Copyright, © Qiming Zhou GEOG1150/2015. Cartography Thematic Mapping

2  Objectives of map design  Data measurement  Basic statistical concepts and processes  Thematic map representations

Thematic Mapping3 Objectives of map design  Geographical variables are so diverse and complex, we must understand their essential nature.  Geographical ordering - locational relationships. Discrete phenomena. Continuous phenomena.

Thematic Mapping4 Data measurement  Scales of measurement Nominal Ordinal Interval Ratio  Use of the scales of measurement in thematic mapping

Thematic Mapping5 Nominal scales of measurement PointLineArea TownRiverSwamp MineRoadDesert ChurchGraticuleForest Bench mark Boundary Census regions Examples of differentiation of point, line and area features on a nominal scale of measurement. After Robinson, et al., 1995

Thematic Mapping6 Ordinal scales of measurement Examples of differentiation of point, line and area features on an ordinal scale of measurement. After Robinson, et al., 1995 PointLine (roads)Area Large Medium Small National Provincial County Township Industrial regions MajorMinor Smoke pollution

Thematic Mapping7 Interval-ratio scales of measurement Examples of differentiation of point, line and area features on an interval or ratio scale of measurement. After Robinson, et al., 1995 PointLine (roads)Area

Thematic Mapping8 Basic statistical concepts and processes  It is often necessary to manipulate raw data prior to mapping.  Pre-map data manipulation stage: Making data to be mapped comparable.

Thematic Mapping9 Absolute and derived data  Absolute qualities or quantities: “raw data” maps showing landuse categories, production of goods, elevations above sea level, etc.  Derived values. Summarisation or relationship between features. Four classes of relationships: averages, ratios, densities and potentials.

Thematic Mapping10 Averages  Measures of central tendency  Three commonly used averages in cartography: Arithmetic mean Median Mode

Thematic Mapping11 Arithmetic mean Geographical mean

Thematic Mapping12 Median and mode  Median - the attribute value in the middle of all ordered attribute values Geographic median - the attribute value below which and above which half the total area occurs  Mode - the value that occurs most frequently in a distribution Area modal class - the class which occupies the greatest proportion of an area

Thematic Mapping13 Ratios  Something per unit of something else  Quantities that are not comparable should never be made the basis for a ratio Ratio or rateProportionPercentage

Thematic Mapping14 Densities  Relative geographical crowding or sparseness of discrete phenomena

Thematic Mapping15 Potentials  Individuals comprising a distribution (e.g. people or prices) interact or influence one another.  The gravity concept:

Thematic Mapping16 Thematic map representations  Indices of variation Mode - variation ratio Median - quantile range (quartiles, ceciles or centiles (percentiles)) Arithmetic mean - standard deviation

Thematic Mapping17 Scaling systems

Thematic Mapping18 Some basic statistical relations  Regression analysis  Correlation analysis Spatial autocorrelation

Thematic Mapping19 Example AreaPer Capita Personal Income ($) Per Capita Educational Expenditure ($) Number of First- degree Graduates ($) A B C D E F G H J K L M N P Q (Source: Robinson, et al., 1995)

Thematic Mapping20 Regression analysis Scattergrams with fitted linear regression line.

Thematic Mapping21 Areal units

Thematic Mapping22 Observed, predicted and residuals Maps showing observed per capita educational expenditures, predicted per capita educational expenditures based on per capita income, and residuals from the regression. From Robinson, et al., 1995

Thematic Mapping23 Observed, predicted and residuals (cont.) Maps showing observed numbers of first-degree graduates, predicted numbers of first-degree graduates based on per capita income, and residuals from the regression. From Robinson, et al., 1995

Thematic Mapping24 Classification  Natural breaks  Equal interval  Equal area  Quartile  Standard deviation

Thematic Mapping Classification data set

Natural break Thematic Mapping

Equal Interval Thematic Mapping27 Max = 8597 Min = 15 Interval = (8597 – 15) / 5 =

Equal area Thematic Mapping Total area = 441 Classes = 5 Area interval =

Quintile Thematic Mapping Total units = 54 Classes = 5 Unit Interval =

Standard Dev Thematic Mapping Mean = Sta Dev =

Thematic Mapping31 Example: world population density Maximum = Minimum = 0 Mean = Std =

Thematic Mapping32 Natural breaks

Thematic Mapping33 Equal interval

Thematic Mapping34 Equal area

Thematic Mapping35 Quartile

Thematic Mapping36 Standard deviation Mean = SD =