In the study of school goals among students in grades 4–6, what test determines if grade level is related to the most desired school goal (make good grades, be popular, be good at sports)?

In the study of school goals among students in grades 4–6, what test determines if grade level is related to the most desired school goal (make good grades, be popular, be good at sports)?

• A. Chi-square goodness-of-fit
• B. ANOVA
• C. Chi-square test of independence
• D. Fisher's exact test

Answer: (C)

When you want to see whether two categorical factors relate to each other, use the chi-square test of independence. Here, both grade level (4th, 5th, 6th) and the most desired school goal (make good grades, be popular, be good at sports) are categories, so you arrange the data in a contingency table and ask: are the proportions of students choosing each goal different across grades, or are they about the same regardless of grade? The chi-square test checks whether the observed counts differ from what would be expected if grade level and goal choice were independent. A significant result means there is an association between grade level and the preferred goal. Why this fits better than the others: chi-square goodness-of-fit looks at whether a single categorical variable fits a specified distribution, not at the relationship between two variables. ANOVA compares averages of a numeric outcome across groups, which isn’t our setup since both variables are categorical. Fisher’s exact test is an exact alternative for small samples, typically used for 2x2 tables; with three grades and three goals, the standard approach is the chi-square test of independence.

When you want to see whether two categorical factors relate to each other, use the chi-square test of independence. Here, both grade level (4th, 5th, 6th) and the most desired school goal (make good grades, be popular, be good at sports) are categories, so you arrange the data in a contingency table and ask: are the proportions of students choosing each goal different across grades, or are they about the same regardless of grade? The chi-square test checks whether the observed counts differ from what would be expected if grade level and goal choice were independent. A significant result means there is an association between grade level and the preferred goal.

Why this fits better than the others: chi-square goodness-of-fit looks at whether a single categorical variable fits a specified distribution, not at the relationship between two variables. ANOVA compares averages of a numeric outcome across groups, which isn’t our setup since both variables are categorical. Fisher’s exact test is an exact alternative for small samples, typically used for 2x2 tables; with three grades and three goals, the standard approach is the chi-square test of independence.