A software lead evaluates the efficiency of 7 different sorting algorithms (P,Q,R,S,T,U,VP, Q, R, S, T, U, VP,Q,R,S,T,U,V) based on their code elegance and then ranks them from most efficient to least efficient.
The lead's ranking, in decreasing order of efficiency, is: Q,P,R,T,S,V,UQ, P, R, T, S, V, UQ,P,R,T,S,V,U.
An automated benchmarking suite provides objective efficiency scores (out of 100, where 100 is maximum efficiency) for the 7 algorithms, shown in the table below:
| Algorithm | P | Q | R | S | T | U | V |
|---|---|---|---|---|---|---|---|
| Benchmark Score | 85 | 92 | 80 | 65 | 62 | 40 | 55 |
Calculate Spearman's rank correlation coefficient (rsr_srs) between the software lead's ranking and the ranking derived from the benchmark scores. Use a rank of 1 for the most efficient algorithm. Show your working clearly.
Using a 5% level of significance, test whether there is evidence of a positive correlation between the lead's qualitative ranking and the benchmark scores. State your hypotheses and the critical value.
Explain why Spearman's rank correlation coefficient is more appropriate than the Product Moment Correlation Coefficient (PMCC) in this specific task.
The lead discovers that Algorithm S's benchmark score was recorded incorrectly. If Algorithm S's score were corrected to 80, explain what effect this would have on the rankings of the benchmark scores.