NAP: Data Models

Data Models

A data model is a mental model of the nature of some data. It answers such questions as the following:

What values can the data take?

Are they all numeric? Are they all integers? Is the set of possible values finite? What are the minimum and maximum possible values? Are ∞ and NaN possible values? Do some values have special meanings, such as indicating undefined or missing data?

What is the measurement level?

Data is often classified as follows according to measurement level:

Name
of
Level Description Valid
Operations Appropriate
Measure of
Central Tendency Examples
nominal values denote categories
which have no order = ≠ mode color, postal code (e.g. zip)
chemical species (e.g. CO₂)
ordinal values are ordered
differences meaningless = ≠ < ≤ > ≥ median Richter earthquake scale
dates in form YYYYMMDD
interval differences are valid
quotients meaningless = ≠ < ≤ > ≥
+ − arithmetic mean temperature in °C
ratio quotients are valid = ≠ < ≤ > ≥
+ − × ÷ geometric mean temperature in °K

Name of Level	Description	Valid Operations	Appropriate Measure of Central Tendency	Examples
nominal	values denote categories which have no order	= ≠	mode	color, postal code (e.g. zip) chemical species (e.g. CO₂)
ordinal	values are ordered differences meaningless	= ≠ < ≤ > ≥	median	Richter earthquake scale dates in form YYYYMMDD
interval	differences are valid quotients meaningless	= ≠ < ≤ > ≥ + −	arithmetic mean	temperature in °C
ratio	quotients are valid	= ≠ < ≤ > ≥ + − × ÷	geometric mean	temperature in °K

How accurate are the values?

A measurement error is the difference between the true value and the measured value. Measured values can differ from true values due to:

finite precision of instrument
systematic errors (e.g. inadequately calibrated instrument)
random errors (due to finite size of sample)
sampling errors (due to non-randomness of sample)
blunders (e.g. a human misreading an instrument)

It is desirable to include error estimates with data.

Are the data located in some space?

A time series consists of values located along the time dimension. Geographic data is located along spatial dimensions such as latitude, longitude and altitude and may also have a time dimension. Note that longitude is cyclic.

The dimensions of the space can have a measurement level of nominal. For example, an accounting spreadsheet might have columns corresponding to charge codes and rows corresponding to company divisions.

Data located in a continuous space can be either gridded or scattered. Both types are discussed in NAP Grids.

Author: Harvey Davies © 2002, CSIRO Australia. Legal Notice and Disclaimer
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