Chi-Square Test for Independence

Posted: August 27th, 2021

Chi-Square Test for Independence

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Chi-Square Test for Independence

The Chi-square test of independence is a statistical test applied in determining the existence of a significant relationship between two categorical variables. In this paper, two Chi-Square Tests are performed on CongressionalVotes.xlsx data. The objective is to test if the party and vote for a balanced budget are independent. A 0.05 level of significance is applied in implementing the test. Thus, the test statistic and p-value are calculated to help reach the decision based on the hypothesis.

Hypothesis Specification

The purpose of the test is to evaluate whether parties and votes for a balanced budget are independent. Hence the following hypothesis is used:

Null Hypothesis, H0:Party and Votes for the balanced budget are independent

Alternative Hypothesis, HA: Party and Votes for the balanced budget are not independent.

Chi-Square Test

Chi-Square Test 1

The first assessment tests whether votes fora balanced party budget between Republican and Democrats are independent based on the following hypothesis;

H0: Votes for the balanced budget are independent

HA: Votes for a balanced budget are not independent.

The analysis (See Excel Worksheet-Chi-Sq. Test 1) shows that the calculated Chi-Square (Stat) is more significant than Chi-Square (Critical), hence reject Null Hypothesis (H0). It thus implies the votes for a balanced budget between Republicans and Democrats are dependent.

Chi-Square Test 2

The second assessment tests whether votes for bipartisan party budget is independent based on the following hypothesis;

H0: Votes for bipartisan party budgets are independent

HA: Votes for bipartisan party budgets are independent

The analysis (See Excel Worksheet-Chi-Sq. Test 2) shows that the calculated Chi-Square (Stat) is more significant than Chi-Square (Critical), hence reject Null Hypothesis (H0). It thus implies that the bipartisan budget for parties is not independent; it is dependent. 

Conclusion

The analysis demonstrates that whether parties have a balanced or bipartisan budget, none is independent at the 0.05 significance level.