In a study comparing the effectiveness of two malaria treatment regimens in rural India, researchers used chi-square test to analyze categorical outcomes. All of the following are correct regarding the chi-square test EXCEPT:

Question

Accepted Answer

C. The chi-square test can be used for both 2×2 contingency tables and larger (r×c) tables with the same formula and interpretation. ## Correct Answer Analysis

**High-Yield:** The chi-square test has specific conditions and limitations that determine when it can be validly applied.

### Conditions and Limitations of Chi-Square Test

| Condition | Details | Clinical Relevance |
|---|---|---|
| **Sample size requirement** | Expected frequency in each cell should be ≥ 5 | Small cells require Fisher's exact test or Yates' correction |
| **Independence** | Observations must be independent | Paired/matched data require McNemar's test |
| **Categorical data** | Data must be categorical (nominal or ordinal) | Cannot use for continuous data |
| **Formula variation** | 2×2 tables use simplified formula; larger tables use general formula | Both follow chi-square distribution but with different df |

### Why Option 0 (Correct Answer) is Wrong

**Key Point:** Option 0 claims that the chi-square test can be used for both 2×2 and larger (r×c) tables **with the same formula and interpretation**. This is **INCORRECT**:

**High-Yield:** While both 2×2 and r×c tables use the chi-square distribution, the **formulas differ**:

1. **2×2 contingency table:** Often uses a simplified formula or Yates' continuity correction:
   $$\chi^2 = \frac{N(ad - bc)^2}{(a+b)(c+d)(a+c)(b+d)}$$

2. **Larger (r×c) tables:** Use the general formula:
   $$\chi^2 = \sum \frac{(O - E)^2}{E}$$
   where O = observed frequency, E = expected frequency.

3. **Interpretation differences:** The degrees of freedom differ: 2×2 has df = 1, while r×c has df = (r−1)(c−1).

**Warning:** Saying "same formula" is a common trap. The computational approach differs, and the degrees of freedom are calculated differently.

### Why the Other Options Are Correct

1. **Option 1 (Expected frequencies < 5):** Correct. When any cell has expected frequency < 5, Fisher's exact test (for 2×2 tables) or Yates' continuity correction should be used.

2. **Option 2 (Independence & McNemar's test):** Correct. Chi-square assumes independence. For paired/matched categorical data, McNemar's test is the appropriate alternative.

3. **Option 3 (Degrees of freedom):** Correct. The degrees of freedom for chi-square in an r×c table is (r−1)×(c−1). For a 2×2 table, df = (2−1)×(2−1) = 1.

[cite:Park 26e Ch 12]

Answer

A. When expected frequencies in any cell are less than 5, Fisher's exact test or Yates' continuity correction should be considered as alternatives

Answer

B. The chi-square statistic follows a chi-square distribution with degrees of freedom equal to (number of rows − 1) × (number of columns − 1)

Answer

D. The chi-square test assumes independence of observations; if data are paired or matched, McNemar's test should be used instead

In a study comparing the effectiveness of two malaria treatment regimens in rural India, researchers used chi-square test to analyze categorical outcomes. All of the following are correct regarding the chi-square test EXCEPT:

Explanation

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