| Exam Board | OCR |
|---|---|
| Module | Further Statistics AS (Further Statistics AS) |
| Year | 2019 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Sketch scatter diagram scenarios |
| Difficulty | Challenging +1.2 Part (a) requires understanding that rs < 1 occurs with one pair swapped, leading to a formula-based calculation (standard but requires insight into the coefficient's structure). Part (b) demands conceptual understanding of the difference between rank and linear correlation, requiring students to sketch data that is perfectly negatively ranked but not perfectly linearly related—this tests deeper understanding beyond routine application. |
| Spec | 5.08e Spearman rank correlation |
| Answer | Marks | Guidance |
|---|---|---|
| Minimum possible non-zero value of \(\Sigma d^2\) ... | M1 | Find minimum \(\Sigma d^2\) |
| ... is 2 | A1 | 2 stated or used |
| \(1 - \dfrac{6 \times 2}{9 \times 80}\) | M1 | Use correct formula |
| \(\frac{59}{60}\) or \(0.983(33\ldots)\) | A1 [4] | Answer, exact or 0.983 or better |
| Answer | Marks | Guidance |
|---|---|---|
| Diagram showing points strictly decreasing, not in straight line | M1 A1 [2] | Points strictly decreasing; Not in straight line, no errors; SC: Curve, no points: M1 |
# Question 3:
## Part (a)
Minimum possible non-zero value of $\Sigma d^2$ ... | **M1** | Find minimum $\Sigma d^2$ | Allow for $\Sigma d^2 = 1$
... is 2 | **A1** | 2 stated or used
$1 - \dfrac{6 \times 2}{9 \times 80}$ | **M1** | Use correct formula | Allow $1 - \dfrac{6\Sigma d^2}{9\times 80}$ used
$\frac{59}{60}$ or $0.983(33\ldots)$ | **A1 [4]** | Answer, exact or 0.983 or better
## Part (b)
Diagram showing points strictly decreasing, not in straight line | **M1 A1 [2]** | Points strictly decreasing; Not in straight line, no errors; SC: Curve, no points: M1 | Ignore lines drawn; $< 5$ points: M1A0; $> 5$ points: M1A1; Needn't be in first quadrant
---3
\begin{enumerate}[label=(\alph*)]
\item Shula calculates the value of Spearman's rank correlation coefficient $r _ { s }$ for 9 pairs of rankings.\\
Find the largest possible value of $r _ { s }$ that Shula can obtain that is less than 1 .
\item A set of bivariate data consists of 5 pairs of values. It is known that for this data the value of Spearman's rank correlation coefficient is - 1 but the value of Pearson's product-moment correlation coefficient is not - 1 .
Sketch a possible scatter diagram illustrating the data.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Statistics AS 2019 Q3 [6]}}