| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Sketch scatter diagram scenarios |
| Difficulty | Standard +0.3 Part (i) is a routine calculation of Spearman's rank correlation coefficient following a standard algorithm. Part (ii) requires conceptual understanding that Spearman measures monotonic relationships while PMCC measures linear relationships, but sketching a simple curved monotonic relationship (e.g., exponential curve through 5 points) is straightforward once this distinction is understood. This is slightly above average due to the conceptual element in part (ii), but well within reach of a competent S1 student. |
| Spec | 5.08e Spearman rank correlation5.08f Hypothesis test: Spearman rank |
| Project | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) |
| First assessor | 38 | 91 | 62 | 83 | 61 |
| Second assessor | 56 | 84 | 41 | 85 | 62 |
| Answer | Marks | Guidance |
|---|---|---|
| \(r_s = 1 - \frac{6 \times 8}{5 \times 24} = 0.6\) | B2 | For correct ranks (or reversed); B1 if 1 error |
| M1 | For correct values of \(d\) or \(d^2\) | |
| M1 | For use of the Spearman formula | |
| A1 | For correct answer 0.6 or fractional equivalent |
| Answer | Marks | Guidance |
|---|---|---|
| (e.g. scatter plot showing non-linear increasing relationship) | B2 | For 5 points, showing any non-linear 'increasing' relationship |
**Part (i)**
Ranks are: $\begin{matrix} 1 & 5 & 3 & 4 & 2 \\ 2 & 4 & 1 & 5 & 3 \end{matrix}$
Values of $d$ are $-1, 1, 2, -1, -1$
$r_s = 1 - \frac{6 \times 8}{5 \times 24} = 0.6$ | B2 | For correct ranks (or reversed); B1 if 1 error
| M1 | For correct values of $d$ or $d^2$
| M1 | For use of the Spearman formula
| A1 | For correct answer 0.6 or fractional equivalent
**Part (ii)**
(e.g. scatter plot showing non-linear increasing relationship) | B2 | For 5 points, showing any non-linear 'increasing' relationship
---2 Two independent assessors awarded marks to each of 5 projects. The results were as shown in the table.
\begin{center}
\begin{tabular}{ | l | c c c c c | }
\hline
Project & $A$ & $B$ & $C$ & $D$ & $E$ \\
\hline
First assessor & 38 & 91 & 62 & 83 & 61 \\
Second assessor & 56 & 84 & 41 & 85 & 62 \\
\hline
\end{tabular}
\end{center}
(i) Calculate Spearman's rank correlation coefficient for the data.\\
(ii) Show, by sketching a suitable scatter diagram, how two assessors might have assessed 5 projects in such a way that Spearman's rank correlation coefficient for their marks was + 1 while the product moment correlation coefficient for their marks was not + 1 . (Your scatter diagram need not be drawn accurately to scale.)
\hfill \mbox{\textit{OCR S1 Q2 [7]}}