Ordinal data analysis requires a different set of analyses than other qualitative variables. These methods incorporate the natural ordering of the variables in order to avoid loss of power. Stevens argued that, because the assumption of equal distance between categories does not hold for ordinal data, the use of means and standard deviations for description of ordinal distributions and of inferential statistics based on means and standard deviations was not appropriate. Instead, positional measures like the median and percentiles, in addition to descriptive statistics appropriate for nominal data number of cases, mode, contingency correlation , should be used.
In place of means and standard deviations, univariate statistics appropriate for ordinal data include the median,  : 59—61 other percentiles such as quartiles and deciles ,  : 71 and the quartile deviation. In lieu of testing differences in means with t -tests , differences in distributions of ordinal data from two independent samples can be tested with Mann-Whitney ,  : — runs ,  : — Smirnov ,  : — and signed-ranks  : — tests. Test for two related or matched samples include the sign test  : 80—87 and the Wilcoxon signed ranks test. Tests for more than two related samples include the Friedman two-way analysis of variance by ranks  : — and the Page test for ordered alternatives.
Ordinal data can be considered as a quantitative variable. In logistic regression , the equation. Linear trends are also used to find associations between ordinal data and other categorical variables, normally in a contingency tables. A correlation r is found between the variables where r lies between -1 and 1. To test the trend, a test statistic:.
R is calculated by:. Classification methods have also been developed for ordinal data.
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- Examples of ordinal logistic regression.
- Multilevel Models for Ordinal and Nominal Variables.
The data are divided into different categories such that each observations are similar to each other. Dispersion is measured and minimized in each group to maximize classification results.
The dispersion function is used in information theory. There are several different models that can be used to describe the structure of ordinal data . However, this generalization can make it much more difficult to fit the model to the data. This model does not impose an ordering on the categories and so can be applied to nominal data as well as ordinal data.
This model can be applied to nominal data. This model can only be applied to ordinal data, since modelling the probabilities of shifts from one category to the next category implies that an ordering of those categories exists. The proportional odds model has a very different structure to the other three models, and also a different underlying meaning. There are variants of all the models that use different link functions, such as the probit link or the complementary log-log link.
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The Assignment of Scores Procedure for Ordinal Categorical Data
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Analysis of Ordinal Categorical Data, Second Edition provides an introduction to basic descriptive and inferential methods for categorical data, giving thorough coverage of new developments and recent methods. Special emphasis is placed on interpretation and application of methods including an integrated comparison of the available strategies for analyzing ordinal data. Practitioners of statistics in government, industry particularly pharmaceutical , and academia will want this new edition.
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