📊Two-sample t-Test
The t-test determines whether the means of two groups are statistically different. The independent (two-sample) t-test compares two separate groups; the paired t-test compares the same subjects under two conditions. Developed by William Gosset ('Student') at Guinness Brewery.
- 1t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)
- 2x̄ = group mean · s² = variance · n = sample size
- 3df calculated by Welch-Satterthwaite equation
- 4Compare t-statistic to t-distribution at given df and α
Group 1: mean=10, SD=2, n=20 · Group 2: mean=8, SD=2.5, n=20=t = 2.94 · p ≈ 0.005 → significantReject null hypothesis at p<0.05
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Fun Fact
William Gosset published the t-test in 1908 under the pseudonym 'Student' because Guinness employees were forbidden from publishing — they feared revealing trade secrets.
References
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