Applications of Analysis of Variation for Data Measured on Ordinal Scale Base

• Activity Number: 400
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Tamar Gadrich*+ and Emil Bashkansky
• Companies: Ort Braude College and ORT Braude College
• Keywords: Ordinal data ; ANOVA ; Dispersion measure ; Statistical inference

Abstract

Dispersion measure can be used for practical engineering applications such as: quality classification, repeatability or cluster analysis and so on. When the data is measured on an ordinal scale basis, re-definition of classical statistical measure is needed, since only equal/unequal or greater/less than relations are allowed between ordinal variables values. Particularly, ORDinal ANalysis Of VAriation (ORDANOVA) is proposed as a tool for splitting the total variation of the ordinal data into the "between" and "within" components just as it is done in ANOVA for quantitative data. Moreover, an indicator - ratio of "between" component (divided by corresponding number of df) to the "total" variation (divided by total number of df) is suggested as a tool for identification the most segregative factor among those that are under considerations. Thereafter the "trouble-making" factor level can be detected by a procedure similar to jackknife. In the case when the property under study is measures on a binary scale basis, inference about binomial proportions based on small samples is studied and unbiased estimators for the between and within components of ordinal variation are established