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Difficulty: MediumInferential Statistical Tests

A hospital epidemiology team is investigating a localized cluster of carbapenem-resistant *Acinetobacter baumannii* (CRAB) infections in an intensive care unit. An independent case-control study is designed to evaluate whether prior exposure to a specific shared diagnostic equipment cart is associated with the infection. The study includes 8 patients with CRAB (cases) and 12 patients without CRAB (controls) who were in the unit during the same period. Among the 8 cases, 6 were exposed to the equipment cart. Among the 12 controls, 3 were exposed to the equipment cart. The researchers wish to determine if there is a statistically significant association between equipment exposure and CRAB infection. Which of the following is the most appropriate statistical test to analyze these study data?

  1. Fisher's exact testAnswer
  2. B
    Pearson's chi-square test
  3. C
    McNemar's test
  4. D
    Unpaired Student's t-test
  5. E
    Mann-Whitney U test

Answer

Fisher's exact test
The study aims to evaluate the association between two binary categorical variables (CRAB infection status and equipment exposure) across two independent groups. To determine statistical significance for a 2x2 contingency table, either the chi-square test or Fisher's exact test is used. However, because the sample sizes are small, the expected cell frequencies must be checked. The expected frequency for an exposed case is calculated as (Total Exposed × Total Cases) / Grand Total = (9 × 8) / 20 = 3.6. Because at least one expected cell frequency is less than 5, Fisher's exact test is required.

Step-by-Step Solution

1
Identify the variable types in the study.
The independent variable is clinical status (Case vs. Control, which is nominal/binary). The dependent variable is equipment exposure (Exposed vs. Unexposed, which is nominal/binary).
Knowing that the data consists of two binary categorical variables narrows the appropriate tests down to Chi-square, Fisher's exact, or McNemar's test.
2
Determine whether the samples are independent or paired.
The cases and controls are two separate, independent groups of patients; there is no indication of 1:1 matching.
This rules out McNemar's test, which is reserved for dependent (paired) samples.
3
Calculate the expected cell frequencies to determine if Chi-square assumptions are met.
Total N = 20. Total exposed = 9, total unexposed = 11. Total cases = 8, total controls = 12. Expected frequency for exposed cases = (9 × 8) / 20 = 3.6. Since 3.6 < 5, the assumption is violated.
When the expected frequency of any cell in a 2x2 contingency table is less than 5, Pearson's chi-square test is invalid, and Fisher's exact test must be used.

Key Concept

Selection of statistical tests for categorical data with small sample sizes
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Topics

Inferential Statistical Tests

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