In a research to determine the relationship between performance of students in an entrance examination and subsequent school performance, the results of ten...
Question 1 Report
In a research to determine the relationship between performance of students in an entrance examination and subsequent school performance, the results of ten randomly selected students wre obtained as follows;
| Students | A | B | C | D | E | F | G | H | I |
| Performance in Entrance Examination | 11 | 12 | 8 | 13 | 6 | 15 | 10 | 14 | 17 |
| School Performance | 5 | 10 | 9 | 7 | 4 | 8 | 6 | 14 | 11 |
1, Calculate the spearman's rank correlation coefficient
2. What would be the researcher's from the result in a?
Answer Details
The data provided cover 9 students (A to I), so \(n = 9\). Rank each set with 1 for the highest score.
| Student | Entrance | Rank \(R_x\) | School | Rank \(R_y\) | \(d = R_x - R_y\) | \(d^2\) |
|---|---|---|---|---|---|---|
| A | 11 | 6 | 5 | 8 | -2 | 4 |
| B | 12 | 5 | 10 | 3 | 2 | 4 |
| C | 8 | 8 | 9 | 4 | 4 | 16 |
| D | 13 | 4 | 7 | 6 | -2 | 4 |
| E | 6 | 9 | 4 | 9 | 0 | 0 |
| F | 15 | 2 | 8 | 5 | -3 | 9 |
| G | 10 | 7 | 6 | 7 | 0 | 0 |
| H | 14 | 3 | 14 | 1 | 2 | 4 |
| I | 17 | 1 | 11 | 2 | -1 | 1 |
| Total \(\sum d^2\) | 42 | |||||
1. Spearman's rank correlation coefficient.
\[ r_s = 1 - \frac{6\sum d^2}{n(n^2 - 1)} = 1 - \frac{6 \times 42}{9(81 - 1)} = 1 - \frac{252}{720} = 1 - 0.35 = \mathbf{0.65} \]2. Conclusion. \(r_s = 0.65\) is a fairly strong positive correlation. Students who perform well in the entrance examination tend also to perform well subsequently in school, so the researcher would conclude that entrance-examination performance is a reasonably good indicator of later school performance.
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