Ordered Categories: Graphs Showing Empirical Relations Between One Proportion and Another, and Comparison with Theories

SYNOPTIC ABSTRACT

Some dependent variables are not fully quantitative and cannot be exactly measured, yet the categories are not merely qualitatively different states: rather, observations are classified into ordered grades. Are the proportions of observations in the several grades related to one another in some systematic way, for example, do they arise from an underlying normal distribution? In some datasets, there are just three grades, and comparison is made of several different circumstances. An important question is whether the proportion in category 3 is positively correlated with the ratio of the proportions in categories 2 and 1. Statistical models are given which permit methods of linearizing this relationship to be suggested. The areas of application considered are as follows: injury severity in road accidents; “don't know” responses in contingent valuation surveys; fracturing and shape of particles; taphonomy (i.e., the extent of deterioration of biological material over time); heart rate variability; pyrolysis (liquid may be intermediate between gas and solid); errors in neuropsychological tests (some may be less serious than others); errors in speechreading (one condition may be more difficult than another).

Key Words and Phrases:

• ordinal categories
• linearizing transformations
• P-P plots
• injury severity
• particle science
• contingent valuation
• “don't know” responses
• taphonomy
• heart rate variability
• pyrolysis
• cognitive neuropsychology
• speechreading