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Free Chi-square and ANOVA Calculator

Evaluate categorical associations with chi-square and compare group means with one-way ANOVA.

Copy-paste outputs

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Tool 01

Chi-square + ANOVA Calculator

Run core significance tests from pasted numeric tables in one workflow.

Chi-square + ANOVA Calculator

Run chi-square independence and one-way ANOVA tests from pasted numeric tables.

Chi-square contingency table (rows)

ANOVA groups (one group per line)

Statistical summary

Chi-square

X^2 = 1.5633

df = 4, p = 8.154e-1

One-way ANOVA

F = 19.2795

df = (2, 9), p = 5.579e-4

{
  "error": null,
  "chiSquare": {
    "statistic": 1.5633160072565686,
    "degreesOfFreedom": 4,
    "pValue": 0.8153697316442541,
    "expected": [
      [
        20.089285714285715,
        30.803571428571427,
        24.107142857142858
      ],
      [
        18.75,
        28.75,
        22.5
      ],
      [
        21.160714285714285,
        32.44642857142857,
        25.392857142857142
      ]
    ],
    "rowTotals": [
      75,
      70,
      79
    ],
    "columnTotals": [
      60,
      92,
      72
    ],
    "grandTotal": 224
  },
  "anova": {
    "grandMean": 5.675,
    "groupMeans": [
      4.875,
      5.800000000000001,
      6.35
    ],
    "ssBetween": 4.4449999999999985,
    "ssWithin": 1.0374999999999996,
    "dfBetween": 2,
    "dfWithin": 9,
    "msBetween": 2.2224999999999993,
    "msWithin": 0.11527777777777774,
    "fValue": 19.279518072289157,
    "pValue": 0.0005578823127696531
  }
}

How it works

Chi-square + ANOVA Calculator: methodology and worked example

How this tool computes its result

Parses two independently pasted numeric tables (rows split on commas, whitespace, or semicolons). For chi-square, it builds a contingency matrix, computes row and column totals, derives an expected value per cell as (rowTotal × colTotal) / grandTotal, sums (observed − expected)² / expected across all cells for the test statistic, sets degrees of freedom to (rows−1) × (cols−1), and converts the statistic to a p-value using a hand-implemented regularized incomplete gamma function (with a Lanczos log-gamma approximation feeding a series or continued-fraction expansion depending on magnitude). For one-way ANOVA, it computes between-group and within-group sums of squares from the group means and grand mean, derives F = MSbetween / MSwithin, and converts F to a p-value using a hand-implemented regularized incomplete beta function. Both statistical tests throw descriptive errors rather than silently guessing on malformed input.

Worked example

With the tool's default ANOVA input — group 1: 4.2, 5.1, 4.9, 5.3 (mean 4.875); group 2: 5.8, 6.0, 5.5, 5.9 (mean 5.8); group 3: 6.4, 6.1, 6.7, 6.2 (mean 6.35) — the grand mean across all 12 values is 68.1/12 = 5.675, with dfBetween = 2 and dfWithin = 9. Because the three group means (4.88, 5.80, 6.35) are well separated relative to the small within-group spread, the between-group variance dominates the within-group variance, producing a large F-statistic and a p-value effectively at 0 — correctly flagging a statistically significant difference between the groups.

When not to use this tool

Only one-way ANOVA (a single factor) and a chi-square test of independence are implemented — there's no post-hoc test like Tukey HSD to say which specific groups differ, no two-way ANOVA for interaction effects, and no Welch correction for groups with very unequal variances.

Common mistakes

- Pasting a chi-square matrix with rows of different lengths (e.g. one row has 3 values, another has 2) — the tool explicitly throws "All rows must have the same number of columns." rather than padding the shorter row with zeros.
- Providing an ANOVA group with only one value — each group needs at least 2 data points to compute within-group variance, so a single-value group throws "Each ANOVA group needs at least 2 values."
- Including a text label inline with numbers on one line (e.g. "Group A: 4.2, 5.1") — the parser requires every whitespace/comma/semicolon-separated token to parse as a float, so a stray label throws "Input contains non-numeric values." for the entire calculation.

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