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t‑Test Calculator Guide — One‑Sample, Two‑Sample, Paired — GetCalcMaster

t-test workflow and formulas: one-sample, two-sample, and paired t-tests. Includes degrees of freedom, assumptions, and links to the t critical values table.

A t-test compares means while estimating variability from the sample. It’s used when σ is unknown and you’re working with (approximately) normal errors or sufficiently large samples.

Open Statistics Calculator Use Notebook Guides

Important: Educational. Choose the test variant (equal-variance vs Welch vs paired) that matches your design and assumptions.

What this calculator is

The Statistics Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.

Key features

Explains which t-test matches which design
Shows the core t statistic and degrees of freedom (df)
Links to the t table (critical values) for quick checks
Highlights assumptions and common failure modes

Formula

One-sample:  t = (x̄ - μ0) / (s / sqrt(n)),   df = n-1

Two-sample (equal variances):
t = (x̄1 - x̄2) / (s_pooled * sqrt(1/n1 + 1/n2)),   df = n1+n2-2
s_pooled = sqrt(((n1-1)s1^2 + (n2-1)s2^2)/(n1+n2-2))

Paired:  t = (d̄) / (s_d / sqrt(n)),   df = n-1   (where d are paired differences)

Quick examples

Two-sample t-test pairs naturally with Cohen’s d (standardized mean difference).
With small n, assumptions matter more; check plots or use robust alternatives if needed.
t critical values approach z critical values as df → ∞.

How to use it (quick steps)

Choose the correct design: one-sample, two-sample (independent), or paired.
Compute the relevant mean(s) and standard deviation(s).
Compute the t statistic and df.
Get a p-value from the t distribution (or compare to t critical values).
Report the estimate (mean difference) with a confidence interval and effect size.