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 In probability theory and statistics, the probit function is the quantile function associated with the standard normal distribution. It has applications in data analysis and machine learning, in particular exploratory statistical graphics and ...

and

logit In statistics, the logit ( ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations. Mathematically, the logit is the i ...

. A ''ridit'' describes how the distribution of the dependent variable in row ''i'' of a contingency table compares ''r''elative to an ''i''dentified ''d''istribution (''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 :

p_j=Prob().

Determining ridits

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

w_j=0.5p_j+\sum_.

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 ''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 rank In statistics, the percentile rank (PR) of a given score is the percentage of scores in its frequency distribution that are less than that score. Its mathematical formula is : PR = \frac \times 100, where ''CF''—the cumulative frequency—is ...

s. For any j, if ''x_j'' has a low (close to 0) ridit score, one can conclude that :

\sum_

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 science The following outline is provided as an overview of and topical guide to health sciences: Health sciences are those sciences which focus on health, or health care, as core parts of their subject matter. Health sciences relate to multiple aca ...

s (including nursing and

epidemiology Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population. It is a cornerstone of public health, and shapes policy decisions and evide ...

) 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 LevineBrockett, Patrick L. and Levine, Arnold (1977) "On a Characterization of Ridits," ''The Annals of Statistics'', 5 (6):1245-1248 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