t-test
t = (x̄₁ - x̄₂) / SE
Student SE = s_p * sqrt(1/n₁ + 1/n₂)
Welch SE = sqrt(s₁²/n₁ + s₂²/n₂)
Welch's version is safer when group variances are unequal.
BioStats Quick Calculator — Welch's t-test, Chi-square, One-way ANOVA
Data & Test Selection
Examples: “control vs treatment t-test”, “3 groups one-way ANOVA”, “2×3 contingency table chi-square”.
Results
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Detailed Results Table
| Metric | Value |
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Run a calculation to see the summary, chart placeholder, and table here.
Understanding Common BioStats Tests
Release Updates
- Added a Welch vs Student method selector for two-sample t-tests, with Welch's t-test set as the default.
- Expanded results with 95% confidence intervals, Hedges' g, Cramer's V, and eta-squared effect sizes.
- Added richer descriptive summaries and stronger data-quality checks, including invalid-number detection and chi-square expected-count diagnostics.
Choosing the right statistical test is crucial for drawing valid conclusions from your biological data. Here's a brief overview of the tests available in this calculator:
Chi-square
χ² = Σ (O - E)² / E
E = (row total * column total) / grand total
V = sqrt(χ² / (N * min(r-1, c-1)))
The calculator reports both the test statistic and Cramer's V effect size.
One-way ANOVA
F = MS_between / MS_within
MS = SS / df
η² = SS_between / SS_total
ANOVA tests whether at least one group mean differs from the others.
Two-sample t-tests
The t-test is used to compare the means of two groups. Use Welch's t-test when group variances may differ, and use the classic Student's t-test only when equal-variance assumptions are reasonable.
- Assumptions: Data should be approximately normally distributed. Welch's t-test is more robust when variances differ.
- Input: Two sets of numerical data.
- Output: t-statistic, degrees of freedom, p-value, confidence interval, and effect size.
Chi-square Test (χ²)
The chi-square test is used to determine if there is a significant association between two categorical variables. It compares observed frequencies with expected frequencies. It's commonly used in genetics (e.g., Mendelian ratios), ecology (e.g., species distribution), or epidemiology (e.g., disease prevalence across categories).
- Assumptions: Data must be frequencies or counts, not percentages or ratios. Expected frequencies should not be too small (typically, no more than 20% of expected counts are less than 5).
- Input: Observed frequencies organized in a contingency table (e.g., enter counts per category for each group).
- Output: Chi-square statistic, degrees of freedom, p-value, expected-count diagnostics, and Cramer's V.
One-way ANOVA (Analysis of Variance)
ANOVA is used to compare the means of three or more independent groups. It determines if there is a statistically significant difference between the means of these groups. If ANOVA shows a significant difference, post-hoc tests (not included in this simple calculator) are typically used to identify which specific groups differ from each other.
- Assumptions: Data should be normally distributed within each group, and variances should be roughly equal across groups.
- Input: Three or more sets of numerical data.
- Output: F-statistic, degrees of freedom, p-value, group summaries, and eta-squared effect size.
P-value Interpretation: The p-value helps you determine the significance of your results. A commonly used threshold is 0.05. If your p-value is less than 0.05, it suggests that the observed differences are statistically significant, meaning they are unlikely to have occurred by random chance.
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FAQ
Do my data leave my device?
No. All computations run entirely in your browser (client-side). Nothing is uploaded or stored on a server.
What assumptions do these tests require?
t-test and one-way ANOVA assume approximate normality and similar variances; chi-square assumes count data with adequately large expected counts. Check assumptions before drawing conclusions.
Does this include post-hoc tests or effect sizes?
This calculator now includes core effect sizes for its built-in tests, but post-hoc comparisons and multiple-testing corrections should still be calculated separately.
Is this medical advice?
No. This tool is for education/research support only and does not replace professional statistical or medical guidance.
5 Fun Facts about Quick Biostats
Student was a brewer
The “Student” in Student’s t-test was William Gosset, a Guinness brewer who published under a pen name to protect the brewery’s trade secrets.
Pub origin
Chi-square hates tiny boxes
Expected counts under ~5 per cell can inflate χ² p-values; collapsing sparse categories often stabilizes the test.
Assumption check
ANOVA = regression in disguise
One-way ANOVA and dummy-coded linear regression produce the same F-statistic and p-value—they’re two views of the same model.
Model twins
Shuffle to sanity-check
Randomly permuting group labels and re-running a test (a quick permutation test) shows how often “significance” appears by chance.
Null play
Huge N shrinks p
With very large samples, even tiny effect sizes can look “significant.” Pair p-values with effect sizes or confidence intervals.
Practical vs. statistical