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One-way ANOVA

Classical one-way ANOVA with 2 to 20 independent groups, at least 2 values per group and 5000 values overall.

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Classical one-way ANOVA with 2 to 20 independent groups, at least 2 values per group and 5000 values overall. It assumes normal errors with equal variance. No post-hoc comparison is included. With zero within-group variance, F and p are unavailable.

Model, grammar and limits

F=[SSᵦ/(k−1)]/[SS𝓌/(N−k)]

Limits: 256000 raw data characters, 5000 source records and 50000 cells in total; decimals up to 48 characters; up to 20 groups or contributions and 50 columns. Limits for exact and bootstrap methods are stated with each tool. Parsing and resource checks run before the calculation, and the worker stops after 15 seconds. Editing, canceling or resetting discards pending results.

Check assumptions, ties and missing values before drawing conclusions. Results show 10 significant digits; CSV keeps the numeric values and units. Exact enumeration means exact counts, not exact displayed decimals. Numerical tail zeros, floors and unavailable intervals are labeled. Nothing here is a diagnosis, proof of causation or validity approval.

Your data stays in this browser. The calculation runs in a local worker, and CSV and backup files are local downloads you choose to make. Your data is not sent anywhere or saved silently, so keep your original data. Input data, formulas and filenames are never sent. Only with your optional consent, Refentra sends aggregate counts of actions and outcomes, without input content.

Independent sample groups
Use a decimal point. Commas/tabs separate matrix columns; newlines separate rows. NA or empty matrix cells are missing. No automatic deletion of extremes.
Use a decimal point. Commas/tabs separate matrix columns; newlines separate rows. NA or empty matrix cells are missing. No automatic deletion of extremes.
Use a decimal point. Commas/tabs separate matrix columns; newlines separate rows. NA or empty matrix cells are missing. No automatic deletion of extremes.

Use the chosen model

  1. Model, grammar and limits

    Enter one numeric sample per group, all in the same measurement unit. Choose reject-missing or complete-cases on purpose, and use independent groups.

  2. Calculate

    Use two groups, 1,2,3 and 4,5,6. Classical one-way ANOVA gives F = 13.5, between df = 1 and within df = 4.

  3. Download CSV report

    Read the sample counts, means and residuals alongside F and p. Record any exclusions for missing data before you save the report or CSV.

Model questions

What does this result mean?

The global p tests whether the population means are equal under the model. It doesn't tell you which pairs differ, and it doesn't establish causation.

How do I resolve rejected or missing input?

If all the within-group variance is zero, F and p are not available. That is not evidence of certainty. Check for repeated constants and for the sample sizes.

What are the limits of this tool?

Classical independent-group ANOVA assumes normal errors and equal variances. The tool doesn't check those assumptions or run post-hoc comparisons.