| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2009 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Multiple judges or comparisons |
| Difficulty | Moderate -0.3 This is a straightforward application of Spearman's rank correlation coefficient with clear ranking and standard formula application. Part (i) requires routine calculation with small dataset (n=5), and part (ii) is simple interpretation of given correlation values. Slightly easier than average due to small sample size and direct interpretation, but requires careful ranking and arithmetic. |
| Spec | 5.08e Spearman rank correlation |
| Student | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) |
| Tutor 1 | 73 | 67 | 60 | 48 | 39 |
| Tutor 2 | 62 | 50 | 61 | 76 | 65 |
| Tutor 3 | 42 | 50 | 63 | 54 | 71 |
4 Three tutors each marked the coursework of five students. The marks are given in the table.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | c | }
\hline
Student & $A$ & $B$ & $C$ & $D$ & $E$ \\
\hline
Tutor 1 & 73 & 67 & 60 & 48 & 39 \\
\hline
Tutor 2 & 62 & 50 & 61 & 76 & 65 \\
\hline
Tutor 3 & 42 & 50 & 63 & 54 & 71 \\
\hline
\end{tabular}
\end{center}
(i) Calculate Spearman's rank correlation coefficient, $r _ { \mathrm { s } }$, between the marks for tutors 1 and 2 .\\
(ii) The values of $r _ { \mathrm { s } }$ for the other pairs of tutors, are as follows.
$$\begin{array} { c c }
\text { Tutors } 1 \text { and 3: } & r _ { \mathrm { s } } = - 0.9 \\
\text { Tutors } 2 \text { and 3: } & r _ { \mathrm { s } } = 0.3
\end{array}$$
State which two tutors differ most widely in their judgements. Give your reason.
\hfill \mbox{\textit{OCR S1 2009 Q4 [7]}}