Analysis of Variance and co-variance and two stage test procedure

Abstract

In the first part of the thesis, the analysis of groups of experiments located at different places has been considered in the line of Scheffe’s mixed model (1956), postulated for an industrial experiment. The usual analysis, based on the independence of the effect of the places and treatment x places interaction effect, does not seem to be justified in the actual experimental conditions. Therefore, the analysis has been considered under the model in which the effect due to places depends upon the effect of the interaction between places and treatments and moreover their joint distribution has been assumed to follow a multivariate normal distribution. In the present thesis two types of experiment-factorial experiments and experiments conducted in incomplete blocks, have been considered for the case of the model under consideration. The usual ‘F’ test for testing the component of variation due to interaction is valid for the model under consideration. When the interaction is present, the ratio of interaction M.S. to error M.S. will not have a non central ‘F’ distribution but will still yield an unbiased test. The exact test for the test of treatment means can be made using Hotelling’s T2-statistic.

In the second part of the thesis an attempt has been made to use auxiliary information in Scheffe’s mixed model for the analysis of groups of experiments. It has been seen that the usual “F” test for the test of the component due to interaction of places with treatment holds good. The property of unbiasedness of the test has also been justified for the test. In the third part of the thesis Stein’s two sample theory for the test of means of normal populations with common unknown variance has been considered for the case when the amount of sampling from the populations in question is unequal. This results in division of “studentized scale factor” into components which minimize the cost of taking section sample.