A health professional sampled 100 patients from each of four major hospital emergency rooms to see if primary reasons for ER visits are similar across hospitals. Primary reasons: accident, illegal activity, illness, or other. What test evaluates whether the distribution across hospitals is the same?

A health professional sampled 100 patients from each of four major hospital emergency rooms to see if primary reasons for ER visits are similar across hospitals. Primary reasons: accident, illegal activity, illness, or other. What test evaluates whether the distribution across hospitals is the same?

• A. Chi-Square Test of Homogeneity
• B. ANOVA
• C. T-Test
• D. Regression Analysis

Answer: (A)

This question examines whether the pattern of primary ER visit reasons is the same across different hospitals, using a method suited for categorical data across multiple groups. You have a 4-by-4 table: four hospitals and four reason categories. The goal is to test if the distribution of reasons is identical across all hospitals. The appropriate approach is a chi-square test of homogeneity. The null hypothesis states that the distribution of categories is the same in every hospital; the alternative is that at least one hospital has a different distribution. To do the test, pool the data across all hospitals to get the overall category proportions, then compute expected counts for each hospital by multiplying its 100 patients by those overall proportions. Sum (observed − expected)² / expected across all cells to obtain the chi-square statistic, and compare it to a chi-square distribution with degrees of freedom (rows − 1) × (columns − 1) = (4 − 1) × (4 − 1) = 9. Why not the other options: ANOVA, T-test, or regression are designed for numerical outcomes or for assessing relationships between variables, not for comparing distributions of a categorical variable across groups. They don’t directly test whether the category distributions are the same across hospitals.

This question examines whether the pattern of primary ER visit reasons is the same across different hospitals, using a method suited for categorical data across multiple groups. You have a 4-by-4 table: four hospitals and four reason categories. The goal is to test if the distribution of reasons is identical across all hospitals.

The appropriate approach is a chi-square test of homogeneity. The null hypothesis states that the distribution of categories is the same in every hospital; the alternative is that at least one hospital has a different distribution. To do the test, pool the data across all hospitals to get the overall category proportions, then compute expected counts for each hospital by multiplying its 100 patients by those overall proportions. Sum (observed − expected)² / expected across all cells to obtain the chi-square statistic, and compare it to a chi-square distribution with degrees of freedom (rows − 1) × (columns − 1) = (4 − 1) × (4 − 1) = 9.

Why not the other options: ANOVA, T-test, or regression are designed for numerical outcomes or for assessing relationships between variables, not for comparing distributions of a categorical variable across groups. They don’t directly test whether the category distributions are the same across hospitals.