%0 Journal Article
%T Not Significant: What Now?
%A Gerhard Marinell
%A Gabriele Steckel-Berger
%A Hanno Ulmer
%J Journal of Probability and Statistics
%D 2012
%I Hindawi Publishing Corporation
%R 10.1155/2012/804691
%X In a classic significance test, based on a random sample with size , a value will be calculated at size aiming to reject the null hypothesis. The sample size , however, can retrospectively be divided into partial samples and a test of significance can be calculated for each partial sample. As a result, several partial samples will provide significant values whereas others will not show significant values. In this paper, we propose a significance test that takes into account the additional information from the values of the partial samples of a random sample. We show that the £¿£¿ values can greatly modify the results of a classic significance test. 1. Introduction In this day and age testing for significance has become a ritual which, if it leads to a significant result, still opens the doors to many well-known journals in nearly every scientific field. This is the case even though for a long time the application of null hypothesis significance testing has been criticized and even rejected [1]. What will be shown here is that by extending the classic significance test additional information from a random sample can be obtained and a ¡°not significant¡± result can possibly be made ¡°significant¡±. A misuse of null hypothesis significance testing can however not be prevented with this method [2]. In the significance test as defined by Fisher [3, 4] the probability that a specific sample will occur is calculated based on the validity of the null hypothesis. This probability is usually abbreviated with and is compared with a conventionally determined level of significance which is normally 5%. When is equal to or less than this level of significance then the null hypothesis is rejected. If this is not the case then, as defined by Fisher, the null hypothesis cannot be rejected but also not accepted [5]. This procedure is valid for a given sample provided it is a random sample. This means that the units of the sample are drawn from the population randomly and the probability with which a unit is drawn out of the population is given. If you presuppose, as is customary, a simple random sample (¡°idd¡± assumption = ¡°independent and identically distributed¡± assumption), then we have the same probability for each unit being part of the sample and the drawings from the population occur independently of each other. Even though the randomness of the sample is a premise for a test of significance, it is seldom certified. Additionally, the ¡®¡®iid¡¯¡¯ assumption requires that the order of drawings from the population is known and this allows the split of a random sample into a
%U http://www.hindawi.com/journals/jps/2012/804691/