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Kruskal–Wallis group test

For independent groups, using pooled midranks and a tie correction. H compares the distributions; to read it as a comparison of medians, the groups need similar shapes.

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For independent groups, using pooled midranks and a tie correction. H compares the distributions; to read it as a comparison of medians, the groups need similar shapes. The chi-square p-value is asymptotic, and groups with fewer than 5 values are flagged. Use 2 to 20 groups and up to 5000 values in total. No post-hoc test is implied.

Model, grammar and limits

H=12/[N(N+1)] × Σ[Rᵢ−nᵢ(N+1)/2]²/nᵢ / Cₜ

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

    For independent groups, using pooled midranks and a tie correction. H compares the distributions; to read it as a comparison of medians, the groups need similar shapes. The chi-square p-value is asymptotic, and groups with fewer than 5 values are flagged. Use 2 to 20 groups and up to 5000 values in total. No post-hoc test is implied.

  2. Calculate

    H=12/[N(N+1)] × Σ[Rᵢ−nᵢ(N+1)/2]²/nᵢ / Cₜ. 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.

  3. Download CSV report

    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.

Model questions

Model, grammar and limits

For independent groups, using pooled midranks and a tie correction. H compares the distributions; to read it as a comparison of medians, the groups need similar shapes. The chi-square p-value is asymptotic, and groups with fewer than 5 values are flagged. Use 2 to 20 groups and up to 5000 values in total. No post-hoc test is implied. H=12/[N(N+1)] × Σ[Rᵢ−nᵢ(N+1)/2]²/nᵢ / Cₜ

Unit

Missing-data policy; Measurement / score unit; Group observations. 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.

Model 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.

Download input backup

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.