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| In [[econometrics]], '''ridit scoring''' is a statistical method used to analyze ordered qualitative measurements.
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| The tools of ridit analysis were developed and first applied by Bross,<ref>Bross, Irwin D.J. (1958) "How to Use Ridit Analysis," ''Biometrics'', 14 (1):18-38 {{jstor|2527727}}
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| </ref> who coined the term "ridit" by analogy with other statistical transformations such as [[probit]] and [[logit]].
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| ==Calculation of ridit scores==
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| ===Choosing a reference data set===
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| 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.
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| ===Determining the probability function===
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| After a reference data set has been chosen, the reference data set must be converted to a probability function. To do this, let ''x<sub>1</sub>'', ''x<sub>2</sub>'',..., ''x<sub>n</sub>'' denote the ordered categories of the preference scale. For each ''j'', ''x<sub>j</sub>'' represents a choice or judgment. Then, let the probability function ''p'' be defined with respect to the reference data set as
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| :<math>p_j=Prob({x_j}).</math>
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| ===Determining ridits===
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| The ridit scores, or simply ridits, of the reference data set are then easily calculated as
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| :<math>w_j=0.5p_j+\sum_{k<j}{p_k}.</math>
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| Each of the categories of the reference data set are then associated with a ridit score.
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| More formally, for each <math>1\le j\le n</math>, the value ''w<sub>j</sub>'' is the ridit score of the choice ''x<sub>j</sub>''.
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| ==Interpretation and examples==
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| Intuitively, ridit scoring can be understood as a modified notion of percentile. For any j, if ''x<sub>j</sub>'' has a low (close to 0) ridit score, one can conclude that
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| :<math>\sum_{k<j}{Prob(x_k)}</math>
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| is very small, which is to say that very few respondents have chosen a category "lower" than ''x<sub>j</sub>''.
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| ==Applications==
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| Ridit scoring has found use primarily in the [[health science]]s (including nursing and [[epidemiology]]) and econometric preference studies.{{Citation needed|date=June 2011}}
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| ==A mathematical approach==
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| Besides having intuitive appeal, the derivation for ridit scoring can be arrived at with mathematically rigorous methods as well. Brockett and Levine<ref>Brockett, Patrick L. and Levine, Arnold (1977) "On a Characterization of Ridits," ''The Annals of Statistics'', 5 (6):1245-1248 {{jstor|2958658}}
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| </ref> presented a derivation of the above ridit score equations based on several intuitively uncontroversial mathematical postulates. | |
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| ==See also==
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| * [[Logit]]
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| * [[Probit]]
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| * [[Percentile]]
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| ==Notes==
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| R statistical computing package for Ridit Analysis: http://CRAN.R-project.org/package=Ridit
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| {{reflist}}
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| ==Further reading==
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| {{cite doi|10.1016/S1090-3801(98)90018-0}}
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| [[Category:Econometrics]]
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| [[Category:Categorical data]]
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I'm Dawna and I live with my husband and our 2 children in Montbrelloz, in the south part. My hobbies are Sculpting, Table football and Gymnastics.
My web site Top Hair Salons NC