1. CHI SQUARE TEST OF INDEPENDENCE

2. 1The chi- square test of independence is used to test independence of two variables 2Suppose we want to test independence of two factors: a. Service Time b.Personally knowing someone at a bank branch 3 Data on customers is collected to find out information on the above 2 factors. 4It is classified into a two way table called a contingency table

3. Test of Independence: Contingency Tables
1. Set up the null and alternative hypotheses.
2. Select a random sample and record the observed
frequency, fij , for each cell of the contingency table.
3. Compute the expected frequency, eij , for each cell.

4. Test of Independence: Contingency Tables
4. Compute the test statistic.
5 Reject H0 if
(where  is the significance level and with n rows and m columns there are
(n - 1)(m - 1) degrees of freedom).
NOTE: NULL HYPOTHESIS IS ALWAYS OF INDEPENDENCE OF TWO FACTORS

5. Example: Modern Homes (B)
Contingency Table (Independence) Test
Each home sold can be classified according to price and to style. Modern Homes’ manager would like to determine if the price of the home and the style of the home are independent variables for purchase decisions.
The number of homes sold for each model and price for the past two years is shown below. For convenience, the price of the home is listed as either Rs35,00,000 or less or more than Rs35,00,000.
Price Colonial Ranch Split-Level A-Frame
< Rs35,00,
> Rs35,00,

6. Example: Modern Homes (B)
Contingency Table (Independence) Test
Hypotheses
H0: Price of the home is independent of the style of the home that is purchased
Ha: Price of the home is not independent of the
style of the home that is purchased
Expected Frequencies
Price Colonial Ranch Split-Level A-Frame Total
< Rs350K
> Rs350K
Total

7. Example: Modern Homes (B)
Contingency Table (Independence) Test
Test Statistic
= =
Rejection Rule
With  = .05 and (2 - 1)(4 - 1) = 3 d.f.,
Reject H0 if 2 > 7.81
Conclusion
We reject H0, the assumption that the price of the home is independent of the style of the home that is purchased.