Hypothesis testing chi square test for independence

1. HYPOTHESIS
TESTING
Chi-Square Test for Independence:
NADEEM UDDIN
ASSOCIATE PROFESSOR
OF STATISTICS

2. Chi-Square Test for Independence:
This lesson explains how to conduct a chi-
square test for independence. The test is
applied when you have two categorical
variables from a single population. It is
used to determine whether there is a
significant association between the two
variables.

3. Procedure Test Concerning for independence
1-Hypothesis
H0: The two attributes are not associated.
H1: The two attributes are associated.
2-Level of significance = 1% or 5% or any given
value.
3-Test of statistic 𝝌 𝟐 =
𝒐−𝒆 𝟐
𝒆
Where o = observed value
e = estimated value

4. 4-Critical region 𝜒2
, 𝑟−1 (𝑐−1)
5-Computation
6-Conclusion
If the calculated value of test statistic
falls in the area of rejection, we reject
the null hypothesis otherwise accept it.

5. Weather
Total
Good Bad
Result
Win 12 4 16
Draw 5 8 13
Lose 7 14 21
Total 24 26 50
Example-11:
The members of a sports team are interested in
whether the weather has an effect on their results.
They play 50 matches, with the following results:
Test the claim at 1% significance level that
the result independent of weather.

6. Solution:
1-Hypothesis
H0: Result independent of
weather.H1: Result dependent of
weather.
2- Level of significance = 0.01
3- Test of statistic 𝜒2
=
𝑜−𝑒 2
𝑒

7. 4. Critical Region
𝜒2
, 𝑟−1 (𝑐−1)
𝜒2
0.01, 3−1 (2−1)
𝜒2
,2 = 9.21 9.21

8. 5. Computation
Good Bad Total
Win 12
24 × 16
50
= 7.68
4
26 × 16
50
= 8.32 16
Dra
w
5
13 × 24
50
= 6.24 8
26 × 13
50
= 6.76 13
Loos
e
7
24 × 21
50
= 10.08
14
26 × 21
50
= 10.92
21
Total 24 26 50

9. O e
12 7.68 2.43
5 6.24 0.246
7 10.08 0.941
4 8.32 2.243
8 6.76 0.227
14 10.92 0.868
 
2
o e
e

2
6.956cal 
6. Conclusion:
Accept H0.
And conclude that the team’s
result are independent of the weather.