Correlation and Casual Connection

Two variables can be one of the following.

• Perfectly correlated
• Partly correlated
• Uncorrelated

Perfect Correlation

Partial Correlation

No Correlation

Hence, in looking at a scatter chart we should be able to see:

Whether points are scattered:

Randomly	No Correlation
Upward Line	Positive Correlation
Downward Line	Negative Correlation

How close the points are to the straight line:   

Close to the Line	Strong Correlation
Scattered About the Line	Weak Correlation

CORRELATION AND CAUSAL CONNECTION

If two variables are related, i.e. the points lie close to a straight line, this shows only that there us an association between the variables – it does not show that changes in one cause changes in the other.  We quite often find that two variables are correlated because they are both related to the same underlying variable.  Consider the following:

• If you obtain data on the life expectancy and number of cars per thousand population, for a number of countries, and plot a scatter chart you will find a positive correlation.  This does not mean that you can increase the life expectancy in a country by increasing the number of cars.  It just means that both life expectancy and ownership of cars are related to the general standard of living in a country.

• If you plot the price of a loaf of bread against the price of a pair of shoes (using data over, say, the past ten years) you will almost certainly get a strong positive correlation.  This does not imply that increases in the price of a pair of shoes cause increase in the price if bread.  The correlation reflects the fact that the factors that influence prices of these products tend to be similar.

• A much quoted example is the close relationship between the number of storks observed in a particular year and the number of births.

The above are examples of spurious correlation.  It is vital that you remember (even if some politicians don’t!) that a high correlation does not provide a causal connection.

Activity

Think of two examples of pairs of variables that you expect to be related, but where there is no causal connection.  If possible, obtain data in order to plot the scatter chart.