Question

Lets apply the Chi-square Test of Independence to our example where we have as random sample of 500 U.S. adults who are questioned regarding their political affiliation and opinion on a tax reform bill. We will test if the political affiliation and the opinion on a tax reform bill are dependent at a 5% level of significance. The observer contingency table is given below. Also we often want to include each cell's expected count and contribution to the Chi-square test statistic which can be done by the software

	favor	indifferent	total
democrat	138	83	285
republican	64	67	215
total	202	150	500

1. Describe the type of the relationship between Political Affiliation and Opinion on Tax Reform.
2. Calculate the Chi-square statistic and check the independency of the two variables - Political Affiliation and Opinion on Tax Reform. Use alpha = 1%.

Answer 1

Solution:

i)

We have to check dependent or independent of two variables Political Affiliation and Opinion on Tax Reform.

Doing a Chi-square test we have to check.

The null and alternative hypothesis is

H0: There is independence between Political Affiliation and Opinion on Tax Reform.

H1: There is the dependency between Political Affiliation and Opinion on Tax Reform.

ii)

Test statistic is

O: Observed frequency

E: Expected frequency.

E = ( Row total*Column total) / Grand total

Degrees of freedom = ( Number of rows - 1)*(Number of columns - 1) = ( 2 - 1 ) ( 3 - 1 ) = 1 2 = 2

Level of significance = 0.01

Critical value = 9.210 ( Using chi-square table)

Test statistic > Critical value we reject null hypothesis.

Conclusion: There is the dependency between Political Affiliation and Opinion on Tax Reform.