# Ridit scoring

In econometrics, ridit scoring is a statistical method used to analyze ordered qualitative measurements. The tools of ridit analysis were developed and first applied by Bross,[1] who coined the term "ridit" by analogy with other statistical transformations such as probit and logit.

## 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 taste survey answers of a competing or historically important product are often used as the reference data set against which taste 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 as

$p_j=Prob({x_j}).$

### Determining ridits

The ridit scores, or simply ridits, of the reference data set are then easily calculated as

$w_j=0.5p_j+\sum_{k

Each of the categories of the reference data set are then associated with a ridit score. More formally, for each $1\le j\le n$, the value wj is the ridit score of the choice xj.

## Interpretation and examples

Intuitively, ridit scoring can be understood as a modified notion of percentile. For any j, if xj has a low (close to 0) ridit score, one can conclude that

$\sum_{k

is very small, which is to say that very few respondents have chosen a category "lower" than xj.

## Applications

Ridit scoring has found use primarily in the health sciences (including nursing and epidemiology) and econometric preference studies.[citation needed]

## A mathematical approach

Besides having intuitive appeal, the derivation for ridit scoring can be arrived at with mathematically rigorous methods as well. Brockett and Levine[2] presented a derivation of the above ridit score equations based on several intuitively uncontroversial mathematical postulates.