Quantative Analysis

UNIT 16 CHI-SQUARE TESTS

Objectives By the time you have successfully completed this unit, you should be able to: • • • • • • appreciate the role of the chi-square distribution in testing of hypotheses design and conduct tests concerning the variance of a normal population perform tests regarding equality of variances from two normal populations have an intuitive understanding of the concept of the chi-square statistic use the chi-square statistic in developing and conducting tests of goodness of fit and tests concerning independence of categorised data.

Chi-Square Tests

Structure 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 Introduction Testing of Population Variance Testing of Equality of Two Population Variances Testing the Goodness of Fit Testing Independence of Categorised Data Summary Self-assessment Exercises Further Readings

16.1 INTRODUCTION

In the previous unit you have studied the meaning of testing of hypothesis and also how some of these tests concerning the means and the proportions of one or two populations could be designed and conducted. But in real life, one is not always . concerned with the mean and the proportion alone-nor is one always interested in only one or two populations. A marketing manager may want to test if there is any significant difference in the proportion of high income households where his brand of soap is preferred in North, South, East, West and Central India,. In such a situation, the marketing manager is interested in testing the equality of proportions among five different populations: Similarly, a quality control manager may be interested in testing the variability of a manufacturing process after some major modifications were carried out on the machinery vis-à-vis the variability before such modifications. The methods that we are going to introduce and discuss in this unit will help us in the kind of situations mentioned above as well as in many other types of situations. Earlier (section 15.6 in the previous...