# Statistical Methods-Correlation Ratio (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 3 of 3

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## Question number: 1

» Statistical Methods » Correlation Ratio

Appeared in Year: 2012

### Describe in Detail

Two persons Amal and Bimal come to the club at random points of time between 6 p. m. and 7 p. m. , and each stays for 10 minutes. What is the chance that they will meet?

### Explanation

Let *x* denote the time Amal arrives at the bar and *y* denote the time Bimal arrives at the bar from 6 p. m. We will draw the lines *y* = *x* – 10 and *y* = *x* + 10 and shade the area in between these two lines to denote the event.

They will meet if x - 10 < y < x + 10 that is (x, y) falls in the s

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## Question number: 2

» Statistical Methods » Correlation Ratio

Appeared in Year: 2012

### Describe in Detail

Scores in a UPSC examination in Statistics Paper-I and Paper-II awarded to10 candidates were as under:

Candidate | A | B | C | D | E | F | G | H | I | J |

Score in Paper- I | 91 | 65 | 80 | 120 | 80 | 140 | 105 | 80 | 42 | 72 |

Score in Paper-II | 86 | 38 | 75 | 135 | 85 | 135 | 94 | 101 | 45 | 65 |

Calculate Spearman’s rank correlation coefficient between the scores in the two papers.

### Explanation

The method of calculating the association between the ranks is known as Spearman’s rank correlation. The candidates are rank by the UPSC examination taken for two papers which is independent. The Spearman’s rank correlation is

where n is the number of candidates and d _{i} is the difference between the rank of the i ^{th } individu

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## Question number: 3

» Statistical Methods » Correlation Ratio

Appeared in Year: 2009

### Describe in Detail

Define correlation ratio η· Show that

0 ≤ ρ ^{2} ≤ η ^{2} ≤ 1.

### Explanation

In statistics, the correlation ratio is a measure of the relationship between the statistical dispersion within individual categories and the dispersion across the whole population or sample. The measure is defined as the ratio of two standard deviations representing these types of variation.

Suppose a value of X _{i} has n _{i} values of Y say, Y _{i1}

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