Yates' correction for continuity

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Yates' correction for continuity, or Yates' chi-square test, adjusts the formula for Pearson's chi-square test by subtracting 0.5 from the difference between each observed value and its expected value in a 2 × 2 contingency table. This reduces the chi-square value obtained and thus increases its p-value. It prevents overestimation of statistical significance for small data. This formula is chiefly used when at least one cell of the table has an expected frequency less than 5.

\chi_{Yates}^2 = \sum_{i=1}^{N} {(|O_i - E_i| - .5)^2 \over E_i}

where:

Oi = an observed frequency
Ei = an expected (theoretical) frequency, asserted by the null hypothesis
N = number of distinct events

As a short-cut, for a 2x2 table with the following entries:

  S F  
A a b NA
B c d NB
  NS NF N

we can write:

\chi_{Yates}^2 = \frac{N(|ad - bc| - N/2)^2}{N_S N_F N_A N_B}

Other sources say that this correction should be used when the expected frequency is less than 10.

Yet other sources say that Yates corrections should always be applied.

[edit] References

Yates, F (1934). Contingency table involving small numbers and the χ2 test. Journal of the Royal Statistical Society (Supplement) 1: 217-235.


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