This paper deals with an experimental design problem where multinomial categorical data are the responses of experiments with a view to a comparison of analysis tools for categorical data such as parameter design originated by Taguchi and multinomial logistic regression. This paper demonstrates that the parameter design settings can be easily converted into multinomial logistic regression framework. Although the parameter design methods are still useful in the case that statistical analysis tools are not readily available, they may not be sound in both statistical and practical senses. Some issues that can arise when handling the categorical response data, are discussed in relation to designed experiments within the framework of logistic regression.).