
• eg Smoking and Cancer are correlated. They
  also have a causal relationship.
• If you do something to increase smoking, you
  increase the chance of cancer
• eg Ice cream sales and crime rates also have a
  correlation. However, they do NOT have a causal
  relationship. (Can you think why they are
  correlated?)
• If you do something to increase ice cream sales,
  you do not see an increase in crime

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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 causation!
• 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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Causation (aka Causality)

• Causation One variable A, actually causes a
  change in B.
• Here are some examples of correlations that also
  have a causality
• Increase smoking ? Increased likelihood of lung
  cancer
• Increase exercise ? Decreased likelihood of heart
  disease
• Key point Many, many, many things in life have
  correlations. But this does not mean that they
  have causation.
• See next slide

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Correlation does NOT imply causation!

• OFTEN (very often!), two items that are
  correlated are falsely assumed to have a causal
  relationship.
• Usually, the reason for falsely assuming
  causation is the presence of a common underlying
  factor. That is, A may be correlated with B, but
  this is due to some other factor, C.
• Example None of these three correlations have a
  causal relationship. Can you identify the other
  factor?
• As ice cream sales go up, so do crime rates
• Summer! Crime always goes up in the summer. Not
  surprisingly, more people buy ice cream in the
  summer as well.
• People who wear top-hats live longer (An actual
  study from the Victorian era)
• Income. Wealthier people wear top hats and can
  also afford better health care, medicines,
  doctors, etc.
• Hormone therapy for breast cancer decreases
  likelihood of heart disease
• As with the previous example socioeconomic
  status. Hormone therapy in of itself increases
  the likelihood of heart disease! However, people
  who are wealthier are more likely to have better
  general medical care resulting in early detection
  of breast cancer, proper treatments, etc. For
  this reason, they are also more likely to be more
  educated about heart disease (eat better,
  exercise more, smoke less, etc). So even though
  hormone therapy causes heart disease, on the
  whole, the majority of people on this therapy
  tend to have less heart disease.

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Causation or not?

• What do you think of this example?
• Studies have demonstrated a clear correlation
  between ease of faculty grading and faculty
  evaluations. That is, faculty who taught less
  challenging courses routinely receive better
  evaluations.

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Correlation v.s. Causation

• Do not confuse correlation with causation.
• Just because two things are correlated (e.g.
  height and weight) does not mean that there is a
  causal relationship.
• In other words, making a change in A will
  predictably cause a change in B
• Giving somebody a top-hat will not make them live
  longer (see next slide).
• This is an example of where there is a
  correlation, but there is not causation.
• Very important point expect 1-2 exam questions
  on this idea!

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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)?