Which of the following is the correct condition for using an independent samples t-test instead of a Mann-Whitney U test?

Explanation

## Parametric vs Non-Parametric Tests **Key Point:** The independent samples t-test is a parametric test that requires specific assumptions about the underlying data distribution. ### Assumptions for Independent Samples t-test 1. **Normality**: Data in both groups must be approximately normally distributed 2. **Homogeneity of variance**: Variances in both groups should be equal (Levene's test checks this) 3. **Independence**: Observations must be independent 4. **Scale of measurement**: Data must be continuous (interval or ratio) ### When to Use t-test vs Mann-Whitney U | Criterion | t-test (Parametric) | Mann-Whitney U (Non-parametric) | |-----------|-------------------|--------------------------------| | Distribution | Normal | Non-normal or unknown | | Variance | Homogeneous | Can be unequal | | Sample size | Any (but normality assumed) | Especially useful for small n | | Data type | Continuous | Ordinal or continuous | | Power | Higher (if assumptions met) | Lower but robust | **High-Yield:** When data are normally distributed AND variances are homogeneous, the t-test is the appropriate choice and is more powerful than non-parametric alternatives. **Clinical Pearl:** In practice, the t-test is robust to minor violations of normality, especially with larger sample sizes (n > 30), but homogeneity of variance should always be assessed using Levene's test. **Tip:** Remember that unequal sample sizes do NOT violate t-test assumptions — normality and equal variances are the critical requirements.