Yates Correction for Continuity for  2x 2Tables

If any cell frequency in  2x 2 table isles  than 5thenfor the application of X² 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 x² 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 X² after applying Yates correction will be .

X²= 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.