Spearmen's Rank Correlation || Gnani The Knowledge ||

Summary

In this video, the presenter explains how to calculate Spearman's Rank Correlation Coefficient, a statistical method used to measure the strength of association between two variables. The formula is outlined and broken down with a worked example, involving the calculation of rank differences and their squares. The video also contrasts this method with Pearson's correlation coefficient, emphasizing the simplicity of Spearman's method for non-linear relationships. The final result, a Spearman coefficient of 0.43, demonstrates a moderate positive correlation between the two series.

Takeaways

• 😀 Spearman's Rank Correlation Coefficient is a measure of the relationship between two ranked variables.
• 😀 The formula for Spearman's rank correlation coefficient is: r_s = 1 - (6 * Σd^2) / (n * (n^2 - 1))
• 😀 In the formula, d represents the difference between the ranks of the paired values from two series.
• 😀 n stands for the number of observations in the data sets.
• 😀 The formula calculates the sum of squared differences (Σd^2) between the ranks of the two variables.
• 😀 To calculate Spearman's rank correlation coefficient, first rank both the X and Y series.
• 😀 After ranking, find the difference between corresponding ranks (d), and then square the differences (d^2).
• 😀 Once you have the sum of squared differences, substitute the values into the formula to find the coefficient.
• 😀 The coefficient ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.
• 😀 In the example calculation, the Spearman's rank correlation coefficient for the given data was found to be approximately -0.214, indicating a slight negative correlation.
• 😀 Spearman's rank correlation is useful when the data is ordinal or ranks are assigned, rather than when the data is continuous.

Q & A

What is Spearman's rank correlation coefficient?

Spearman's rank correlation coefficient is a statistical measure that assesses the strength and direction of the association between two variables. It uses ranks of the data rather than the actual values, making it useful for ordinal data or when the relationship is not linear.

How is Spearman's rank correlation coefficient calculated?

The formula for Spearman's rank correlation coefficient (R) is: R = 1 - (6 * Σd²) / (n * (n² - 1)), where d is the difference between the ranks of corresponding values from two series, and n is the number of observations.

What does 'd' represent in the formula for Spearman's rank correlation coefficient?

'd' represents the difference between the ranks of corresponding values from the two series being compared (X series and Y series).

In the formula for Spearman's rank correlation, what does 'n' represent?

'n' represents the number of observations or paired data points in the series.

What is the role of the summation in the formula?

The summation in the formula involves calculating the sum of the squared differences (d²) for each pair of corresponding ranks between the two series. This value is then used to determine the correlation strength.

How do you handle the calculation of 'd²' in Spearman's rank correlation?

To calculate 'd²', you first find the difference (d) between the ranks of corresponding values, then square this difference (d²) for each pair. Finally, you sum all the squared differences to get Σd².

Can you explain the calculation process with an example from the script?

In the example provided, the X series and Y series are given with their corresponding ranks. For each pair, the difference in ranks (d) is calculated. These differences are then squared (d²), and the squared values are summed to get Σd², which is used in the formula to calculate the correlation.

What do you do if 'd' is negative when calculating Spearman's rank correlation?

If 'd' is negative, you still square the value of 'd' when calculating d². Squaring eliminates the negative sign, as the formula requires d² (the squared difference), not d itself.

What is the significance of the final result of Spearman's rank correlation coefficient?

The final result ranges from -1 to +1. A value of +1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation. In this case, the result was 0.43, indicating a moderate positive correlation.

How is Spearman's rank correlation different from Pearson's correlation coefficient?

Spearman's rank correlation is based on ranks and can be used for ordinal data or when the relationship is not linear. In contrast, Pearson's correlation measures linear relationships between variables using actual values, and it assumes that the data are normally distributed.