Syed Ejaz Alam  ( PMRC Research Centre, Jinnah Postgraduate Medical Centre, Karachi. )

X²(Chi-square) test
So far we have been dealing with the test of sig­nificance between two means but in actual practice there may be occasions when we may need to compare the characteristics of more than two groups. For example, we may be interested in comparing the proportions of vac­cinated children, and to see whether the proportion attacked varies with the duration of time lapsed since vaccination. For problems like this the X -test was developed. However it is important to note that X2-test can only be carried out on the actual numbers. It cannot be done in percentages, proportions, means or others derived statistics.

To illustrate the use and application of X2-test. Let us consider the following example which shows the distribu­tion of intelligence quotients in a group of children.


Each intelligence group were clinically assessed as having nor­mal or subnormal nutrition¹. We may therefore say that our null hypothesis is wrong and we conclude that Nutritional status and intel­ligence are associated.
Further application of X²:
Suppose we wish to compare two treatments; Adrenalectomy and hypophysectomy for patients with advanced breast cancer. A total of 149 patients were allocated at random to the treatment and comparison was made of patients who survived 3 months after the opera­tion. 75 patients had Adrenalectomy, out of those 53 survived and 70 had Hypophysectomy and of these 57 survived. Solution: This data can be put in 2*2 contingency table with the null hypothesis that "Two treatments are equally effective".

1. Siddiqui, M.A. Role of Statistics in Medical Research, Pakistan Medical Research Coun­cil, Minhas House Annexe PECHS, Karachi. pp 60-61.