Yates's correction for continuity

In statistics, Yates's correction for continuity (or Yates's chi-squared test) is used in certain situations when testing for independence in a contingency table. It aims at correcting the error introduced by assuming that the discrete probabilities of frequencies in the table can be approximated by a continuous distribution (chi-squared). In some cases, Yates's correction may adjust too far, and so its current use is limited.

Correction for approximation error

Using the

To reduce the error in approximation, Frank Yates, an English statistician, suggested a correction for continuity that adjusts the formula for Pearson's chi-squared test by subtracting 0.5 from the difference between each observed value and its expected value in a 2 × 2 contingency table.^[1] This reduces the chi-squared value obtained and thus increases its p-value.

The effect of Yates's correction is to prevent overestimation of statistical significance for small data. This formula is chiefly used when at least one cell of the table has an expected count smaller than 5. Unfortunately, Yates's correction may tend to overcorrect. This can result in an overly conservative result that fails to reject the

The following is Yates's corrected version of Pearson's chi-squared statistics:

${\displaystyle \chi _{\text{Yates}}^{2}=\sum _{i=1}^{N}{(|O_{i}-E_{i}|-0.5)^{2} \over E_{i}}}$

where:

O_i = an observed frequency

E_i = an expected (theoretical) frequency, asserted by the null hypothesis

N = number of distinct events

2 × 2 table

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

${\displaystyle \chi _{\text{Yates}}^{2}={\frac {N(|ad-bc|-N/2)^{2}}{(a+b)(c+d)(a+c)(b+d)}}.}$

In some cases, this is better.

${\displaystyle \chi _{\text{Yates}}^{2}={\frac {N(\max(0,|ad-bc|-N/2))^{2}}{N_{S}N_{F}N_{A}N_{B}}}.}$

See also

• Continuity correction
• Wilson score interval with continuity correction

References