In the context of the $\chi 2^{}$ Test for Independence, what does the test allow us to determine about the relationship between two categorical variables based on experimental observations?

• A. It allows us to determine whether there is a statistically significant association between the two categorical variables.
• B. It allows us to predict the value of one variable based on the other.
• C. It allows us to calculate the mean difference between two groups.
• D. It allows us to estimate the population variance from a sample.

Answer: (A)

Verified step by step guidance

1. Understand that the Chi Square Test for Independence is used to analyze the relationship between two categorical variables by comparing observed frequencies in a contingency table to expected frequencies under the assumption of independence.
2. Formulate the null hypothesis (\(H_0\)) which states that the two categorical variables are independent, meaning there is no association between them.
3. Calculate the expected frequency for each cell in the contingency table using the formula: \(E_{ij} = \frac{(\text{row total}_i)(\text{column total}_j)}{\text{grand total}}\).
4. Compute the Chi Square test statistic using the formula: \(\chi^2 = \sum \frac{(O_{ij} - E_{ij})^2}{E_{ij}}\), where \(O_{ij}\) is the observed frequency and \(E_{ij}\) is the expected frequency for each cell.
5. Compare the calculated \(\chi^2\) value to the critical value from the Chi Square distribution with appropriate degrees of freedom to determine if the association between the two variables is statistically significant.