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Welch's t-testFree in-browser calculator

General Stats Calculator.

Welch's t-test with Cohen's d and Pearson correlation with Fisher z CI. Enter raw data or summary statistics. Data never leaves your browser.

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Validated2026-04-05
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When to use

  • Compare means between two independent groups using Welch's t-test
  • Assess linear association between two continuous variables with Pearson correlation
  • Report effect sizes (Cohen's d or R-squared) with confidence intervals
  • Generate APA-style methods paragraphs for basic statistical analyses
  • Analyze data from published summary statistics (n, mean, SD) when raw data is unavailable

Do not use for

  • Paired or repeated-measures designs — a paired t-test or repeated-measures ANOVA is needed
  • More than two groups — use ANOVA (not available in this tool)
  • Non-normal data with small samples — consider a non-parametric test (Mann-Whitney U)
  • Method comparison / agreement analysis — use the Method Comparison Analyzer

Always use Welch's t-test as the default

Welch's t-test does not assume equal variances and performs well even when variances are equal. Student's t-test is only slightly more powerful under strict equal-variance conditions, which are rarely verifiable in practice.

Report effect size, not just p-value

A statistically significant p-value tells you the effect is unlikely to be zero, but not whether the effect is meaningful. Always report Cohen's d (for t-tests) or R-squared (for correlation) with confidence intervals.

Fisher z transformation is essential for correlation CIs

The sampling distribution of Pearson r is skewed, especially when |r| is large. Computing a CI directly on r gives inaccurate coverage. The Fisher z transformation normalizes the distribution for proper CI computation.

Correlation does not imply causation

Pearson r measures linear association only. A strong correlation can be driven by confounders, restricted range, or outliers. Always inspect a scatter plot and consider the study design before interpreting r as evidence of a relationship.

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Method

Welch's t-test uses the Welch-Satterthwaite degrees of freedom approximation, which does not assume equal variances. Cohen's d is computed as the mean difference divided by pooled SD, with CI from the noncentral t distribution. Pearson correlation uses the Fisher z transformation (z = 0.5 ln((1+r)/(1-r))) for CI computation, then back-transforms to the r scale. All calculations run client-side in the browser.

2

Validated

Last validated 2026-04-05. Calculations are designed for planning and documentation support; verify procurement decisions against manufacturer specifications or institutional SOPs.

3

How to cite

How to Cite

ConductScience General Stats Calculator (v1.0). ConductScience, Inc. 2026. Available at: https://conductscience.com/tools/general-stats-calculator

Welch BL. The generalization of "Student's" problem when several different population variances are involved. Biometrika. 1947;34(1-2):28-35. doi:10.1093/biomet/34.1-2.28

Statistical Testing Fundamentals

Statistical hypothesis testing follows a standard workflow:

1. State hypotheses: H₀ (no difference/association) vs H₁ (difference/association exists) 2. Choose test: Based on data type, design, and assumptions 3. Compute test statistic: t, F, χ², or r 4. Report p-value and effect size: The p-value alone is insufficient — always report the effect size and confidence interval

Modern reporting standards (APA, CONSORT) require: test statistic, degrees of freedom, p-value, effect size, and CI. This tool generates all of these automatically.

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