The Statistical Analysis And Its Application For The Interval Differences Between Categories Of Ordinal Data

Statistical analysis of qualitative data is one of the hottest but difficult issues to study recently. Qualitative data always comes up as ordered categorical variables, especially in the data set collected by marketing and social science researching. Ordered categorical variables means the response variables that has more than three categories between which are ordered. We found that the interval between each two categories was different when we on the process of such kind of data. For example, when people choose to evaluate a thing, their attitude from"strongly unlike"to"unlike", and then from"like"to"strongly like"should be asymmetrically distributed. Most of us always ignore it and treat it has equal intervals, which may lead to draw an inexact conclusion.Though this subject have been mentioned among some research papers overseas, it hasn't gone thoroughly and mostly focused on how to evaluate ordinal data, let alone within our nation. Under such condition, this paper attempt to analyze the intervals between categories of ordinal data elaborately, systematically and practically from the statistic point of view. The paper is divided into four parts as follows:Part one: chapter one. Take a review on the foreign and domestic documents concerning ordinal data through half a century. It turns out that the theory of ordinal data analysis has been fully developed overseas compared to our country where hasn't established its own theory in this field.Part two: chapter two and three. Put forward the statistic and test method to evaluate the differences between categories of ordinal data as Likert type. On this basis, we make an emendation on cumulative logistic model and demonstrate it in application (innovation point one). For Likert measurement, if there exists interval differences, one should introduce instrument dummy variable to modify cumulative logistic model so as to advance its precision.Part three: chapter four. Propose the method of rank analysis to evaluate the differences between categories of ordinal data (innovation point two). On this basis, apply the cluster analysis to the quantification of the ordinal data and obtain a similar conclusion of predecessor's, but enhance the efficiency.Part four: chapter five. Take the regional discrepancies of our nation as the case; present the method of evaluating and testing the interval differences between grouped ordinal data (innovation point three). Then apply econometrical models to analyze the regional discrepancies and put forward my own understanding on this issue.