If the difference between the rank of the 4 observations is 2.5, 0.5, -1.5, -1.5, then Spearman's rank correlation coefficient equals:

The correct answer is -0.1.

 Key Points

• Spearman's rank correlation coefficient is used to measure the association between two variables when the data are ordinal or ranked.
• The formula for calculating the Spearman's rank correlation coefficient is given by:
  • ​, where n is the sample size and the sum of differences is the sum of squared differences between the ranks of the two variables.
• In this case, given that the difference between the rank of the 4 observations are 2.5, 0.5, -1.5, and -1.5, the sum of squared differences would be.
• Plugging in n = 4, we have:
• The Spearman's rank correlation coefficient measures the association between two variables when the data are ordinal or ranked.
• The formula for calculating Spearman's rank correlation coefficient involves finding the sum of squared differences between the ranks of the two variables and using that value in the formula.

Additional Information

• A positive value of Spearman's rank correlation coefficient indicates a positive association between the variables, a negative value indicates a negative association and a value of zero indicates no association.
• Spearman's rank correlation coefficient is often used when Pearson's correlation coefficient cannot be applied, for example, when the data are not normally distributed or are not continuous.
• Spearman's rank correlation coefficient ranges from -1 to 1, with -1 indicating a perfect negative association, 1 indicating a perfect positive association, and 0 indicating no association.
  • It is important to choose the appropriate correlation coefficient based on the nature of the data and the research question being studied.
• The interpretation of the correlation coefficient and its statistical significance depends on the sample size and the strength of the association between the variables.