Chi-Square Independence Statistic Calculator

Description

Calculate Pearson's uncorrected independence statistic and expected counts for an RxC contingency table, without a p-value or small-sample validity claim.

A contingency table records counts for combinations of two categorical variables. Under independence, row and column margins determine expected counts. Pearson chi-square summarizes disagreement between observed and expected counts; its statistic is separate from a p-value or a decision about significance.^[1]

Calculate Pearson's uncorrected independence statistic and expected counts for an RxC contingency table, without a p-value or small-sample validity claim.

When to use this tool

Use this tool to calculate chi square independence under the units, normalization, and boundary conventions below.

How to use the tool and how it works

Supply observed in the field shapes below.
Run the calculation. Correct format, shape, range, or undefined-statistic errors before interpreting a result.
Read chiSquare, degreesOfFreedom, expected, total. Use the conventions below.

Sum observed nonnegative integer counts by row and column, set each expected count to rowTotal×columnTotal/grandTotal, and accumulate (observed−expected)²/expected. Return expected counts, the statistic, total and (rows−1)(columns−1) degrees of freedom.^[2]

Input field	Meaning and units	Accepted input
observed	Observed counts	Required. Array of Array of Safe integer; minimum 0.; minimum items 2; maximum items 32.; minimum items 2; maximum items 32.

Output field	Interpretation	Returned shape
chiSquare	Pearson statistic	Required. Finite number; minimum 0.
degreesOfFreedom	Degrees of freedom	Required. Safe integer; minimum 1.
expected	Expected counts	Required. Array of Array of Finite number...
total	Total count	Required. Safe integer; minimum 1.

json

{
  "input": {
    "observed": [
      [
        20,
        10,
        0
      ],
      [
        0,
        20,
        10
      ],
      [
        10,
        0,
        20
      ]
    ]
  },
  "output": {
    "chiSquare": 60,
    "degreesOfFreedom": 4,
    "expected": [
      [
        10,
        10,
        10
      ],
      [
        10,
        10,
        10
      ],
      [
        10,
        10,
        10
      ]
    ],
    "total": 90
  }
}

Limitations and assumptions

The table must be rectangular with positive row/column marginals and a safe-integer total. This is uncorrected Pearson independence chi-square: no Yates correction, p-value, sparse-cell remedy or independent-sampling verification is included.
The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.

Alternative or Complementary methods

Choose the statistic according to the question and data conventions. Inspect the supplied series or matrix and the stated assumptions before comparing outputs from implementations with different defaults.

References

SciPy: contingency-table independence and expected frequencies — SciPy
Tool behavior and example: Chi-Square Independence Statistic Calculator — tool.io

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