![]() Statistical Significance of the Correlation Coefficient Two relationships could have the same correlation coefficient, but completely different patterns. ![]() The correlation coefficient by itself does not tell us everything about the relationship between two variables. The correlation coefficient is not a replacement for examining the scatter plot to study the variables’ relationship. A scatter plot or X-Y diagram can help to discover and understand additional characteristics of the relationship between variables. With the same correlation coefficient, two variables might have completely different dependence patterns. The correlation coefficient indicates the direction and strength of the linear dependence between two variables but it does not cover all the existing relationship patterns. When variables are non-linearly related, they are not independent of each other but their correlation coefficient could be zero. The correlation coefficient only indicates the linear dependence between two variables. WARNING! If the correlation coefficient of two variables is zero, it does not imply they are independent. If two variables are independent, the correlation coefficient is zero. As the weather is hotter, more people consume ice cream and more people swim in the ocean, making them susceptible to shark attacks. In this example, it is hot weather that is a common factor. This example demonstrates a common mistake that people make: assuming causation when they see correlation. They are triggered by a third factor: summer. For example, if ice cream sales at the beach are highly correlated with the number of shark attacks, it does not imply that increased ice cream sales cause increased shark attacks. It is possible that an unknown third variable C is causing both A and B to change. If variable A is highly correlated with variable B, it does not necessarily mean A causes B or vice versa. There are clear relationships but they are not linear and therefore cannot be determined with Pearson’s correlation coefficient. Notice the scatter plots below with a correlation equal to 0. It is possible that two variables have a perfect non-linear relationship when the correlation coefficient is low. Pearson’s correlation coefficient is only sensitive to the linear dependence between two variables.
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