# Statistical Methods-Non-Parametric Test (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 6 of 16

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## Question number: 1

» Statistical Methods » Non-Parametric Test » Wald-Wolfowitz

Appeared in Year: 2011

### Describe in Detail

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

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## Question number: 2

» Statistical Methods » Non-Parametric Test » Sign

Appeared in Year: 2010

### Describe in Detail

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

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## Question number: 3

» Statistical Methods » Non-Parametric Test » Mann-Whitney

Appeared in Year: 2009

### Describe in Detail

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

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## Question number: 4

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2009

### Describe in Detail

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

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## Question number: 5

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2012

### Describe in Detail

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

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## Question number: 6

» Statistical Methods » Non-Parametric Test » Wald-Wolfowitz

Appeared in Year: 2013

### Describe in Detail

The values of two random samples are arranged below in an increasing order with X denoting the value of sample I and Y denoting the value of sample 2:

XXXYXYYYYXXYXXXYXXYYY

Use Wald-Wolfowitz run test to test whether the two samples may be regarded as coming from a common population.

### Explanation

Wald-Wolfowitz run test uses the data of two random samples, sample 1 is X variables of size n = 11 and sample 2 is Y variables of size m = 10 from two population F _{X} (x) and F _{Y} (y) respectively.

The hypothesis under the test is that the null hypothesis is the two population are identical otherwise the alternative is the population is differ.

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