20-11-2012, 12:13 PM
Chi-Square Tests
chi-square.ppt (Size: 68 KB / Downloads: 104)
Introduction to Chi-Square Tests
Chi-square test do hypothesis testing for categorical (nominal) variables
Focus is the number of people in each category rather than means of dimensions
How many male versus female students on campus
Favorite brand of soft drink in America? How different are they in their popularity?
The observed frequency in each category is reported and compared to the expected frequency for each category (H0)
Steps for Chi-square Test
State null hypothesis (H0) and select alpha level
Observed frequencies are like expected frequencies
State alternative hypothesis (H1)
Observed frequencies are not like expected frequencies
Locate critical region
df = C – 1 (c = number of categories)
Find chi-squarecritical for specific df and alpha level on table page 699
Calculating Chi-Square
Determine the expected frequency for each category
No preference in the population
Difference from a comparison population
Determine the actual observed frequency of each category
For each category, take observed minus expected frequency
Square each of these differences
Divide each squared differences by the expected frequency for its category
Add up the results of step #5 for all the categories
Chi-square distribution
Is the mismatch between observed frequency and expected frequency bigger than what would be expected by chance?
Get certain chi-square statistics by chance
Shape of chi-square distribution depends on degrees of freedom
All chi-squared distributions are skewed to the right, since the chi-square statistic cannot be less then zero
Chi-Square Test for Independence
Most often in real research there will be two nominal variables, each having several categories.
If there is no relation between the two nominal variables it will be called independent.
For chi-square test of independence a contingency table needs to be created.
Includes the frequencies of the totals as well as of the combinations.
Square of Independence
Each individual in sample is measured on two separate variables.
Null hypothesis – H0
The two variables measured are independent (no consistent, predictable relationship between them)
Alternative hypothesis – H1
The two variables measured are dependent (a relationship between both variables exists)