In a study examining four bathroom stalls, which statistical test would determine if stalls are used with equal frequency?

In a study examining four bathroom stalls, which statistical test would determine if stalls are used with equal frequency?

• A. Chi-square goodness-of-fit
• B. Chi-square test of independence
• C. Paired t-test
• D. One-way ANOVA

Answer: (A)

You’re assessing whether four categories (the stalls) are used as often as each other. That means you’re comparing observed counts in each stall to what you’d expect if usage were equal across all stalls. The right approach is a chi-square goodness-of-fit test. You set the expected count for each stall to be the total number of uses divided by four, then compute the chi-square statistic across the four stalls. With degrees of freedom equal to the number of categories minus one (three), you see whether the observed distribution matches the equal-usage expectation. A non-significant result suggests no evidence against equal usage; a significant result indicates some stalls are used more or less frequently. This test is appropriate because it handles one categorical variable with multiple categories and checks how the observed frequencies align with a specified (equal) distribution. The other tests don’t fit: the chi-square test of independence looks for a relationship between two categorical variables, not whether one categorical distribution is uniform; the paired t-test compares means of paired continuous data; and one-way ANOVA compares means of a continuous outcome across groups.

You’re assessing whether four categories (the stalls) are used as often as each other. That means you’re comparing observed counts in each stall to what you’d expect if usage were equal across all stalls.

The right approach is a chi-square goodness-of-fit test. You set the expected count for each stall to be the total number of uses divided by four, then compute the chi-square statistic across the four stalls. With degrees of freedom equal to the number of categories minus one (three), you see whether the observed distribution matches the equal-usage expectation. A non-significant result suggests no evidence against equal usage; a significant result indicates some stalls are used more or less frequently.

This test is appropriate because it handles one categorical variable with multiple categories and checks how the observed frequencies align with a specified (equal) distribution. The other tests don’t fit: the chi-square test of independence looks for a relationship between two categorical variables, not whether one categorical distribution is uniform; the paired t-test compares means of paired continuous data; and one-way ANOVA compares means of a continuous outcome across groups.