Analysis and Inference for Incompletely Specified Models Involving the Use of Preliminary Test(s) of Significance

statistical-mathematical model. (B) Problems of estimation and tests of hypotheses. These involve a choice of appropriate functions of the sample observations, called statistics, to estimate the values of, or to test hypotheses concerning, the parameters in the statistical-mathematical model. (C) Problems of distribution. These include the mathematical derivation of the distributions in random samples of the statistics used as estimators or test criteria in order that valid inferences may be made concerning the population parameters in the specified statistical-mathemnatical model. In more recent times non-parametric or distribution-free statistical inference procedures, not requiring a model specification, have been and are being considerably extended: nevertheless most applications of statistics in scientific research are still parametric in nature. This paper will be concerned with problems of specification. In discussing problems of specification Fisher [1922] was of the opinion that an appropriate statistical-mathematical model, to be used in describing an observation in an investigation, should be determined in advance by the investigator. Further, that this should be done from theoretical considerations in the particular substantive field and/or from curve fitting studies based on independent extensive uniformity type data. In this latter case the adequacy of the choice of the model may be tested a posteriori; for example, by some 'goodness of fit' test.