Statistical Methods

Unit 7 - Chi-square distribution

7.5. Fisher’s correction for continuity
Where a, b, c and d are cell frequencies of 2 x 2 contingency table and N is the total frequency. This has 1 degree of freedom. If, the expected cell frequencies are large, the discrete distribution of probabilities of all frequencies approximate to normal distribution. This approximation holds good fairly well when the degrees of freedom are more than 1 and the expected cell frequency in the various classes is not small. As the degrees of freedom of statistic of 2 x 2 contingency table is 1, approximation in this case will not be satisfactory and leads to over estimation of significance. This is corrected by the method suggested by Yates which is known as ‘Yates correction’. The correction consists of adding ½ to the observed minimum frequency and adjusting the other cell frequency for the observed marginal totals and then computing the .
Formula for using the Yates correction in a 2x2 contingency table is given by,

This correction is suitable when the expected frequency of classes is less than 5, but estimation with correction can do no harm even when the frequencies are large. Hence it is always better to use the correction as a matter of routine.

Example: In a series of experiments to test whether advanced stages of MyxcoboIus infection is cured by ‘me treatment, the following observations were found:

	Not cured	Cured	Total
Lime treated	86	14	100
Untreated (control)	88	12	100
Total	174	26	200

Test whether lime has any effect in curing the infection
Answer:
(i) Hypotheses
H_o : There is no association between lime treatment and curing of infection.
H₁ : There is association between lime treatment and curing of infection
(ii) Test statistics

Where a =86, b=14, c = 88, d = 12

(iii) Statistical decision
Since calculated (with and without Yates correction) is less than the table value (3.84 at 5%, 6.64 at 1%), H₀ is not rejected.