Yates Correction for Continuity for 2x 2Tables
If any cell frequency in 2x 2 table isles than 5thenfor the application of X^{2} test it is pooled with the preceding or succeeding frequency so that total become greater than 5. This will decrease the degree freedom. Since for 2x2 table the degree of freedom is equal 1 and the degree of freedom after adjusting for pooling would be equal to ( 1-1) zero. This is absurd because we must have at least 1 degree of freedom for application of x^{2} test.
In such situation we apply Yates correction for continuity. Thus by adding 0.5 to the cell frequency which is less than 5 and adjusting the remaining frequencies accordingly because the totals of rows and columns are fixed in 2x2 contingency table the value of X^{2} after applying Yates correction will be .
X^{2}= N( |ad -b c|-N c)^{2}/ (a + c) (b + d) (a+ b) ( c + d)
Where |ab - bc | is the absolute value of deviation after ignoring negative sings if any.
You should remember Yates correction for continuity = 1 and N is small.
Is applied only when the degree of freedom is.