Worked example II
Our second example is the same as one we use for Pearson's chi square test. We stay with trials of antimalarials but here consider a fictitious trial to assess the side effects of two prophylactic drugs. Individuals with falciparum malaria are randomly allocated to two treatment groups  one group receives drug A and the other drug B. The proportion of patients suffering neuropsychiatric side effects is compared between drug A and drug B.
Antimalarial drug  Neuropsychiatric reactions 
Totals  Propn affected 
Present  Absent 
A  3 (a)  22 (b) 
25  0.12 
B  9 (c)  16 (d) 
25  0.36 
Totals  12  38 
50  
 
As the smallest expected frequency is only 6.5 we will use the continuity correction to obtain a conventional Pvalue (although a midPvalue would be perfectly acceptable).
Using
z = 
0.12 − 0.36 − (1/25 + 1/25)/2 
= 1.6556 

√ 

0.24 × 0.76 
[ 
1 
+ 
1 
] 

  
25  25 
 
Note that if we square the zvalue we obtained (1.6556) we get 2.7412, the value of Pearson's chi square statistic for these data.
This has a Pvalue of 0.098 indicating that the proportions are not significantly different at the conventionally accepted level of P = 0.05.
However, if you had not used the continuity correction, the zvalue would have come out at 1.987, which would have indicated that the proportions were indeed (just) significantly different (P = 0.047). Similarly, if you had had any justification to use a onetailed test (say there was already evidence that drug B produced more neuropsychiatric reactions), the test would have come out significant (P = 0.049).
Since statisticians differ over whether or not the correction should be used, the only conclusion one can draw is that drug B may have had a higher incidence of undesirable side effects. Do not fall into the trap of the P = 0.05 syndrome and believe that a value of 0.098 really tells you anything different from a value of 0.047. What the result is trying to tell you is that further trials should be carried out with a larger sample size and hence greater power to detect any real difference between the drugs.