Measurement

Objectives of lecture:

• Levels of Measurement: a framework for geographic attributes
• Measurement Frameworks: <Didn't get to this part on 2 April...>
  based on choice of dimension to measure & how to control

Measurement of Attributes

The main key to an effective map is by matching the graphic treatment to the attribute.

What kinds of attributes are there?

Stanley Stevens (1947) distinguished four (4) "levels of measurement" largely as a way to decide what kind of statistics were applicable.

Cartographers adopted Stevens' "Levels of Measurement" as the framework for cartography, it works (mostly, to some extent...).

An example:

an arctic climate

hot, warm, temperate, cool, cold, frigid...

- 7 degrees F average January high temperature

Levels of Measurement

Stevens' four levels of measurement are the common background for measurement in geography and cartography.



Variants of nominal categories: sharp sets (perfect boundaries), 'fuzzy' (% membership) or 'prototype'

Examples:

• Topographic feature codes (from BC Ministry of Environment): NOMINAL (just names) (an excerpt if those happen to move...)
• Earthquake damage maps for Western Washington; what kind of attribute is this? Ordered categories=ordinal...; fill in their survey about movement - most questions are ORDERED categories...
• Interval, relatively few actually [Cleanest example: time: seconds from midnight, Julian days from start of year, years...] (the current UW weather observations are all ratio data except the degrees F, the wind direction also has an arbitrary zero - it is cyclical)
• Ratio: the SI system (note the distinction between base units and "derived");
• tour of the wall maps

What Stevens doesn't handle:

Distinction between "raw" and "derived" (comaparibility for different "sized" spatial units) eg. population versus population density; David Douglas (and many other cartographers) call this "absolute" and "relative" - see his treatise on the distinction [temporarily offline, pardon the inconvience].

Beyond Stevens' levels:

Absolute level (0 and 1 fixed) as Probability
Counts (real zero - just like Ratio, but discrete [no half people] and units are not arbitrary);

Cyclical measures (such as wind direction, clocks that just repeat)

More about Attributes and Levels of Measurement

• slides from a presentation (AUTO-CARTO 11)
• lecture from next course (get ahead?)
• a non-event: find the attributes

<This was as far as I actually reached on 2 April.>

Measurement Frameworks

Dent has some attempts to cover this division with his "natural" and "artificial" areal units (page 76), but that scheme does not stand up to all kinds of thematic maps...

Sinton characterized thematic mapping information involving three components:
Location, Theme (Attribute) and Time (see last lecture)
In order to measure one, one must be fixed and one "controlled": for example...

• Population density by state in 1980 : time fixed at 1980, location controlled as states, attribute of total people summed within state, divided by area
• Oil Spill 0900 30Mar89 : time fixed, category (attribute) controlled [oil spill exists or doesn't], location of edge of spill measured
• Flood Hydrograph : location fixed (under Green River Bridge), time controlled (measurement recorded every minute or hour), height of water measured

An overview of possible measurement frameworks:

Object Control Frameworks

Control: attribute; Measure: location

Isolated Objects

• Spatial Object Single category distinguishes from void
  Control: identity of object; Measure its location (edge)
  
• Isoline Regular slices of continuous variable
  Control: fixed heights; Measure location of that value

Connected Objects

• Network Spatial objects connect to each other, form topology
  
• Categorical Coverage Region subdivided by exhaustive classification

Spatial Control Frameworks

Control: location (grid); Measure: Attribute

Many variants, but cells (pixels) are spatially uniform, each recording an attribute value...

Composite Frameworks

Choropleth Collection zones used to tabulate more primitive attribute objects

First: Control: identity of object; Measure its location (edge) => base map
Second: use base map objects as Spatial control; Measure attribute within objects.

Temporal examples:

Control: Time (hour) Measure: Attribute (water level) => strip chart (tides) [overhead]
Control: Poland@date Measure: location => Historic Poland, [wall map]

Stuff that doesn't exactly fit...

Interaction data such as international trade, interegional flows ($, commodities or people)