Fisher t Test Calculator (Two Independent Samples)
Enter summary statistics for two groups. This tool computes the t-statistic, degrees of freedom, p-values, confidence interval, and a quick decision at your selected significance level.
Sample 1
Sample 2
Tip: Use the pooled option when group variances are reasonably similar. Use Welch when variance equality is doubtful.
What is a Fisher t test?
The Fisher t test is commonly used to compare the means of two independent groups. In many contexts, this refers to the classic pooled-variance Student t-test, where variances are assumed equal. You may also see people loosely use this label when they mean an independent-samples t-test more generally.
This calculator gives you both approaches:
- Pooled t-test (equal variances): the traditional Fisher/Student version.
- Welch t-test (unequal variances): safer when standard deviations are notably different.
When should you use this calculator?
Use it when you have two separate groups (e.g., treatment vs control, Group A vs Group B) and you want to test whether their population means differ. You can compute results quickly from summary data: mean, standard deviation, and sample size for each group.
Typical use cases
- A/B test score comparisons
- Clinical pilot studies with two arms
- Education outcomes between two classes
- Performance comparisons across two production methods
How the calculation works
The core test statistic is:
t = (x̄₁ − x̄₂) / SE
where SE is the standard error of the difference in means.
Pooled (equal-variance) version
For the pooled test, the combined variance estimate is:
sp2 = [ (n₁−1)s₁² + (n₂−1)s₂² ] / (n₁+n₂−2)
Then:
SE = √( sp2(1/n₁ + 1/n₂) ) and df = n₁ + n₂ − 2.
Welch (unequal-variance) version
For Welch’s test:
SE = √( s₁²/n₁ + s₂²/n₂ )
Degrees of freedom use the Welch–Satterthwaite approximation.
Interpreting your output
- t-statistic: standardized mean difference.
- Degrees of freedom (df): controls the t-distribution shape.
- Two-tailed p-value: probability of observing an effect this extreme if true difference is zero.
- 95% CI (or your selected α): plausible range for the mean difference.
- Decision: reject or fail to reject the null hypothesis at level α.
Assumptions checklist
- Two independent samples
- Outcome is approximately continuous
- No severe outliers (or robust handling in your workflow)
- For pooled test: group variances are reasonably similar
Quick practical guidance
If you are unsure about equal variances, run Welch by default. It is generally more robust and usually close to pooled results when variances are actually equal. Report your test type clearly in your write-up so readers know which assumptions were used.