| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Hypothesis test of Spearman’s rank correlation coefficien |
| Type | Determine ranks from coefficient |
| Difficulty | Moderate -0.8 Part (i) is a straightforward calculation of Spearman's coefficient using the standard formula with given ranks—pure procedural work. Part (ii) requires understanding that rs = -1 means perfect negative correlation, so ranks must be in reverse order, which is conceptually simple once the definition is known. Both parts are routine applications with no problem-solving required, making this easier than average. |
| Spec | 5.08e Spearman rank correlation |
| \(A\) | 1 | 2 | 3 | 4 | 5 |
| \(B\) | 4 | 1 | 3 | 2 | 5 |
| \(B\) | 4 | 1 | 3 | 2 | 5 |
| \(C\) |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(\Sigma f^2 = 14\), \(1 - \frac{6 \times \text{their } 14}{5 \times (25-1)} = 0.3\) | M1 A1 | Subtract & square 5 pairs & add |
| (ii) Reverse rankings attempted: 2 5 3 4 1 | M1 A1 | 5 correct: T & I to make \(\Sigma d^2 = 40\): 2 marks or 0 marks |
(i) $\Sigma f^2 = 14$, $1 - \frac{6 \times \text{their } 14}{5 \times (25-1)} = 0.3$ | M1 A1 | Subtract & square 5 pairs & add
(ii) Reverse rankings attempted: 2 5 3 4 1 | M1 A1 | 5 correct: T & I to make $\Sigma d^2 = 40$: 2 marks or 0 marks1 (i) Calculate the value of Spearman's rank correlation coefficient between the two sets of rankings, $A$ and $B$, shown in Table 1.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | l | l l l l l | }
\hline
$A$ & 1 & 2 & 3 & 4 & 5 \\
\hline
$B$ & 4 & 1 & 3 & 2 & 5 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{center}
\end{table}
(ii) The value of Spearman's rank correlation coefficient between the set of rankings $B$ and a third set of rankings, $C$, is known to be - 1 . Copy and complete Table 2 showing the set of rankings $C$.
\begin{table}[h]
\begin{center}
\begin{tabular}{ | l | l l l l l | }
\hline
$B$ & 4 & 1 & 3 & 2 & 5 \\
\hline
$C$ & & & & & \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{center}
\end{table}
\hfill \mbox{\textit{OCR S1 2005 Q1 [6]}}