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,[1] 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 (e.g., the marginal distribution of the dependent variable).

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,..., 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

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

Determining ridits

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.

Interpretation and examples

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

${\displaystyle \sum _{k<j}{Prob(x_{k})}}$

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

Applications

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

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.

Notes

R statistical computing package for Ridit Analysis: https://cran.r-project.org/package=Ridit

1. Bross, Irwin D.J. (1958) "How to Use Ridit Analysis," Biometrics, 14 (1):18-38 JSTOR 2527727
2. Brockett, Patrick L. and Levine, Arnold (1977) "On a Characterization of Ridits," The Annals of Statistics, 5 (6):1245-1248 JSTOR 2958658

Further reading

Donaldson, G. W. (1998). "Ridit scores for analysis and interpretation of ordinal pain data". European Journal of Pain. 2 (3): 221–227. doi:10.1016/S1090-3801(98)90018-0. PMID 15102382.