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?

##### Explanation

(a)

R(_1) | 4 | 5 | 2 | 6 | 1 | 8 | 3 | 7 | 10 |
9 |

R(_2) | 2 | 7 | 6 | 4 | 1 | 5 | 3 | 10 | 8 | 9 |

d(_1) | 2 | -2 | -4 | 2 | 0 | 3 | 0 | -3 | 2 | 0 |

d(_2) | 4 | 4 | 16 | 4 | 0 | 9 | 0 | 9 | 4 | 0 |

Then (sum d_1^2) = 50

The spearman’s coefficient = 1 – (frac{6 times 50}{10(100 – 1)}) = 1 – 0.30303 = 0.697

(b) We conclude that there exist positive correlation between performance in entrance examination and school performance