Rank Correlation Coefficient between Profit and Investment for Last 6 Years

Introduction
The rank correlation coefficient is a statistical measure that determines the strength and direction of the relationship between two variables. In this case, we will compute the rank correlation coefficient between profit and investment for the last 6 years.

Step 1: Data Collection
To compute the rank correlation coefficient, we need data on profit and investment for each of the last 6 years. The data should be collected accurately and from reliable sources. Ensure that the data is organized in a tabular format with profit and investment as the columns and the years as rows.

Step 2: Rank the Data
Ranking the data is necessary to eliminate any bias caused by the differences in the magnitude of the values. Follow these steps to rank the data:
1. Sort the data in ascending order for both profit and investment.
2. Assign ranks to each value. The smallest value gets rank 1, the second smallest gets rank 2, and so on. In case of tied values, assign the average rank to them.
3. Repeat this process for both profit and investment columns.

Step 3: Calculate the Differences
Once the data is ranked, calculate the difference between the ranks of profit and investment for each year. The difference should be calculated as follows:
1. Subtract the rank of investment from the rank of profit for each year.
2. Take the absolute value of each difference to eliminate the negative sign.

Step 4: Calculate the Rank Correlation Coefficient
To calculate the rank correlation coefficient, use the following formula:

rank correlation coefficient (ρ) = 1 - ((6 * ∑d^2) / (n^3 - n))

Where:
- ρ is the rank correlation coefficient.
- ∑d^2 is the sum of squared differences between ranks.
- n is the number of years (6 in this case).

Step 5: Interpretation of the Result
The rank correlation coefficient (ρ) ranges from -1 to 1. A positive value indicates a positive correlation between profit and investment, while a negative value indicates a negative correlation. The closer the value is to 1 or -1, the stronger the correlation. A value close to 0 suggests no correlation between the variables.

Conclusion
Computing the rank correlation coefficient between profit and investment for the last 6 years involves data collection, ranking the data, calculating the differences in ranks, and finally, using the formula to obtain the correlation coefficient. This coefficient will help determine the strength and direction of the relationship between profit and investment.