Measurement Levels

Objectives of lecture:

1. Present Levels of Measurement
   • Stevens and Beyond
   • Provides a framework for Attribute Reference Systems
2. Support for Discussion Events and Exercises
   • Exercise 1.(BEGINS NEXT WEEK).
   • Next week: Discussion 1 All students should be in a team [1-4] assigned at D0 on wednesday/thursday. Remember to meet with your team next week.

Pop Quiz

Take a blank sheet of paper, quick answers to a few questions

Levels of Measurement

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.

Central contention of Stevens and his followers:

• Number scales determine appropriate technique.

A fine idea fifty years ago to explain statistical options, not sufficient for GIS

Beyond Stevens

Situations not handled by Steven's four levels:
Absolute | Counts | Cyclical | Multi Dimensional

Attribute Reference Systems

Now the idea of an attribute reference system may make some sense. The basic information required depends on the level of measurement.

Information content of attribute reference systems.

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....

What to measure?

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?