Statistics & probability

Chi-square goodness of fit

Compare observed category counts with expected relative weights.

Chi-square goodness of fit
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A clear answer. Here’s how.

Normalises positive expected weights to the observed count total, then sums (observed−expected)²/expected. Degrees of freedom = categories−1−fitted parameters. Requires at least two categories, whole non-negative observed counts and positive total count. Uses the asymptotic chi-square tail, with a warning for expected counts below 5; no automatic category pooling is performed.

See a worked example

Worked example

A fixed demonstration, separate from the values you enter above.

CSV: Category,Observed,Expected weight
Category,Observed,Expected weight
A,20,1
B,30,1
C,50,1
Parameters estimated from these counts
0

Example result

Example result
CategoryObservedExpectedChi-square contribution
A2033.33333333335.33333333333
B3033.33333333330.333333333333
C5033.33333333338.33333333333

df 2; asymptotic p-value 0.000911881965555. Expected counts are all at least 5.

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