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math.chi-square-goodness-fit Calculator
Computes the chi-square goodness-of-fit statistic directly from observed and expected frequency vectors. Goodness-of-fit is how statisticians determine whether a theoretical distribution (like Poisson or normal) fits empirical data.
Inputs
Observed1
Reference formula or conversion factor shown for context.
Expected1
Reference formula or conversion factor shown for context.
Observed2
Reference formula or conversion factor shown for context.
Expected2
Reference formula or conversion factor shown for context.
Observed3
Reference formula or conversion factor shown for context.
Expected3
Reference formula or conversion factor shown for context.
Results
chi² statistic
The value at the specified point or condition.
degrees of freedom df
The magnitude or severity on the applicable scale.
critical value (α=0.05, df=2)
The threshold the test statistic must exceed to reject the null hypothesis at the chosen significance level.
reject H₀?
Reference formula or conversion factor shown for context.
chi² = Σ(O-E)²/E
Reference formula or conversion factor shown for context.
p-value approx
Probability of observing this result (or more extreme) if the null hypothesis were true. Below 0.05: conventionally significant. Below 0.01: strong evidence. A low p-value does not measure the size or practical importance of the effect.