Use this calculation to reproduce a defined quantitative method when the observations, units, sampling process, and assumptions match the method shown here.

Observed counts

Required list. Observed count per category.

Expected probabilities

Optional list. Probability per category; defaults to a uniform distribution.

Significance level

Optional number. Significance threshold for rejecting the expected distribution.

The cited overview of Statistics supplies background for the terminology and domain context used by this tool.^[1]

Test how well observed category counts fit an expected distribution. Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Chi-square statistic

Returned number. Chi-square statistic of the sample.

Degrees of freedom

Returned integer. Degrees of freedom, one less than the categories.

p-value

Returned number. p-value of the goodness-of-fit test.

Significant

Returned boolean. Whether to reject the expected distribution at the level.

• A numerical result does not by itself establish data quality, causation, representativeness, independence, distributional fit, or practical significance.
• Significance level must be at least 0.
• Significance level must be no greater than 1.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Inspect the underlying data, visualize its distribution, report uncertainty and sample size, and compare the result with a robust or domain-specific method where appropriate.

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