Question 26

A chi-square test for independence is used to determine whether the values of one categorical variable are related to the values of another categorical variable.

A chi-square test for independence assesses the relationship between two categorical variables to determine if they are independent of one another.

A) Whether two populations have the same mean for a single numerical variable

This option is incorrect as it pertains to a different statistical test, specifically the t-test, which evaluates whether there is a significant difference between the means of two groups. The chi-square test for independence does not measure means or numerical variables.

B) Whether the values of one categorical variable are related to the values of another categorical variable

This option is correct because the chi-square test for independence specifically examines the association between two categorical variables to determine if a relationship exists. It analyzes the frequency counts of the categories to assess independence.

C) Whether categories of a single variable are equally represented in a distribution

This option refers to the chi-square goodness-of-fit test, which evaluates if the observed distribution of a single categorical variable fits a specified distribution. It does not address the relationship between two variables, making it incorrect in this context.

D) Whether there is a linear association between two quantitative variables

This option is incorrect, as it describes a correlation test, such as Pearson’s correlation coefficient, which is used for examining linear relationships between two continuous variables. The chi-square test does not apply to quantitative variables or linear associations.

Conclusion

The chi-square test for independence is specifically designed to analyze the relationship between two categorical variables, making option B the definitive correct answer. Other options either describe different statistical tests or address aspects that do not apply to the chi-square test, highlighting the unique purpose of this statistical method.