A nutrition researcher in Mumbai is analyzing data from a randomized controlled trial comparing the mean hemoglobin levels (in g/dL) of 45 anemic women receiving iron supplementation vs. 45 women receiving placebo. Both groups had baseline hemoglobin measured and post-intervention hemoglobin measured after 3 months. The researcher wants to determine if there is a significant difference in the change in hemoglobin between the two groups. What is the most appropriate next step in statistical analysis?

Question

Accepted Answer

B. Perform an independent samples t-test comparing the mean change in hemoglobin between the two groups. ## Comparing Mean Changes Between Independent Groups

**Key Point:** When comparing the mean change (or difference) in a continuous variable between two independent groups, an independent samples t-test is the appropriate choice.

### Study Design Analysis

| Feature | Details |
| --- | --- |
| **Outcome variable** | Hemoglobin change (continuous: g/dL) |
| **Independent variable** | Group (categorical: iron vs. placebo) |
| **Number of groups** | 2 (independent samples) |
| **Sample size per group** | 45 (adequate for t-test) |
| **Measurement** | Pre-post within each subject, but comparison is between groups |

### Calculation Approach

1. Calculate change score for each subject: Δ Hb = Post Hb − Baseline Hb
2. Compare mean Δ Hb between iron group and placebo group using independent samples t-test:

$$t = \frac{\bar{x}_1 - \bar{x}_2}{SE_{difference}}$$

where $SE_{difference} = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$

**High-Yield:** The key distinction is that you are comparing **between groups** (iron vs. placebo), not within a single group over time. This mandates independent samples t-test.

**Mnemonic:** **ICOT** — **I**ndependent groups → **C**ompare **O**utcome (continuous) **T**-test.

### Assumptions
- Continuous outcome (hemoglobin in g/dL) ✓
- Two independent groups ✓
- Approximately normal distribution of change scores (n = 45 allows CLT) ✓
- Homogeneity of variance (can be tested; Levene's test) ✓

Answer

A. Perform a two-way ANOVA with time and group as factors

Answer

C. Perform a chi-square test on the hemoglobin categories (mild, moderate, severe anemia)

Answer

D. Perform a paired t-test within each group separately and then compare p-values

Explanation

Comparing Mean Changes Between Independent Groups

Study Design Analysis

Calculation Approach

Assumptions

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Feature	Details
Outcome variable	Hemoglobin change (continuous: g/dL)
Independent variable	Group (categorical: iron vs. placebo)
Number of groups	2 (independent samples)
Sample size per group	45 (adequate for t-test)
Measurement	Pre-post within each subject, but comparison is between groups