A hospital in Mumbai conducted a study to compare the mean systolic blood pressure reduction (in mmHg) following two antihypertensive regimens. Group A (n=25) received atenolol monotherapy with mean reduction of 18 mmHg (SD=6 mmHg), while Group B (n=25) received atenolol plus amlodipine with mean reduction of 24 mmHg (SD=7 mmHg). Both groups were independent, and the data were normally distributed. The researcher wants to test if the combination therapy produces significantly greater blood pressure reduction. What is the appropriate test and the most likely outcome at p<0.05?

Explanation

## Unpaired t-Test for Continuous Data Comparison **Key Point:** When comparing means of a continuous variable (systolic BP reduction in mmHg) between two independent groups with normally distributed data, the unpaired (independent samples) t-test is the appropriate choice. ### Conditions Met for Unpaired t-Test | Criterion | Status | Justification | |---|---|---| | **Data Type** | Continuous | Blood pressure reduction in mmHg | | **Independent Groups** | Yes | Different patients in each group (n=25 each) | | **Normality** | Yes | Explicitly stated in stem | | **Sample Size** | Adequate | n=25 in each group (>30 is ideal, but 25 is acceptable) | | **Variance Homogeneity** | Likely | SD values similar (6 vs. 7 mmHg) | ### Unpaired t-Test Formula $$t = \frac{\bar{X}_1 - \bar{X}_2}{SE_{diff}}$$ where $SE_{diff} = \sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$ ### Calculation of Effect Size - **Mean difference:** 24 − 18 = 6 mmHg - **Pooled SD:** $\sqrt{\frac{(25-1) \times 6^2 + (25-1) \times 7^2}{25+25-2}} \approx 6.5$ mmHg - **Standard error of difference:** $\sqrt{\frac{6.5^2}{25} + \frac{6.5^2}{25}} \approx 1.84$ mmHg - **t-statistic:** $\frac{6}{1.84} \approx 3.26$ - **Degrees of freedom:** 25 + 25 − 2 = 48 - **Critical value at p<0.05 (two-tailed):** ≈ 2.01 **High-Yield:** Since calculated t (3.26) > critical t (2.01), the result is statistically significant at p<0.05. ### Why Unpaired t-Test? 1. **Continuous outcome:** BP reduction is measured on a continuous scale 2. **Two independent groups:** Different patients, not paired measurements 3. **Normal distribution:** Assumption satisfied 4. **Parametric test:** More powerful than non-parametric alternatives when assumptions are met **Clinical Pearl:** A 6 mmHg greater reduction with combination therapy is both statistically significant and clinically meaningful (target BP reduction in hypertension is typically 10-20 mmHg). **Mnemonic:** **TINCT** — **T**wo groups → t-test; **I**ndependent → unpaired t-test; **N**ormal distribution → parametric test; **C**ontinuous data; **T**est the difference in means