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Pearson Chi-Square: One Cell’s Contribution

Calculate one observed-versus-expected count’s contribution to a Pearson chi-square statistic, with explicit inverse branches.

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Enter the known values in the units shown. Results update as you type.
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An observed count of 12 and expected count of 9 contribute (12 − 9)²/9 = 1 to the chi-square sum.

Single-cell contribution = (observed − expected)² / expected

Enter these known values and leave the other values blank.

The observed count is a nonnegative integer. Expected count is positive and may be fractional; the contribution is nonnegative.
This is one term, not a complete test. A full test needs every cell, a suitable probability model, degrees of freedom and assumptions for its reference distribution.
Inverse solutions need not be unique. Recovering observed count chooses E + √(contribution × E). Recovering expected count chooses the larger quadratic root.
An inverse observed result must still be a whole count. A fractional inverse is not rounded into a valid observation.

No. This is one contribution to a sum and provides neither a p-value nor a hypothesis-test decision.

The squared difference loses a sign. With observed count 12 and contribution 1, expected counts 9 and 16 both fit; this inverse selects 16.

Bookify requires a nonnegative whole observed count, positive expected count and nonnegative chi-square contribution.