Abstract:

Mathematical statistics is an obligatory subject, frequently included in the study programmes at all universities of life sciences in Poland. The subject content usually includes the problem of testing hypotheses. Students are usually taught to resolve this problem by means of classical approach in which sample sizes are defined in advance. In this approach it is a common practice to apply t-Student test to compare mean values from two populations from normal distribution. However, in many cases it appears more effective to abandon the standard practice and take advantage of sequential approach, where sample size is a random variable, and choose one of group sequential tests. The use of sequential tests gives the benefit of a smaller sample size because observations are collected group by group and each group of observations can lead to stopping the experiment. This paper is an attempt to compare sample sizes necessary to verify the hypothesis on the difference between mean values from two populations while using t-Student test and group sequential Haybittle-Peto test. Comparative analysis was performed on the basis of simulations which had been carried out for the values distinguishing these populations and for selected parameters of normal distribution. The maximum sample size for the Haybittle-Peto test was calculated to determine a number of groups and a group size. The simulations were conducted using R project software both in the case when the hypothesis was true and when it was false. The results have revealed the advantage of the sequential test since it requires smaller sample sizes. At the end, there were indicated possible applications of group sequential Haybittle-Peto test in the area of natural sciences (for instance, in such experiments where time has no effect on analysed feature values and thus new observation groups can be included in the sample at any moment). Simultaneously, it was emphasized that this test is relatively easy to apply and may prove extremely useful for natural sciences students as well as graduates pursuing careers in line with their education. As a rule, experiments using sequential analysis methods are less time-consuming and more cost-effective – they may lead to impressive practical solutions in the area of natural sciences.

Keywords:

Statistics, t-Student test, group sequential Haybittle-Peto test.