9.4.20 Correlation Coefficients: Spearman’s and Pearson’s

Interprets Correlation Coefficients and their Significance: Spearman’s and Pearson’s

Correlation coefficients are used to measure the strength and direction of the linear relationship between two variables. There are two main types of correlation coefficients: Spearman’s rank correlation coefficient and Pearson’s correlation coefficient.

Spearman’s rank correlation coefficient:

Spearman’s rank correlation coefficient is used when the data is not normally distributed or when there is a non-linear relationship between the variables. It is calculated by ranking the data for each variable and then calculating the correlation between the ranked data. The resulting coefficient ranges from -1 to +1, with -1 indicating a perfect negative correlation, 0 indicating no correlation, and +1 indicating a perfect positive correlation.

Pearson’s correlation coefficient:

Pearson’s correlation coefficient is used when the data is normally distributed and there is a linear relationship between the variables. It is calculated by dividing the covariance between the two variables by the product of their standard deviations. The resulting coefficient also ranges from -1 to +1, with the same interpretation as Spearman’s correlation coefficient.

Interpreting the significance of correlation coefficients involves determining whether the observed correlation is statistically significant or due to chance. This is typically done by calculating a p-value, which represents the probability of observing the correlation if there is truly no relationship between the variables. A p-value less than 0.05 is commonly used as the threshold for statistical significance, indicating that the observed correlation is unlikely to be due to chance.

For example, a study may investigate the relationship between smoking and lung cancer by collecting data on the number of cigarettes smoked per day and the incidence of lung cancer in a population. Pearson’s correlation coefficient may be used to calculate the strength and direction of the linear relationship between these two variables. If the resulting coefficient is significantly positive, this would suggest that there is a positive association between smoking and lung cancer incidence.

References:

1. Altman DG. Practical statistics for medical research. London: Chapman and Hall; 1991.