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Difficulty: MediumInferential Statistical Tests

A hospital epidemiology department is analyzing an outbreak of Burkholderia cepacia bacteremia in a neonatal intensive care unit. They suspect that a specific lot of contaminated ultrasound gel may be the source. The investigators review the medical records of 25 neonates to compare the infection rate between those who were exposed to the suspected gel lot (n = 12) and those who were not exposed (n = 13). Overall, 4 of the neonates developed bacteremia. When the investigators organize the exposure and outcome data into a 2x2 contingency table, they calculate that the expected frequency in one of the table cells is 1.9. Which of the following is the most appropriate statistical test to evaluate the association between exposure to the suspected gel lot and the development of bacteremia?

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

Answer

Fisher's exact test is the correct statistical method for comparing two categorical variables when expected cell counts are small (less than 5).
The study aims to determine the association between two categorical variables (exposure to a specific gel lot and development of bacteremia) across two independent groups. While the Pearson chi-square test is the standard test for evaluating differences in proportions between independent groups, it assumes that the expected frequency of each cell in the contingency table is at least 5. Because the expected cell frequency in this scenario is 1.9, this assumption is not met. Therefore, the exact probability must be calculated using Fisher's exact test.

Step-by-Step Solution

1
Identify the independent and dependent variables in the study design.
The independent variable is exposure to the ultrasound gel lot (categorical: exposed vs. unexposed), and the dependent variable is the development of bacteremia (categorical: yes vs. no).
Determining the types of variables is the first step in selecting the correct statistical test.
2
Select a test for comparing two categorical variables between independent groups.
The options for this scenario are typically the Pearson chi-square test or Fisher's exact test.
Both tests evaluate the association between categorical variables in independent samples.
3
Evaluate the sample size assumptions for the selected tests.
The scenario explicitly states that the expected frequency in one of the cells is 1.9. Since this is less than 5, the assumptions for the chi-square test are violated, making Fisher's exact test the required method.
The chi-square test is an approximation that becomes inaccurate with small expected frequencies, whereas Fisher's exact test calculates the exact probability.

Key Concept

Fisher's exact test is used in place of the Pearson chi-square test to evaluate the association between two independent categorical variables when the sample size is small, specifically when the expected frequency in any cell of a 2x2 contingency table is less than 5.
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Topics

Inferential Statistical Tests

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