Relationship between the precision and the number of repetitions in an experiment
1996
Barath, Cs. | Szabo, T. (Godolloi Agrartudomanyi Egyetem, Godollo (Hungary)) | Rasch, D. (Agricultural University, Wageningen (Netherlands))
A researcher may face two types of problems during comparing treatment in experiments: he may interpret significant differences which do not actually exist (first kind of error), or he may not recognise differences among treatment means which do exist (second kind of error). This paper deals with the causes of the latter problem. Using an experiment with fish as an example, this paper examines the relationship between the precision requirements of the experiment (alpha and beta probability of error) and the least significant difference among treatment means (d). These two requirements are in close relationship with each other and influence the number of repetitions in treatments (ni). In the experiment mentioned above, there were 5 treatments. When using 4 to 8 repetitions per treatment, there were no statistically justifiable differences among means, however, the differences seemed to be significant. This paper demonstrates in tabulated from the least significant obtainable differences (d) as a function of the precision requirements, as well as the number of repetitions necessary to show a given significant difference when using the methods of the multiple t-test and the Newman-Keuls procedure. The computation was performed using CADEMO (Computer Aided Designs of Experiments and Modelling) software. For the calculation of the necessary number of repetitions in order to achieve a given degree of precision, the authors offer a numerical example which can be applied using manual calculation as well. The results of the calculations show once again, the importance of designing experiments in respect to their statistical aspects. With proper design, the efficiency of experiments can be increased and/or their costs can be reduced
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