Statistics Calculator
Descriptive statistics, Welch's t-test, paired t-test and one-way ANOVA with exact p values.
Welch: t = (m₁ − m₂) / √(s₁²/n₁ + s₂²/n₂). ANOVA: F = (SSB/(k−1)) / (SSW/(n−k)).
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What it does
Most bench comparisons come down to one question: is the difference between groups larger than the noise within them? A t-test answers it for two groups, a paired t-test for matched measurements, and ANOVA for three or more groups while controlling the family-wise error rate. Reporting the test statistic, degrees of freedom, p value and effect size together is what makes the result reproducible.
When to use it
Typical uses include comparing treated and untreated cell populations, analysing before-and-after measurements on the same samples, checking whether several media formulations or time points differ, and screening assay replicates for outliers before fitting a curve. The descriptive mode is also handy for a quick mean, SD and 95% confidence interval before deciding which test to run.
FAQ
- Should I use the two-sample t-test or the paired t-test?
- Use the paired t-test when every value in group A has a natural partner in group B — the same subject before and after treatment, the same sample measured on two instruments, or matched replicates. Use the two-sample t-test when the two groups are independent, such as a treated group and a separate control group. Pairing removes between-subject variation, so a paired test is usually more powerful when the design really is paired.
- Why does this tool use Welch's t-test instead of Student's?
- Welch's test does not assume that the two groups share the same variance, and it computes degrees of freedom with the Welch–Satterthwaite equation. In practice variances are rarely exactly equal, and when they differ Welch keeps the false-positive rate near the nominal level while Student's pooled test can be badly wrong. When the variances and sample sizes are equal, the two give almost identical results.
- What does the p value actually mean?
- The p value is the probability of observing a difference at least as extreme as yours if the null hypothesis were true. It is not the probability that the null hypothesis is correct, and it says nothing about effect size. Report the mean difference or the group means alongside p, and treat p below your alpha (0.05 by default) as evidence against the null rather than as proof of an effect.
- Can I paste data straight from a spreadsheet?
- Yes. Values can be separated by commas, tabs, spaces or line breaks, so a single column copied from Excel or a row of replicate values both paste cleanly. For one-way ANOVA, put each group on its own line and separate groups with a blank line or a semicolon. Non-numeric tokens are ignored.