Ridit scoring

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.

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,..., x_n denote the ordered categories of the preference scale. For each j, x_j represents a choice or judgment. Then, let the probability function p be defined with respect to the reference data set as

${\displaystyle p_{j}=Prob({x_{j}}).}$

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

${\displaystyle w_{j}=0.5p_{j}+\sum _{k<j}{p_{k}}.}$

Each of the categories of the reference data set are then associated with a ridit score. More formally, for each ${\displaystyle 1\leq j\leq n}$, the value w_j is the ridit score of the choice x_j.