Independent Samples t-test Calculator
Run a Welch independent-samples t test from summary statistics.
Enter N, mean, and sample SD for two independent groups to calculate the mean difference, Welch t, approximate degrees of freedom, and two-tailed p value.
Tool area
Formula and calculation
t = (M₁ − M₂) / √(s₁²/n₁ + s₂²/n₂)
Degrees of freedom use the Welch–Satterthwaite approximation; p is calculated from the t distribution. s₁ and s₂ are sample SDs.
Educational applications
Use for means from two independent groups. Check independence, outliers, and distribution shape, especially with small or heavily skewed samples. Statistical significance is not the same as educational importance.
APA / research reporting tip
APA example: “Group A (M = 78.4, SD = 8.2) scored higher than Group B (M = 73.1, SD = 9.5), Welch’s t(59.6) = 2.36, p = .022.” Formal reports should add a confidence interval and effect size.
How to use
- Enter sample size, mean, and sample SD for both groups.
- Confirm observations are independent between groups.
- Interpret the difference, t, df, and two-tailed p together.
Use cases
- Compare mean scores under two teaching methods.
- Compare treatment and control group means.
- Check formal software output from summary statistics.
Content and verification review:
How to verify a Independent Samples t-test Calculator result before relying on it
This section covers the Welch t-test math behind the page’s default two groups, and confirms all seven numbers the page actually displays: mean difference, t, df, two-tailed p, standard error, the 95% confidence interval, and Hedges’ g.
Check the mean difference, t, df, and p against the default groups
The page loads with Group 1: N = 30, mean = 78.4, SD = 8.2, and Group 2: N = 32, mean = 73.1, SD = 9.5. Mean difference = 78.4 − 73.1 = 5.3. The Welch t value comes out to about 2.356, the Welch–Satterthwaite degrees of freedom to about 59.61, and the two-tailed p value to about .022 — these four numbers appear first in the results.
The standard error, confidence interval, and Hedges’ g are also shown
Beyond the mean difference, t, df, and p, the script also computes a standard error, a 95% confidence interval (about [0.80, 9.80] for the default numbers), and a Hedges’ g effect size (about 0.588), and all three render right after the first four values. The confidence interval uses a critical value from the Welch–Satterthwaite degrees of freedom, while Hedges’ g switches to the pooled standard deviation with a small-sample correction — a different variance assumption from Welch’s t itself, which is the standard convention for reporting an effect size alongside a Welch test, not an inconsistency.
Equal means and very small samples are still accepted, with results that need extra care
Set both group means to the same number and Calculate still runs, returning t = 0 and p = 1 — a valid “no difference detected” result, not an error. Reduce both sample sizes to the minimum accepted value of 2 (each group requires an integer greater than 1) and the tool still produces a t, df, and p, but the degrees of freedom collapse to a very small number, and a t value that would look significant with large samples can correspond to a much larger, non-significant p value at df = 2 — small-sample results here need more caution before quoting them.
Acceptance checklist
- Both sample sizes are whole numbers greater than 1, and both standard deviations are entered as sample SDs greater than 0.
- The mean difference shown has been hand-checked as Group 1 mean minus Group 2 mean.
- The standard error, 95% confidence interval, and Hedges’ g shown on the page have been checked; the confidence interval uses the Welch degrees of freedom while Hedges’ g uses the pooled SD — different assumptions, both standard practice.
- A t = 0, p = 1 result from equal group means, or a very small df from tiny samples, is read as a real (if underpowered) result, not a broken calculation.
FAQ
- Why use Welch’s t test?
- It does not require equal group variances and is generally more robust than the pooled-variance version.
- Can I enter population SDs?
- This calculator expects sample standard deviations.
- Does p < .05 mean a large effect?
- No. p also depends on sample size; inspect the difference, confidence interval, and effect size.
Privacy & local processing
🔒 This tool runs entirely in your browser. No data is uploaded to any server.
All input and calculations stay in your browser and are not uploaded to FunnyTools.
Trust & usage note
This tool runs mainly in your browser. Your input is not actively uploaded to a server. Avoid entering highly sensitive data. Results are for reference only.
Disclaimer
This tool is for teaching and preliminary estimates. It does not replace formal statistical software or professional judgment. Verify the data, research design, and assumptions before reporting results.
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