Unpaired t-test
The unpaired (or independent samples) t-test compares two independent sample means using t = (x̄₁ - x̄₂) / SE, where SE = √[s²ₚ(1/n₁ + 1/n₂)] and s²ₚ is the pooled variance. It assumes both samples are normally distributed with equal variances. Degrees of freedom = n₁ + n₂ - 2.
Real World
Researchers comparing average GCSE scores between two different teaching methods use an unpaired t-test because each student appears in only one group — the samples are entirely independent of each other.
Exam Focus
State all three assumptions (independence, normality, equal variances) explicitly; each is a potential mark in 'check assumptions' questions.
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