**8. Examine the formula for the chi-square statistic χ².**a. If two samples are identical, what is the value of χ²? Justify your answer.b. Why is it necessary to square the difference O – E? Justify your answer by giving an example of what happens if you do not.

8 Examine the formula for the chi-square statistic x². a. If two samples are identical, what is the value of x²? Justify your answer. b. Why is it necessary to square the difference O - E? Justify your answer by giving an example of what happens if you do not.

8 Examine the formula for the chi-square statistic x². a. If two samples are identical, what is the value of x²? Justify your answer. b. Why is it necessary to square the difference O - E? Justify your answer by giving an example of what happens if you do not.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

**8. Examine the formula for the chi-square statistic χ².**

a. If two samples are identical, what is the value of χ²? Justify your answer.

b. Why is it necessary to square the difference O – E? Justify your answer by giving an example of what happens if you do not.

Expert Solution

Step 1

The Chi-square test can be used to compare the distribution of a qualitative variable in one sample with that of a qualitative variable in another sample.

The Chi-square test statistic is defined as follows for the test:

$χ_{n}^{2} = \frac{\sum_{i = 1}^{n} {(O_{i} - E_{i})}^{2}}{E_{i}}$ ,

where $O_{i} and E_{i}$ is the observed and expected value, respectively.

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