Counterfeit Correlation

In The Watchman’s Rattle: A Radical New Theory of Collapse by Rebecca D. Costa, she outlines five supermemes that lead to the stagnation and collapse of civilizations: Irrational Opposition, The Personalization of Blame, Counterfeit Correlation, Silo Thinking, and Extreme Economics. This healthymemory blog post will address the Counterfeit Correlation supermeme.

When 1,009 Americans were asked,”Do you believe that correlation implies causation, 62 % responded “yes.” This statistic is both depressing and informative. It’s depressing because such a large percentage of people believe it to be true. It’s informative in that in provides some insight into the current stagnation we are suffering. It is essential that, to the extent possible, there is a good correspondence between beliefs and facts. Confusing correlation with causation can lead to many incorrect facts.

Correlation refers to how to variables or factors vary together. A correlation coefficient is a numerical measure of this co-variation. It varies from -1.00 to 1.00. A correlation of 1.0 indicates that you can predict one variable perfectly if you know the other variable. More of one variable implies a corresponding increase in the other variable. A correlation of -1.0 also indicates that you can predict one variable perfectly if you know the other variable. But the relationship is inverse. That is, more of one variable predicts less of another variable. A correlation of 0.0 implies that there is no relationship between the two variables. In other words, they are independent. You can determine the variability accounted for between the two variables by squaring this correlation coefficient. So a correlation of 0.50 would account for 25% of the variance between the two variables.

Usually the only fact reported in the popular press when a correlation is reported is whether it is statistically significant. Statistical significance refers to the probability that the correlation is due to chance. So if you read that the correlation is statistically significant beyond the p<0.05 level, it means that there is only a 5% probability that the correlation is due to chance. One of the factors determining whether a correlation is statistically significant is the size of the sample on which the correlation was computed. For example, with a sample size of 20,000 a correlation of 0.02, which would account for only 0.04% of the variance, is statistically significant at the 0.05 level. Moreover, statistical significance does not imply practical significance. So do not be impressed when you hear that a study found a statistically significant relationship without knowing the exact value of the correlation coefficient.

Now even if you have an impressively large correlation coefficient that is statistically significant, that does not necessarily imply causality. There are spurious correlations and correlations that result from other related variables. For example, one study found a significant correlation between cell phone use and sleep. That is a large amounts of cell phone use were correlated with poorer quality sleep. However, it was also true that those who had high cell phone use consumed more caffeinated beverages, consumed more alcohol, woke up later, and showed higher levels of anxiety and agitation. It was found that taking away their cell phones made them more anxious, which exacerbated their condition.

There are both spurious correlations that are spurious on the face of it, and spurious correlations that seem reasonable. A good website for exploring these problems more thoroughly can be found at

http://jfmueller.faculty.noctrl.edu/100/correlation_or_causation.htm

Establishing causation is a difficult problem that can require many years of research to establish. Ideally one wants to conduct controlled experiments in which the factors of interest are manipulated. This is not always possible, and correlational studies are clearly needed, but they must be interpreted with care. Often there is not enough time does not allow the definitive establishment of causation. In these cases, one needs to use the best information available, knowing that it might be wrong, and knowing that it might be changed and enhanced in the future.

© Douglas Griffith and healthymemory.wordpress.com, 2012. Unauthorized use and/or duplication of this material without express and written permission from this blog’s author and/or owner is strictly prohibited. Excerpts and links may be used, provided that full and clear credit is given to Douglas Griffith and healthymemory.wordpress.com with appropriate and specific direction to the original content.

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