Calculator Inputs
Example Data Table
| Example | Mean 1 | Spread 1 | n1 | Mean 2 | Spread 2 | n2 | Test | Variance | Approximate Outcome |
|---|---|---|---|---|---|---|---|---|---|
| Training hours | 52.4 | 8.2 | 30 | 47.9 | 7.5 | 28 | T | Welch | Positive statistic with a small p-value |
| Process cycle time | 18.2 | 3.1 | 24 | 19.0 | 2.9 | 26 | T | Equal | Small negative statistic near zero |
Formula Used
Z test for two means
z = ((mean1 - mean2) - null difference) / sqrt((sigma1² / n1) + (sigma2² / n2))
Welch t test
t = ((mean1 - mean2) - null difference) / sqrt((s1² / n1) + (s2² / n2))
df = ((s1² / n1 + s2² / n2)²) / (((s1² / n1)² / (n1 - 1)) + ((s2² / n2)² / (n2 - 1)))
Pooled t test
sp² = [((n1 - 1)s1²) + ((n2 - 1)s2²)] / (n1 + n2 - 2)
t = ((mean1 - mean2) - null difference) / (sp × sqrt(1 / n1 + 1 / n2))
Confidence interval
Difference estimate ± critical value × standard error
How to Use This Calculator
- Enter the first sample mean, spread, and sample size.
- Enter the second sample mean, spread, and sample size.
- Choose Z if spreads are known population sigmas.
- Choose T if spreads are sample standard deviations.
- Select Welch for unequal variance or pooled for equal variance.
- Enter the null difference. Use zero for the common case.
- Set alpha and choose the alternative hypothesis.
- Press Calculate to show the result above the form.
- Review the statistic, p-value, interval, and decision.
- Use the CSV or PDF buttons to export the output.
FAQs
1. What does this calculator test?
It tests whether two independent population means differ by a chosen null difference. You can run a Z test with known population spreads or a T test with sample spreads.
2. When should I choose Welch?
Choose Welch when sample spreads may differ or sample sizes are unbalanced. It is usually the safer default for T testing because it does not force equal variance.
3. When is the pooled option appropriate?
Use pooled only when both populations can reasonably share the same variance. If that assumption is doubtful, Welch is usually the better choice.
4. What does the p-value mean?
The p-value is the probability of seeing a statistic this extreme, or more extreme, if the null hypothesis is true. Smaller values give stronger evidence against the null.
5. Why can I enter a null difference?
Some studies test whether the mean gap equals a target other than zero. Enter that hypothesized difference here. Leave zero for the most common comparison.
6. What does the confidence interval show?
It estimates a plausible range for mean1 minus mean2. If a two-sided interval excludes the null difference, the result is significant at the matching confidence level.
7. Can I use raw observations here?
This page uses summary inputs, not row-level data. First compute each sample mean, spread, and size, then enter those values into the calculator.
8. Why might another tool show slightly different values?
Small differences can appear because software may use different rounding rules, tail conventions, or numerical approximations for distribution values. The interpretation should still match closely.