A clinical trial compares the mean reduction in systolic blood pressure (mmHg) between two antihypertensive drugs in 35 hypertensive patients randomized to Drug X and 38 patients randomized to Drug Y. The data are normally distributed with unequal variances. Which test best discriminates whether the mean blood pressure reduction differs significantly between the two drugs?
A. Paired t-test
B. Chi-square test
C. Kruskal-Wallis test
D. Welch's t-test (unequal variance t-test)
Explanation
Selecting the Correct t-Test Variant
Data Characteristics
Key Point
Outcome: continuous (systolic BP reduction in mmHg)
Groups: two independent samples (Drug X vs. Drug Y)
Distribution: normal (parametric test appropriate)
Variances: unequal (critical discriminator)
Why Welch's t-Test?
High-YieldNEET PG
Welch's t-test (also called unequal variance t-test or Welch–Aspin test) is the appropriate choice when:
1.
Comparing means of two independent groups
2.
Data are approximately normally distributed
3.
Variances are unequal (heteroscedasticity)
4.
Sample sizes may be unequal (35 vs. 38 here)
Comparison of t-Test Variants
Table
Feature
Student's t-test
Welch's t-test
Variances
Equal
Unequal
Assumption
Homogeneity of variance
No homogeneity required
Robustness
Sensitive to variance inequality
Robust to variance inequality
Degrees of freedom
n₁ + n₂ − 2
Adjusted (Welch–Satterthwaite)
When to use
Variances similar
Variances differ
Clinical Pearl
Levene's test is used to assess equality of variances. If p < 0.05, variances are unequal → use Welch's t-test.
Welch's t-Test Formula
t=n1s12+n2s22xˉ1−xˉ2
where s12 and s22 are unequal sample variances.
Mnemonic
UNEQUAL VARIANCES → WELCH'S t — When variances differ, Welch corrects the degrees of freedom and standard error.
Practice similar questions
Sign up free to access AI-powered MCQ practice with detailed explanations and adaptive learning.
