Ridit scoring

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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[edit]

Choosing a reference data set[edit]

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[edit]

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[edit]

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

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 1\le j\le n, the value wj is the ridit score of the choice xj.

Interpretation and examples[edit]

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<j}{Prob(x_k)}

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

Applications[edit]

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

A mathematical approach[edit]

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.

See also[edit]

Notes[edit]

R statistical computing package for Ridit Analysis: http://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[edit]

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.  edit