T-Test Calculator
Test whether a mean differs from a value, or whether two group means differ, from means, standard deviations and sample sizes.
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t-statistic
- Degrees of freedom
- P-value
- Standard error
- 95% confidence interval for the difference
- At α = 0.05
- Work
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How the t-Test Works
One sample: t = (x̄ − μ₀) ÷ (s ÷ √n), df = n − 1
Welch: t = (x̄₁ − x̄₂) ÷ √(s₁²/n₁ + s₂²/n₂), df = (s₁²/n₁ + s₂²/n₂)² ÷ [(s₁²/n₁)²/(n₁−1) + (s₂²/n₂)²/(n₂−1)]
Welch’s test doesn’t assume equal variances and is the default in R’s t.test.
Worked Example
Tips
t-tests assume roughly normal data (or large samples) and independent observations. For paired data (before/after on the same people), run a one-sample test on the differences with μ₀ = 0.