Do age groups and planned Facebook time have independent distributions? Which test is appropriate?

Do age groups and planned Facebook time have independent distributions? Which test is appropriate?

• A. Chi-square test of independence with 4 degrees of freedom
• B. Chi-square test of independence
• C. Fisher's exact test
• D. ANOVA

Answer: (B)

Testing whether two categorical variables have independent distributions means checking if knowing someone’s age group changes the distribution of their planned Facebook time (and vice versa). The standard way to do this is the chi-square test of independence. It looks at a contingency table of counts for each combination of age group and time category and compares the observed counts to what would be expected if the variables were independent. A large difference between observed and expected counts suggests an association between age and planned Facebook time. The exact degrees of freedom depend on the number of categories in each variable (they’re calculated as (rows−1)×(columns−1), not a fixed number). Fisher’s exact test is an alternative for very small samples, especially in 2×2 tables, while ANOVA is used for comparing means across groups when the outcome is continuous, not for testing independence of two categorical distributions.

Testing whether two categorical variables have independent distributions means checking if knowing someone’s age group changes the distribution of their planned Facebook time (and vice versa). The standard way to do this is the chi-square test of independence. It looks at a contingency table of counts for each combination of age group and time category and compares the observed counts to what would be expected if the variables were independent. A large difference between observed and expected counts suggests an association between age and planned Facebook time. The exact degrees of freedom depend on the number of categories in each variable (they’re calculated as (rows−1)×(columns−1), not a fixed number). Fisher’s exact test is an alternative for very small samples, especially in 2×2 tables, while ANOVA is used for comparing means across groups when the outcome is continuous, not for testing independence of two categorical distributions.