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Some Common Statistical Errors
Spurious Correlations
Ó 1996, 1997 by William C. Burns (http://www.burns.com/wcbspurcorl.htm)

The analysis of human resources data typically involves the use of computer databases that were constructed to process transactions. Their purpose normally centers on administration and recordkeeping. Thus the variables that are available for analysis are not necessarily the ones that would be chosen as the ideal set of variables given the purposes of the analysis. A side effect is that in many cases critical analysis variables may be missing. This can lead to "spurious correlations," a common and serious interpretation fallacy. For example, suppose that the critical variable is correlated with race, age, or gender. Thus any other variable that correlates with the critical variable will probably also be correlated with race, age, or gender. These correlations are spurious because their primary cause is the missing critical variable. Nonetheless these spurious correlations are at times used as indicators of discrimination. The purpose of this paper is to illustrate the widespread occurrence of spurious correlations.

My favorite example is to do the following:

  Get data on all the fires in San Francisco for the last ten years.
  Correlate the number of fire engines at each fire and the damages in dollars at each fire.

Note the significant relationship between number of fire engines and the amount of damage. Conclude that fire engines cause the damage.

The reason that I like this example is that the conclusion is so absurd. Anyone will quickly recognize that both variables result from and are correlated with the overall size of the fire. However, many spurious correlations do not seem absurd and some seem compelling.

Read the whole article here

The winners of the Purdue University Indianapolis "Spurious Correlations Contest" are announced below. The contest was fiercely humorous with entries that spanned the globe. The contestants put on their conceptual Rube Goldberg caps and spinned some mighty tall tales to win the fabulous prize money (which will be delivered with post-haste).

The individual category winners are:

1. Amount of ice cream sold and deaths by drownings (Moore, 1993).

Dr. Paul Gardner
Monash University, Australia

Increases in nuclear power generator accidents (Chernobyl, Three Mile Island...) have resulted in greenhouse gas increases, ozone layer reduction, average world temperature rise and increases in the fraction of heavy water in rain. Concerns about nuclear catastrophe have resulted in increases in eating disorders, especially among those with a genetic predisposition to obesity. Heavy water in rain has resulted in an increase in the specific gravity of cream produced by cows, while theincreasing world temperature has resulted in an increasing attendance at beach resorts, coupled with increased consumption of ice cream. The increased weight of fat worried people whose centre of gravity has been lowered by a rising consumption of heavy ice cream has caused an increased number of deaths by drowning. For a detailed account of the research methods used to investigate this complex effect, see my forthcoming paper, "Path analysis methods in lacto-sociological research".

The rest of the article is here