Ridit scoring
In statistics, ridit scoring is a statistical method used to analyze ordered qualitative measurements.
The tools of ridit analysis were developed and first applied by Bross, who coined the term "ridit" by analogy with other statistical transformations such as probit and logit. A ridit describes how the distribution of the dependent variable in row i of a contingency table compares relative to an identified distribution.
Calculation of ridit scores
Choosing a reference data set
Since ridit scoring is used to compare two or more sets of ordered qualitative data, one set is designated as a reference against which other sets can be compared. In econometric studies, for example, the ridit scores measuring test survey answers of a competing or historically important product are often used as the reference data set against which test surveys of new products are compared. Absent a convenient reference data set, an accumulation of pooled data from several sets or even an artificial or hypothetical set can be used.Determining the probability function
After a reference data set has been chosen, the reference data set must be converted to a probability function. To do this, let x1, x2,..., xn denote the ordered categories of the preference scale. For each j, xj represents a choice or judgment. Then, let the probability function p be defined with respect to the reference data set asDetermining ridits
The ridit scores, or simply ridits, of the reference data set are then easily calculated asEach of the categories of the reference data set are then associated with a ridit score.
More formally, for each, the value wj is the ridit score of the choice xj.
Interpretation and examples
Intuitively, ridit scores can be understood as a modified notion of percentile ranks. For any j, if xj has a low ridit score, one can conclude thatis very small, which is to say that very few respondents have chosen a category "lower" than xj.