Hypothesis Testing Part 2: Hypothesis Testing Part 2: Categorical variablesCategorical variables

Intermediate Food Security Analysis TrainingRome, July 2010Rome, 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 Crosstabulation

2086 587 2673

2144.6 528.4 2673.0

78.0% 22.0% 100.0%

48.6% 55.5% 50.0%

2204 470 2674

2145.4 528.6 2674.0

82.4% 17.6% 100.0%

51.4% 44.5% 50.0%

4290 1057 5347

4290.0 1057.0 5347.0

80.2% 19.8% 100.0%

100.0% 100.0% 100.0%

Count

Expected Count

% within Gender of child

% within WAZPREV

Count

Expected Count

% within Gender of child

% within WAZPREV

Count

Expected Count

% within Gender of child

% within WAZPREV

Male

Female

Gender ofchild

Total

.00 1.00

WAZPREV

Total

Chi-Square Tests

16.196b 1 .000

15.921 1 .000

16.223 1 .000

.000 .000

16.193 1 .000

5347

Pearson Chi-Square

Continuity Correction a

Likelihood Ratio

Fisher's Exact Test

Linear-by-Linear Association

N of Valid Cases

Value dfAsymp. Sig.

(2-sided)Exact Sig.(2-sided)

Exact Sig.(1-sided)

Computed only for a 2x2 tablea.

0 cells (.0%) have expected count less than 5. The minimum expected count is 528.40.b.

To calculate chi-squares in SPSSIn SPSS, chi-square tests are run using the

following steps:

1. Click on “Analyze” drop down menu2. Click on “Descriptive Statistics”3. Click on “Crosstabs…”4. Move the variables into proper boxes5. Click on “Statistics…”6. Check box beside “Chi-square”7. Click “Continue”8. 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.

SolutionsSolutions

1. Transform the category you want to analyze into a bivariate variable ( ex. Traders yes/no - 0/1) 1. Re-run the chi- square with two categories (easier to

interpret)2. Use the bivariate variable as a continuous variable – run

anova or t-test