# Statistical Methods-Non-Parametric Test (ISS 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

Essay Question▾

### 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… (156 more words) …

## Question number: 2

» Statistical Methods » Non-Parametric Test » Sign

Appeared in Year: 2010

Essay Question▾

### 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… (83 more words) …

## Question number: 3

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

Appeared in Year: 2009

Essay Question▾

### 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:… (132 more words) …

## Question number: 4

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2009

Essay Question▾

### 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… (202 more words) …

## Question number: 5

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2012

Essay Question▾

### 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

## Question number: 6

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

Appeared in Year: 2013

Essay Question▾

### 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… (84 more words) …

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