The phrase, “correlation” is a very popular buzzword nowadays, turning up in almost any discussion concerning anything from politics to the latest scientific discoveries. But what exactly does correlation mean, and more specifically strong correlation? A correlation is a statistical measure that expresses the extent to which two variables are linearly related. Correlation coefficients range from -1 to +1, with -1 indicating perfect negative correlation, 0 indicating no correlation, and +1 indicating perfect positive correlation.

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However, it is very important to understand that the existence of a strong correlation between two variables does not imply causation. In order to determine causality, other factors, including the plausibility of the causal relationship, must be considered. With this clarification in mind, let’s examine some examples of pairs of variables with strong correlations to see how thoroughly you understand the concept.

Consider these findings:

A. The number of ice cream cones sold at the beach and the number of people who drowned at the beach.
B. The average SAT score of a high school’s graduating class and the average income of the families living in the high school district,
C. Student scores on a standardized math test and student scores on a standardized English test.
D. The amount of money spent on advertising and the number of units sold

Which of the correlations is strongest?

If you guessed the last option, you understand the underlying concept. Many factors can influence the number of ice cream cones sold at the beach, such as the weather; the number of people who drowned at the beach is likely to be influenced by factors such as the presence of lifeguards and the strength of the waves. While there may be some correlation between family income and SAT scores, there may be other factors such as the quality of the teachers and the availability of resources that are more strongly correlated with SAT scores. Student scores on a standardized math test and student scores on a standardized English test are likely to be strongly correlated but indicating which is more strongly correlated than others is a bit tricky. However, the amount of money spent on advertising and the number of units sold have a strong and clear cause-and-effect relationship.

It is important to weigh several things in evaluating the strength of a relationship between variables:

• The magnitude of the correlation coefficient
• The number of data points
• The statistical significance of the correlation
• The possibility of confounding variables

Obviously, a correlation coefficient of 0.9 is stronger than a correlation coefficient of 0.5. Additionally, a correlation coefficient of 0.9 based on 100 data points is stronger than a correlation coefficient of 0.9 based on 10 data points. Statistical significance refers to the likelihood that the correlation is due to chance. Finally, confounding variables are variables that could be influencing both of the variables being considered. For example, if you are considering the correlation between the amount of money spent on advertising and the number of units sold, you would need to consider the possibility that other factors, such as the quality of the product or the price of the product, could be influencing the number of units sold.

Being able to evaluate the strength of a correlation is an important skill. It can reveal important relationships between variables thus providing the potential of making better decisions and predictions. However, it is important to remember that correlation does not imply causation.

Further Reading
www.statisticshowto.com
www.khanacademy.org
www.coursera.org

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Which Of The Following Is The Strongest Correlation