8.12:
Hypothesis Test for Test of Independence
Consider a dataset on alcohol consumption and accident fatality. A hypothesis test is performed to establish whether the two variables are independent. In other words, is there a relationship between alcohol consumption and higher accident fatality?
The null hypothesis states that alcohol consumption and accident fatalities are independent events, while the alternative hypothesis states the contrary.
The product of the row total and column total, divided by the sum of all the frequencies, gives the expected frequency for each table entry.
Using the expected and observed values, calculate the chi-square test statistic.
Next, with the help of a chi-square table, determine the critical value separating an area of 0.05 in the right tail with one degree of freedom.
Since the test statistic is larger than the critical value and falls within the critical region, the null hypothesis – that there is no relationship between alcohol consumption and road accident fatality – is rejected.
Thus, at a 5% level of significance, there is sufficient evidence to conclude that alcohol consumption and accident fatality are dependent variables.
8.12:
Hypothesis Test for Test of Independence
The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
H0: The two variables (factors) are independent.
H1: The two variables (factors) are dependent
First, one identifies the observed frequencies and calculates the expected frequencies. The expected frequency of each entry is obtained by multiplying the row total and column total and dividing it by the sum of all the frequencies. Then the test statistic is calculated using observed frequency values from the contingency tables and the calculated expected frequencies. Then with the help of the chi-square table, the critical values in a one-tailed test with suitable confidence levels are calculated. If the test statistic is larger than the critical value and falls in the critical region, the null hypothesis is rejected; otherwise, it is accepted.
This text is adapted from Openstax, Introductory Statistics, Section 11.5, Comparison of the Chi-Square Tests.