Probit analysis and application fields in statistical studies

This study which is prepared as a master thesis has been made as an applied research. In the first section, probit model which is constituted core of subject has been investigated for the estimation of the place in statistics science. The model of probit has been described with the knowledge which is obtained at generalized linear models (GLM). Because of probit model?s inclution in a group of qualitative dependent variable models, once again in this section, linear probability model, logit model and probit model which are qualitative dependent variable models have been evaluated generally. In the following section, the mathematical structure of the probit model has been investigated by starting with assumptions of binary probit model. In this section for the probit model, parameter estimation methods have been given and parameter estimation methods investigation has been done by probit model assumptions. As parameter estimation methods; weighted least squares, maximum likelihood, minimum chi-square (c 2 ), the iteratively reweighted least square methods have been discussed and, because of the maximum likelihood method?s powerful characteristics, compared to the other methods powerful characteristics have been discussed. This method has been used in application. The other part of this section has constituted the goodness of fit tests for probit models. The probit regression line?s goodness of fit to the data has been clarified by using these tests. At the part of application section, as a goodness of fit test, goodness of data to regression line has been tested by sum of weighted residual square method which is the chi-square (c 2 ) distribution. After these approaches, the probit analysis steps have been described towards to application. At these steps; graphic approach, aritmetic approach and correction methods in the natural death cases have been described respectively. Once again in this section, the part of finding confidence intervals and finding corrected confidence intervals which go towards to the application for heterogeneous data have been investigated. In the indication section, prepared data have been utilized. The indicated methods at the results have been used. Analysed data have constituded with investigation of probit analysis which is showed dose-response relation of insecticide. Data have been calculated by handle according to the application steps. Obtained results have been compared to the statistical package programs? results. According to the aim of research, neglection differences from numerical rounding have been discussed. Furthermore, advantages and disadvantages of probit model calculation by handle and computer package programs have been discussed. Key Words: probit analysis, probit transformation, goodness of fit tests, parameter estimation methods, homogeneous data, heterogeneous data, arithmetic approach, graphic approach, natural death, dose-response.