Correlation & Causal Connections

What does it mean when two variables are said to be correlated? Correlation – the measure of the relation between 2 variables Positive Correlation Negative Correlation No Correlation

Key Steps in Determining Correlation Make an X-Y Scatterplot of the data putting one variable on the x-axis and the other variable on the y-axis Put a linear trendline on the graph and get the R 2 value Interpret the results – A general rule of thumb for this class is if R 2 is above 0.7, most people would say there is a correlation –See TableTable

Don’t want (or need) to make a graph? There is a function in Excel that will calculate the correlation without graphing =RSQ(known y’s,known x’s) =RSQ(C9:C24,B9:B24) on CigarrettesBirthweight.xls Excel files on QRC homepage

Establishing Causality Causality = one thing causes another Search for causality begins with the identification of a correlation Correlation DOES NOT imply causality

Possible Explanations for Correlation The correlation may be merely a coincidence The correlated effects may have a common underlying cause One of the correlated effects may be the cause of the other

Coincidence There is a correlation between the performance of the stock market and the winner of the Super Bowl –When the stock market rises from November until Super Bowl Sunday in January, the winner of the Super Bowl is the team whose city name comes later in the alphabet –Correlation works for all but 3 of 23 Super Bowls

Common Underlying Cause There is a correlation between infant death rates and longevity –Can low infant death rates CAUSE greater longevity? NO! –Common underlying cause: better health care

Causality Correlation between smoking and lung cancer –Smoking causes lung cancer