Part c
Using the adjusted ranks from part (b), compute Spearman’s rank correlation coefficient \(\rho\) utilizing the formula \(\rho = 1 – \frac{6\sum d_i^2}{n(n^2-1)}\). List the adjusted ranks for both datasets, calculate the rank differences \(d_i\), and show the calculation of \(\sum d_i^2\).
Computing Spearman’s Rank Correlation Coefficient Step-by-Step
Given the following dataset of 6 paired observations: X: {12, 15, 18, 22, 30, 35} Y: {20, 25, 30, 35, 45, 50} Compute Spearman’s rank correlation coefficient \(\rho\) step-by-step by first assigning ranks, then calculating rank differences, and finally using the formula \(\rho = 1 – \frac{6 \sum d_i^2}{n(n^2-1)}\).