How do I run a t-test online for free?

Paste your two groups of numbers into Stats Lab, choose a two-sample t-test, and it returns the t statistic, degrees of freedom, an exact p-value, the effect size and a plain-language interpretation.

How is a p-value calculated?

Stats Lab computes exact p-values from the t, chi-square and F distributions using the regularized incomplete beta and gamma functions — the same methods statistical software uses — not lookup tables.

Which statistical test should I use?

Use a one-sample t-test to compare a mean to a target, a two-sample t-test to compare two groups, paired t for before/after, chi-square for categorical tables, and correlation or regression for relationships between numbers.

Statistics Calculator — t-tests, chi-square, correlation, CIs, plain-language results

Which test do you need?

Your data — numbers separated by commas, spaces or new lines

Blanks and stray text are ignored. Everything runs in your browser — nothing is uploaded.

How this works — the formulas used

Descriptives. Mean x̄ = Σx / n; sample SD s = √(Σ(x − x̄)² / (n − 1)); SEM = s / √n. Quartiles use linear interpolation between order statistics (the same method as spreadsheets and NumPy's default).

One-sample t. t = (x̄ − μ₀) / (s / √n), df = n − 1. Cohen's d = (x̄ − μ₀) / s.

Two-sample t. Welch (default): t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂) with Welch–Satterthwaite df = (s₁²/n₁ + s₂²/n₂)² / [ (s₁²/n₁)²/(n₁−1) + (s₂²/n₂)²/(n₂−1) ]. Pooled: sₚ² = [(n₁−1)s₁² + (n₂−1)s₂²] / (n₁+n₂−2), t = (x̄₁ − x̄₂) / (sₚ√(1/n₁ + 1/n₂)), df = n₁+n₂−2. Cohen's d always uses the pooled SD.

Paired t. A one-sample t on the pairwise differences against 0; d = mean difference / SD of differences.

t p-values. Two-tailed p = I_x(df/2, 1/2) with x = df/(df + t²), where I is the regularized incomplete beta function, computed with a Lentz continued fraction and a Lanczos log-gamma. One-tailed p is half of that, assuming the effect is in the hypothesised direction. Critical t values (for CIs) are found by numerically inverting this CDF with bisection.

Chi-square. Expected count E = (row total × column total) / N; χ² = Σ(O − E)²/E; df = (rows−1)(cols−1); p = Q(df/2, χ²/2), the regularized upper incomplete gamma function (series + continued fraction). Yates' correction (optional, 2×2 only) uses (|O − E| − 0.5)²/E. Effect size: φ = √(χ²/N) for 2×2, Cramér's V = √(χ² / (N × min(r−1, c−1))) otherwise.

Correlation & regression. Pearson r = S_xy / √(S_xxS_yy); significance via t = r√((n−2)/(1−r²)) with df = n−2. Spearman ρ ranks both variables (average ranks for ties) and applies the same machinery. OLS: slope b = S_xy/S_xx, intercept a = ȳ − b·x̄, R² = r².

Proportions. One-proportion z test: z = (p̂ − p₀) / √(p₀(1−p₀)/n), p-value from the normal CDF (computed via the incomplete gamma erfc). 95% CI uses the Wilson score interval: (p̂ + z²/2n ± z√(p̂(1−p̂)/n + z²/4n²)) / (1 + z²/n).

Confidence intervals for means use x̄ ± t_crit × SEM at 95%.

Everything runs in your browser — your data never leaves this device. This tool is for learning and quick checks; for publication, confirm results in a statistics package.