Choose the t-test that matches one sample, independent groups, or paired observations; interpret the p-value alongside effect size and study design rather than as a stand-alone verdict.
T-Test Statistical Test Studio
Run one-sample, Welch, pooled Student or paired t-tests from raw observations or summary statistics. Keep the test statistic, exact p-value, confidence interval, standardized effect size, assumption diagnostics and reproducible code in one analysis instead of copying a p-value out of context.
Independent groups; Welch is the default when equal population variances should not be assumed.
Separate values with spaces, commas, semicolons, tabs or line breaks. Paired mode matches values by position.
Paired tests require raw pairs because the SD of within-pair differences cannot be reconstructed from separate group summaries.
Welch independent two-sample t test
H₀: μ₁ − μ₂ = 0
Result status
—t statistic
—degrees of freedom
—p-value
—standard error
—observed difference
Confidence interval
Effect size Hedges’ g
Interpret the estimate, uncertainty and study design together.
Calculated locally in your browser.
Raw-data context and model checks
These are transparent screening diagnostics, not automatic proofs that a t-test is valid. Sampling design, independence and the scientific meaning of pairing still require judgment.
Check
Observed
Interpretation boundary
Reproduce the analysis
The code reflects the same test choice, alternative, null difference and raw values. Summary-only analyses provide the explicit formula recipe because paired structure and raw-shape diagnostics are not recoverable from n/mean/SD alone.
Browser-local analysis history
Save up to 20 analysis states on this device. Export the history as JSON when you need a portable record; nothing is uploaded by this Studio.
Choose and report a t-test deliberately
Welch is the independent-sample default hereWelch’s t-test does not require equal population variances. The pooled Student option is still available when its equal-variance assumption is substantively justified.
Paired means paired by designUse paired mode for repeated or matched observations where row A and row B belong together. Equal sample sizes alone do not create a paired design.
Report estimation with probabilityKeep the observed difference, confidence interval and standardized effect size beside t, df and p. A threshold crossing is not a measure of importance or causation.
Plan power before collecting dataObserved post-hoc power mainly repackages the observed p-value. For planning, specify a meaningful effect to detect and use a prospective sample-size or power calculation.
Method references. The implementation follows the definitions used by R’s stats::t.test: one/two-sample, paired, one/two-sided alternatives, a hypothesized mean/difference, confidence level and Welch as the unequal-variance two-sample method. For independent data, raw and n/mean/SD workflows are both supported; paired analysis remains raw-pair only because the covariance structure matters.
A one-sample, independent-samples, and paired t-test answer different questions. Decide which observations are independent and whether measurements are naturally paired before looking at a p-value.
Interpret more than significance
A small p-value is not an effect size. Review the estimated difference, uncertainty or confidence interval, sample sizes, and the practical importance of the effect alongside the hypothesis test.
Assumptions
T-tests rely on assumptions about the sampling process and distribution of the relevant errors. Small samples, strong outliers, dependence, or unequal variances can change which method is appropriate.
Interpret statistical results in context
Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.
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