A group of 8 cybersecurity analysts (A, B, C, D, E, F, G, and H) completed a high-stakes penetration testing simulation. Their efficiency scores, where a higher score indicates better performance, are recorded in the table below.
| Analyst | A | B | C | D | E | F | G | H |
|---|---|---|---|---|---|---|---|---|
| Efficiency Score | 82 | 45 | 78 | 94 | 36 | 61 | 89 | 52 |
The analysts were also ranked by their years of industry seniority. The list below shows the analysts in order from most senior (rank 1) to least senior (rank 8):
G,D,A,F,C,B,H,E G, \quad D, \quad A, \quad F, \quad C, \quad B, \quad H, \quad E G,D,A,F,C,B,H,ECalculate Spearman's rank correlation coefficient between the analysts' efficiency scores and their seniority ranks.
Stating your hypotheses clearly, test at the 5% level of significance whether there is evidence of a positive correlation between seniority and performance efficiency.
The analysts' annual salaries were also recorded. In this dataset, several analysts earned the exact same salary. Explain how you would calculate the Spearman's rank correlation coefficient between efficiency scores and salaries in the presence of these tied values.
244 exam-style questions on AQA A Level Maths 2.2 L: Data presentation and interpretation, covering 2.2.1 Single-variable data diagrams, 2.2.2 Scatter diagrams and correlation, 2.2.3 Central tendency, variation and standard deviation, 2.2.4 Outliers and cleaning data, and 2.2 L: Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.