# Statistical Methods-Non-Parametric Test [ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)]: Questions 1 - 5 of 16

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## Question 1

Appeared in Year: *2011*

### Describe in Detail

Essay▾Explain the Wald-Wolfowitz run test for randomness in a sequence of two types of symbols. Find E_{Ho} (R) where R denotes the number of runs of elements of one kind.

### Explanation

Suppose we have two sample x_{1} , x_{2} , … x_{n} and y_{1} , y_{2} , … , y_{m} and we wish to test that either both sample come from same population or not. We can use Wald-Wolfowitz run test for randomness.

First we arrange n x՚s and m y՚s in descending order of size (n + m) . Then we consider the array of x՚s and y՚s and count the number of runs (R) . A run is a …

… (125 more words) …

## Question 2

Appeared in Year: *2010*

### Describe in Detail

Essay▾Describe clearly sign test. State its asymptotic relative efficiency with respect to t-test.

### Explanation

Let x_{(1) ,} x_{(2) , … ,} x_{(n)} be the ordered sample values from a population F (X) and M be its median.

Here we test where M_{0} is the given value of the median and hence

To perform the sign test, first find the differences (X_{(i)} -M_{0}) for i = 1,2, … , n and consider their signs. Suppose the number of + ve sign is r and negative sign is (n-r) . For this w…

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## Question 3

Appeared in Year: *2009*

### Describe in Detail

Essay▾wo drugs were given to two batches of 6 students. The numbers of days to get a complete cure are given below:

Durg A | 6 | 7 | 8 | 9 | 12 | 16 |

Durg B | 10 | 11 | 13 | 14 | 15 | 17 |

Using Mann-Whitney test decide whether the median days for cure by the two drugs are equal. (Table values of U - Statistic at 0·05 level are: U_{5,5} = 2, U_{5,6} = 3, and U_{6,6} = 5.)

### Explanation

Let the Durg A consider the population X and Durg B consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is

In Mann-Whitney test, first consider the combined ordered sequence of the sample values is

Sample: 6 7 8 9 10 11 12 13 14 15 16 17

Population: X …

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## Question 4

Appeared in Year: *2009*

### Describe in Detail

Essay▾Ten experts have given scores of effectiveness on two teams A and B as given below.

Expert | Score on A | Score on B |

1 | 7 | 9 |

2 | 4 | 5 |

3 | 8 | 8 |

4 | 9 | 8 |

5 | 3 | 6 |

6 | 6 | 10 |

7 | 8 | 9 |

8 | 10 | 8 |

9 | 9 | 4 |

10 | 5 | 9 |

Are the distribution of scores for group A above that of group B?

### Explanation

Let n_{1} be the number of scores of effectiveness on team A with median score m_{1} , and n_{2} the number of scores of effectiveness on team B with median score m_{2} . Then the hypothesis is that the median score of the two teams are same against the alternative that they are not same.

For this first arrange the observations of the combined samples (n_{1} + n_{2})…

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## Question 5

Appeared in Year: *2012*

### Describe in Detail

Essay▾Name two non-parametric tests for comparing locations of two correlated populations.

### Explanation

The Wald-Wolfowitz runs test and Mann-Whitney U-test comparing locations of two correlated populations. Let the sample 1 consider the population X and sample 2 consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is