THE COCHRAN-ARMITAGE TEST TO ESTIMATE THE SAMPLE SIZE FOR TREND OF PROPORTIONS FOR BIOLOGICAL DATA

Abstract

The biological activity of a substance can be investigated through a series of experiments done with the increased or decreased dosage of it. One of the purposes of such studies is to determine the trend of responses based on dosage. In studies carried out for this purpose, appropriate sample size has an indisputable influence on the reliability of the decisions to be made at the end of the study. There are various statistical methods for determining the trend of proportions. One of them is the Cochran-Armitage test. In a categorical data analysis, the trend between two variables with k categories can be determined through the Cochran-Armitage test. This study aims to explore the sample size calculation method developed by Nam J. (1987) for the Cochran-Armitage test. The power of the test was investigated in different numbers of categories and in different sample sizes for each category when the least biologically significant differences changed as Type I error was taken as 0.05. To this end, the study examined the results obtained by making 10000 repetitions for each case through the Monte Carlo simulation method. When the least biologically significant differences change at the end of simulation studies, the power of test highly varies in different combinations. When the number of categories is 2, determination of trend requires working with very large samples. When the number of categories is 3 or 4, the desired power can be obtained with smaller samples compared to the case where the number of categories is 2. When the number of categories is over 4, a substantial increase is needed in sample size to obtain the desired power. Change in marginal frequencies does not have much influence on sample size.