|Observed Spurious Relationship||Reason for Relationship (the Third Variable)|
|Amount of ice cream sold and deaths by drownings (Moore, 1993)||Season: Ice cream sales and drownings tend to be high during the warm months of the year|
|Ministers’ salaries and price of vodka||Area (i.e., urban or rural): In urban areas, prices and salaries tend to be higher.|
|Shoe size and reading performance for elementary school children||Age: Older children have larger shoe sizes and read better.|
|Number of doctors in region and number of people dying from disease||Population density: In highly dense areas, there are more doctors and more people die.|
|Number of doctors in region and number of people dying from disease||Population density: In highly dense areas, there are more police officers and more crimes.|
|Number of police officers and number of crimes (Glass & Hopkins, 1996)||Population density: In highly dense areas, there are more homicides and more churches.|
|Number of homicides and number of churches||Time: Both variables were increasing over time|
|Number of storks sighted and the population of Oldenburg, Germany, over a six-year period (Box, Hunter, & Hunter, 1978)||Time: Both were increasing during the 1970s.|
|Number of public libraries and the amount of drug use||Time: Both tend to increase over time.|
|Teachers’ salaries and the price of liquor (Moore and McCabe, 1993)||Time: Both tend to increase over time.|
|Tea drinking and lung cancer||Smoking: Tea drinkers have a lower risk only because they smoke less|
Halpern (2003) identified correlations that are often used to erroneously infer causality: illusory correlations, spurious correlations, and accidental correlations.
Illusory correlations are based on an individual’s preconceived notions or beliefs which lead one to look for associations between variables that confirm those.
Accidental correlations have no logical connection between them.
Finally, spurious correlations are correlations between two variables that are actually caused by a third variable.