In this paper, we have considered the modeling and analyses of categorical data. We modeled binary data with categorical predictors, using logistic regression to develop a statistical method. We found that ANOVA-type analyses often performed unsatisfactory, even when using arcsine-square-root transformations. We concluded that such methods are not appropriate, especially in cases where the fractions were close to 0 or 1. The logistic transformation of fraction data could be a promising alternative, but it is not desirable in the statistical sense. The major purpose of this paper is to demonstrate that logistic regression with an ANOVA-model like parameterization aids our understanding and provides a somewhat different, but sound, statistical background. We examined a simple real-world example to show that we can efficiently test the significance of regression parameters, look for interactions, estimate confidence intervals, and calculate the difference between the mean values of the referent and experimental subgroups. This paper demonstrates that precise confidence interval estimates can be obtained using the proposed ANOVA-model like approach. The method discussed here can be extended to any type of fraction data analysis, particularly for experimental design.