Lecture 6 - Area Data

Question 1

TYPES OF AREA OBJECTS (2)

Answer 1

Two main types:

• Natural
• Imposed

Can represent with raster grid of cells or vector polygons

The areas can be either planar & non-planar enforced.

Question 2

GEOMETRIC PROPERTIES OF AREAS (11)

Answer 2

1. SHAPE - regular (like circle or square) or irregular
2. AREA (size) - accuracy depends on resolution/detail
3. PERIMETER
4. LONG AXIS & SHORT AXIS
5. LARGEST INTERNAL CIRCLE RADIUS
6. SMALLEST EXTERNAL CIRCLE RADIUS
7. SKELETON
8. ASPECT RATIO (width to height) - shows if elongated or square
9. COMPACTNESS
10. ORIENTATION (dominant angle)
11. SPATIAL PATTERN

Question 3

LOCATION QUOTIENTS

Answer 3

• measures % of activity in an area relative to a % of the same activity in a wider unit
• fraction of local/global rates of an activity
• measures over or under-representation (is a crime in a specific meshblock more than city-wide crime rates?)
• LQ value <1 means under-represented
• LQ value >1 means over-represented
• LD value = 1 means ratio equal to whole

Question 4

MAPPING APPROACHES

Answer 4

Planimetric Map
Cartogram
Quantile map
Percentile map
Box plot (Inter Quartile Range)
Standard Deviation

Question 5

Natural Areas

Answer 5

• self defined / sharp boundaries (lake, forest, mountain, etc)
• mostly homogenous within border
• often homogeneity displayed on map is fiction (some variation within area, ie. land use) for simplicity and ease of use

Question 6

Imposed Areas

Answer 6

• boundaries are defined independently of phenomenon (by humans)
• a sampling of the underlying reality

often misleading:

• little relationship to underlying patterns
• arbitrary and modifiable (MAUP)
• makes ecological fallacy very real
• gerrymandering

Question 7

Raster Aerial Objects

Answer 7

• cells identical & cover region of interest (raster or vector grids)
• each cell an area object
• can represent continuous & discrete data

Question 8

Planar Enforced

Answer 8

• area objects mesh together neatly and exhaust study region (topology - common borders)
• every location fits within area
• no gaps or overlaps

Question 9

Non-planar enforced

Answer 9

• gaps within area
• entities isolated from each other or overlapped
• more complicated to use for analysis

Question 10

Largest internal circle radius

Answer 10

What is the radius of the largest circle that can be entirely contained in the shape?

Question 11

Smallest external circle radius

Answer 11

What is the radius of the smallest circle that can entirely contain the shape inside?

Question 12

Long axis & short axis

Answer 12

Used to understand length/width and orientation. What is the longest line that can be drawn from one end to the other for a shape in two (perpendicular) directions

Question 13

Skeleton

Answer 13

Reduce shape into simple lines and vertices

• geometric central points
• tree-like structure
• reduce to a central point farthest from the original boundaries and also the centre of the largest circle inside the shape

Question 14

Compactness

Answer 14

Measures the area of the object and compares it to the area of a circle with the same perimeter
Compactness score of 1 means the shape is a circle, smaller number more complex irregular shape

Question 15

Spatial Pattern

Answer 15

look at how many neighbours (shared borders) each shape has

• regular shapes have the same # of neighbours
• complex shapes have different numbers of neighbours, this value is spread around the mode (# that appears most often)
• compare the mode to a random distribution to infer if the shapes are more regular or irregular (smaller than mode = regular, larger than mode = irregular)

Question 16

What is missing if we just look at points?

Answer 16

Underlying location, population density, etc.

Question 17

Unit of aggregation

Answer 17

Units of aggregation:
territoral authority, regional aerial units, meshblocks

Use to aggregate the point data/events than analyse in the context of population density, rates, etc. so areas can be compared.

Question 18

Unit of measurement for area unit variables

Answer 18

• counts
• rates (per 1000 people)
• population density (people/km2)
• location quotient

Question 19

Planimetric maps

Answer 19

used to map location quotient, shows a bar/column for the areas with over or under-representation which show how much more than the rate of the whole
intuitive but with limitations

Question 20

Cartogram

Answer 20

a map in which some thematic mapping variable is substituted for land area or distance. Geometry or space of the map are distorted to convey the information of the specific variable

Question 21

Quantile maps

Answer 21

Map a variable by area divided into 7 (+/-) categories with different colour coding, the categories have an equal range of values
Issues: cannot differentiate between areas in the same colour/category, will also see a difference between two areas but maybe their values are very close but fall in different categories because of how the ranges are set

Question 22

Percentile map

Answer 22

• ranking maps
• group ranked distributions in 6 categories: 0-1, 1-10, 10-50, 50-90, 90-99, 99-100%
• highlights extremes, the top and bottom 1%, maybe not outliers?

Question 23

Inter Quartile Range

Answer 23

• put values in a row from small to large
• divide row into four equal parts, then identify the median (middle) and the Inter Quartile Range
• lower IQ value is the median of the 1st and 2nd parts of the set
• upper IQ values is the median of the 3rd and 4th parts of the set
• the IQR is the difference between the upper IQ value and lower IQ value

Question 24

Box Plot (Hinge)

Answer 24

Denote values 1.5 or 3x the IQR, outside of which values are regarded as outliers
Then map areas based on the quartile they fall in or if they are outliers

Question 25

Standard Deviation

Answer 25

- find the mean - highlights differences in units above and below the mean - typically 7 categories: mean, +3 standard deviations above and below - helps to see extremes