# LifeLine Help Center:

How to Use the __Chi-Square Test__

for Survey Data Analysis

**Note:** *This section is fairly technical in nature and
we do not provide a Chi-Square Calculator. The Chi-Square
test is used when cross-tabulating survey results and all
popular cross-tab software packages include this as a
test option. Please use our handy Chi-Square Significance
Reference Table for help interpreting your cross tabulation
results.*

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)