If ‘m’ individuals receive the same rank. then the correction factor required to be added in the calculation of Spearman’s rank correlation is: 

Key Points

• The correction factor required to be added in the calculation of Spearman's rank correlation when 'm' individuals receive the same rank is given by the formula: \(\rm \frac{m(m^2-1)}{12}\), where, 'm' represents the number of individuals who have the same rank in the data set.
• The correction factor is used to adjust for tied ranks in the calculation of Spearman's rank correlation coefficient. When there are ties in the ranks, it means that multiple individuals have the same rank value. The correction factor takes into account the extent of these ties and helps in providing a more accurate estimate of the rank correlation.
• By adding the correction factor to the rank correlation formula, we account for the impact of tied ranks on the final correlation coefficient. This ensures that the rank correlation calculation appropriately reflects the strength of the relationship between the variables, considering the ties in the data.
• Including the correction factor is important in situations where ties occur in the data set, as it helps to improve the accuracy and validity of the Spearman's rank correlation coefficient as a measure of association between variables.  

Additional Information

• Spearman's rank correlation coefficient, named after Charles Spearman, is a non-parametric measure of correlation between two variables. It is based on the ranks of the observations rather than their actual values.
• Spearman's rank correlation is widely used in various fields, such as social sciences, economics, psychology, and biological research. It provides a robust and flexible measure of association between variables, particularly when the data does not meet the assumptions of parametric correlation measures like Pearson's correlation coefficient.