Examkin

Question

Difficulty: MediumInferential Statistical Tests

A clinical researcher is evaluating the relationship between smoking status and postoperative pulmonary complications following major abdominal surgery. A cohort of 450 adult patients is recruited. Patients are categorized based on their smoking status prior to surgery into three groups: never smokers, former smokers, and current smokers. Following surgery, patients are monitored for 30 days, and their respiratory outcomes are classified into three mutually exclusive categories: no complications, mild complications (requiring supplemental oxygen only), or severe complications (requiring reintubation or intensive care). The investigator plans to perform a statistical analysis to determine if there is a significant association between smoking status and the severity of postoperative pulmonary complications. Assuming all expected cell counts are greater than 5, the researcher sets up a contingency table for a Chi-square test of independence. What is the degrees of freedom for the test statistic in this analysis?

Answer: 4

Answer

4
The appropriate statistical analysis for comparing two categorical variables (smoking status and complication severity) is the Chi-square test of independence. The degrees of freedom for this test are calculated using the formula df=(r−1)×(c−1)df = (r - 1) \times (c - 1), where rr is the number of rows (categories of the first variable) and cc is the number of columns (categories of the second variable). With 3 smoking categories and 3 complication categories, df=(3−1)×(3−1)=2×2=4df = (3 - 1) \times (3 - 1) = 2 \times 2 = 4.

Step-by-Step Solution

1
Identify the appropriate statistical test and its degrees of freedom formula.
The test is a Chi-square test of independence, which uses the formula df=(r−1)×(c−1)df = (r - 1) \times (c - 1).
This formula is standard for evaluating contingency tables to determine how many values can vary freely while maintaining fixed marginal totals.
2
Determine the number of categories for each of the two variables.
Smoking status has 3 categories (r=3r = 3), and pulmonary complications has 3 categories (c=3c = 3).
Mapping the clinical study design to the statistical dimensions is necessary to populate the formula.
3
Calculate the degrees of freedom.
(3−1)×(3−1)=2×2=4(3 - 1) \times (3 - 1) = 2 \times 2 = 4.
Applying the variables to the correct statistical formula yields the final value.

Key Concept

Degrees of freedom for a Chi-square test of independence
Rate this question

Topics

Inferential Statistical Tests

More questions from this topic