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sci.chi-square-goodness-fit Calculator
Calculates the chi-square goodness-of-fit statistic χ² = Σ(O−E)²/E and p-value from observed vs expected frequencies. Degrees of freedom = number of categories − 1 − estimated parameters — p < 0.05 rejects the null hypothesis that observed data follows the expected distribution.
Inputs
O1
Reference formula or conversion factor shown for context.
O2
Reference formula or conversion factor shown for context.
O3
Reference formula or conversion factor shown for context.
O4
Reference formula or conversion factor shown for context.
E Equal
Reference formula or conversion factor shown for context.
Results
chi-square statistic χ²
Chi-squared statistic for testing goodness of fit or independence. Compare to critical chi-squared for your degrees of freedom.
degrees of freedom df
The magnitude or severity on the applicable scale.
critical value (α=0.05, df=3)
The threshold the test statistic must exceed to reject the null hypothesis at the chosen significance level.
p-value assessment
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.
expected count per group (equal H₀)
Total number of items or occurrences.
χ² = Σ(O − E)² / E
Reference formula or conversion factor shown for context.