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a quantity that is added or subtracted in order to increase the accuracy of a scientific measure (同)fudge factor
the act of offering an improvement to replace a mistake; setting right (同)rectification
a drop in stock market activity or stock prices following a period of increases; "market runups are invariably followed by a correction"
treatment of a specific defect; "the correction of his vision with eye glasses"
a rebuke for making a mistake (同)chastening, chastisement
something substituted for an error
the social control of offenders through a system of imprisonment and rehabilitation and probation and parole
the department of local government that is responsible for managing the treatment of convicted offenders; "for a career in corrections turn to the web site of the New Jersey Department of Corrections" (同)department of corrections

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〈U〉『訂正』,修正,調整 / 〈C〉訂正箇所,訂正の書き入れ / 〈U〉(よくするための)処罰,叱責(しっせき)

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出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2017/07/19 09:04:01」(JST)

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In statistics, Yates' correction for continuity (or Yates' chi-squared test) is used in certain situations when testing for independence in a contingency table. In some cases, Yates' correction may adjust too far, and so its current use is limited.

Correction for approximation error

Using the chi-squared distribution to interpret Pearson's chi-squared statistic requires one to assume that the discrete probability of observed binomial frequencies in the table can be approximated by the continuous chi-squared distribution. This assumption is not quite correct, and introduces some error.

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' 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' correction may tend to overcorrect. This can result in an overly conservative result that fails to reject the null hypothesis when it should (a type II error). So it is suggested that Yates' correction is unnecessary even with quite low sample sizes,^[2] such as:

\sum _{i=1}^{N}O_{i}=20\,

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

\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:

	S	F
A	a	b	N_A
B	c	d	N_B
	N_S	N_F	N

we can write

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

In some cases, this is better.

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

References

^ Yates, F (1934). "Contingency table involving small numbers and the χ² test". Supplement to the Journal of the Royal Statistical Society 1(2): 217–235. JSTOR 2983604
^ Sokal RR, Rohlf F.J. (1981). Biometry: The Principles and Practice of Statistics in Biological Research. Oxford: W.H. Freeman, ISBN 0-7167-1254-7.

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