Hypothesis Testing Part 2:
Categorical variables
Intermediate Food Security Analysis Training
Rome, July 2010
Topics to be covered in this presentation
Pearson’s chi square
Hypothesis testing for categorical
variables…
We sometimes want to determine…
Whether the proportion of people with some
particular outcome differ by another variable
Ex. Does the proportion of food insecure households
differ in male and female headed households??
If we want to test whether there is a relationship between
two categorical variables we should use Pearson’s chi
square
Pearson’s chi-square test

Pearson’s chi-squared test is an omnibus test that is
used to test the hypothesis that the row and the
column variables of a contingency table are
independent

It’s a comparison of the frequencies you observe in
certain categories to the frequency you might
expect to get in those categories by chance.
Assumptions of the chi-square test
Two assumptions:
1. For the test to be meaningful it is imperative
that each unit contributes to only one cell of
the contingency table.
2. The expected frequencies should be greater
than 5 in each cell (or the test may fail to
detect a genuine effect)
Chi Square example…

If we do it by spss, we get the same answer
Gender of child * WAZPREV Crosstabulati on
WAZPREV
.00
Gender of
child
Male
Female
T otal
Count
1. 00
T otal
2086
587
2673
Expected Count
2144.6
528.4
2673.0
% within Gender of child
78.0%
22.0%
100.0%
% within WAZPREV
48.6%
55.5%
50.0%
2204
470
2674
Expected Count
2145.4
528.6
2674.0
% within Gender of child
82.4%
17.6%
100.0%
% within WAZPREV
51.4%
44.5%
50.0%
4290
1057
5347
Expected Count
4290.0
1057.0
5347.0
% within Gender of child
80.2%
19.8%
100.0%
100.0%
100.0%
100.0%
Count
Count
% within WAZPREV
Chi -S quare Tests
Value
Asymp. Sig.
(2-sided)
df
Pearson Chi-Square
16.196b
1
.000
Continuity Correction a
15.921
1
.000
Likelihood Ratio
16.223
1
.000
Fisher's Exact Test
Linear-by-Linear Association
N of Valid Cases
Exact Sig.
(2-sided)
.000
16.193
1
.000
5347
a. Computed only for a 2x2 table
b. 0 cell s (.0%) have expect ed cou nt less than 5. The minimum expect ed cou nt i s 528.40.
Exact Sig.
(1-sided)
.000
To calculate chi-squares in SPSS
In SPSS, chi-square tests are run using the following steps:
1.
2.
3.
4.
5.
6.
7.
8.
Click on “Analyze” drop down menu
Click on “Descriptive Statistics”
Click on “Crosstabs…”
Move the variables into proper boxes
Click on “Statistics…”
Check box beside “Chi-square”
Click “Continue”
Click “OK”
Reading the Chi-square test

Chi-Square (Crosstabs) Tests the hypothesis that the
row and column variables are independent, without
indicating strength or direction of the relationship.
Alternatives

If you need to analyse the relationship between two
categories and you want to test the significance of the
differences (for example - traders and poor food
consumption) chi-square is not the most appropriate
test.
Solutions
Transform the category you want to analyze into a bivariate
variable ( ex. Traders yes/no - 0/1)
1.
1.
2.
Re-run the chi- square with two categories (easier to interpret)
Use the bivariate variable as a continuous variable – run anova or ttest