What is the importance of Chi-square test in marketing research?

Agreed with Sir Vinod jetley

The Chi-Square is a statistical test used to examine differences with categorical variables.

The Chi-Square test is used in two circumstances:

1) for estimating how closely an observed distribution matches an expected distribution (a "goodness-of-fit" test), or

2) for estimating whether two random variables are independent.

For survey results, the Chi-Square statistical test comes in most handy when analyzing cross tabulations of the survey data. Since crosstabs show the frequency and percentage of responses to questions by different segments or categories of respondents (gender, income, profession, etc.), the Chi-Square test can tell us whether there is a statistical difference between the segments/categories in how they answered the question.

Note #1: The Chi-Square statistic only tests whether two variables are independent in a "yes" or "no" format. It does not indicate the degree of difference between the respondent categories in terms of which is greater or less.

Note #2: The Chi-Square test requires that you use numerical values (frequency counts), not percentages or ratios.

Chi-Square Calculation Formula

chi-sq = sum[(Ei,j - Ai,j) / Ei,j ]

where Ei,j represents the expected value for cell i, j

E i,j = (Ti x Tj) / N

[Ti = sum of values in columni, Tj = sum of values in row j, N = total of values in table]

A i,j represents the actual value for cell i, j

For significance, test chi-sq against critical values for the Chi Square Distribution

df = (columns-1) x (rows-1)