In this article, an attempt is made to bring into sharp focus the use of c²  in marketing function. By no means, the coverage is exhaustive. The aim is to make the reader appreciate the conceptual framework of Chi-Square analysis through problem illustrations in marketing. The ideas presented in this article certainly can be extended to many decision situations in marketing that can fruitfully employ chi-square tests.

Contents:
1. Chi-Square Analysis - Introduction
2. Chi-Square Test-Goodness of Fit
3. Chi-Square Test of Independence
4. Solution
5. Calculation

1. Chi-Square (c²  ) Analysis - Introduction

Consider the following decision situations:
1) Are all package designs equally preferred?
2) Are all brands equally preferred?
3) 3) Is their any association between income level and brand preference?
4) Is their any association between family size and size of washing machine bought?
5) Are the attributes educational background and type of job chosen independent?

The answer to these questions requires the help of Chi-Square (c²  ) analysis. The first two questions can be unfolded using Chi-Square test of goodness of fit for a single variable while solution to questions 3, 4, and 5 need the help of Chi-Square test of independence in a contingency table. Please note that the variables involved in Chi-Square analysis are nominally scaled. Nominal data are also known by two names - categorical data and attribute data.

The symbol c²  used here is to denote the chi-square distribution whose value depends upon the number of degrees of freedom (d.f.). As we know, chi-square distribution is a skewed distribution particularly with smaller d.f. As the sample size, and therefore, the d.f. increases and becomes large, the c²  distribution approaches normality. c²  tests are nonparametric or distribution-free in nature. This means that no assumption needs to be made about the form of the original population distribution from which the samples are drawn. Please note that all parametric tests make the assumption that the samples are drawn from a specified or assumed distribution such as the normal distribution.

Conditions for using the c²  Test

• The sample observations drawn from a population must be independent and random.

• The data must be in frequency (counting) form. If the original data are in percentages, they must be converted into frequency.

• No frequency in any cell/category must be less than 5. If the frequency is less than 5 for a category, you have to do some regrouping.

Next.....Chi-Square Test-Goodness of Fit

* Prof. P.K. Viswanathan is an Adjunct Professor and Management Consultant based in Chennai, India.