Pooled vs Unpooled Variance

Statistics · Axiom Academy

LESSON Pooled vs Unpooled Variance Understanding when and how to pool variances in two-sample t-tests Pooled variance combines the variance estimates from two independent samples into a single, weighted estimate of their common population variance. More statistical power: A single pooled estimate uses more information Simpler calculations: One variance estimate instead of two Better precision: When the assumption holds, pooled estimates are more accurate 2. The Pooled Variance Formula The pooled variance s²ₚ is a weighted average of the two sample variances, where the weights are the degrees of freedom: n₁, n₂: Sample sizes for groups 1 and 2 s₁², s₂²: Sample variances for groups 1 and 2 (n₁-1), (n₂-1): Degrees of freedom (weights) (n₁+n₂-2): Total degrees of freedom Example calculation: If Group 1 has n₁=10, s₁²=25 and Group 2 has n₂=15, s₂²=30: 3. The Equal Variance Assumption Pooled variance is only appropriate when we can reasonably assume homogeneity of variance (equal population variances). What happens if this assumption is violated? The pooled t-test becomes less accurate Type I error rates (false positives) increase Confidence intervals may not have correct coverage The problem worsens with unequal sample sizes 4. Pooled vs Unpooled: When to Use Each Welch's t-test formula (unpooled): 5. Testing for Equal Variances Before choosing between pooled and unpooled methods, we can formally test the equal variance assumption. Common tests for equal variance:

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