Further Developments in the Terminological Theory of Data Frank Farance Farance Inc Daniel Gillman US Bureau of Labor Statistics

Introduction Statistical Data Axioms Operations Datatypes Values Statistical Data (again) Ontologies

Statistical Data Categorical –Nominal Sex categories –Ordinal Preference Scale Quantitative –Interval Temperature ˚C (Celsius) –Ratio Temperature ˚K (Kelvin)

Axioms All Data Have Equality Nominal –Exact, Non-numeric, Cardinality Ordinal –Nominal + Order Interval –Numeric Ratio –Interval + Approximate

Operations Nominal –Determine Equality, Cardinality; No Arithmetic Ordinal –Determine Equality, Cardinality, Order; Averages Interval –Equality; Addition / Subtraction Ratio –Equality; Multiplication / Division

Datatypes Compare with Statistical Data Typology Assertions –Axioms Characterizing Operations –Operations Value Space –??

Values Value = Element of Value Space –Share Notion of Equality –Equality Differs Across Datatypes Compare Integer Versus Code –Is a Concept Equality – i.e. compare concepts –Integer Integer built from natural numbers Natural number built from sets –Code Designation of (points to) concept Concept description stored in repository

Statistical Data (again) Population –A concept –Therefore, has characteristics Variables Not population characteristics Values –Properties of characteristic Determinant (P) versus Determinable (Ch) What is determined (observed) about respondent

Ontologies Specification of a Conceptualization Common definition Tom Gruber, 1994 Concept system with an associated computational model Farance and Gillman, 2005 –Value space => Concept System –Assertions and Characterizing operations => Computational model

Ontologies Datatype is an ontology Also, Concepts have roles –Property –Characteristic Values, Variables, Populations –Concept system –Computational Model Automatically create variables and associated allowed values

Ontologies Two ontologies for statistical survey work –Datatypes (computational model for data) –Variables (semantical model for data) How to tie these together? –Values