Take a blank sheet of paper, quick answers to a few questions
Concept originates with Stevens (1946):
Nominal | Ordinal
| Interval | Ratio
Levels
A level is a class of measurement scales that share
some common properties. Stevens proposed that you could choose
the correct technique based on measurement levels. This concept
got institutionalized (largely based on books like Blalock and
Seigel) in certain social sciences... Cartographers adopt Stevens
wholesale and use it to present cartographic display options.
A fine idea fifty years ago to explain statistical options, not sufficient for GIS
Situations not handled by Steven's four levels:
Absolute | Counts
| Cyclical | Multi
Dimensional
Now the idea of an attribute reference system may make some sense. The basic information required depends on the level of measurement.
Level of measurement: Information required Nominal definitions of categories Graded membership definition of categories plus degree of membership or distance from prototype Ordinal definitions of categories plus ordering Interval unit of measure plus zero point Extensive ratio unit of measure (additive rule applies) Cyclic ratio unit of measure plus length of cycle Derived ratio units of measure (ratio of units; weighting rule) Counts definition of objects counted Absolute type (probability, proportion, etc.)
The rows in grey are additions to the classical levels of measurement as taught in other geography courses....
The concept of a measurement scale presumes that you already
know what you are measuring. Most sciences have an in-built assumption
about units of analysis, be it "cases", organisms (botany
& zoology etc.). Statistics built around concept of "populations"
represented by "samples" of such individuals.
What if the problem consists of identifying these individuals?
Geographic "cases" are often highly arbitrary and open
to argument. <Subject of next lecture...>
Back to the Pop Quiz
Phase 2: Measure your comprehension?