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Copyright, 1998-2013 © Qiming Zhou GEOG1150/2015. Cartography Thematic Mapping

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

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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.

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

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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

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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

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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

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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.

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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.

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

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Thematic Mapping11 Arithmetic mean Geographical mean

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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

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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

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Thematic Mapping14 Densities Relative geographical crowding or sparseness of discrete phenomena

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

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

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Thematic Mapping17 Scaling systems

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

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Thematic Mapping19 Example AreaPer Capita Personal Income ($) Per Capita Educational Expenditure ($) Number of First- degree Graduates ($) A3882273 330 B4395266 910 C3870240 500 D5695333 40 E4282273 870 F4082276 70 G3952210 240 H5770357 2920 J5938340 530 K5550390 1760 L5304314 460 M4840280 1670 N4830360 580 P5745376 0 Q4570287 2500 (Source: Robinson, et al., 1995)

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Thematic Mapping20 Regression analysis Scattergrams with fitted linear regression line.

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Thematic Mapping21 Areal units

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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

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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

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

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Thematic Mapping25 1 23 34 42 7 16 824 33 43948 2 181028 37 135215 541761935 46 3252627 11 29303132 4201236 4150 38 5 49 475344 2114 22 45 40 51 39 Classification data set

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Natural break Thematic Mapping26 1 23 34 42 7 16 824 33 43948 2 181028 37 135215 541761935 46 3252627 11 29303132 4201236 4150 38 5 49 475344 2114 22 45 40 51 39 15 - 74 140 - 723 943 - 2883 3719 - 5366 7668 - 8597

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Equal Interval Thematic Mapping27 Max = 8597 Min = 15 Interval = (8597 – 15) / 5 = 1716.4 1 23 34 42 7 16 824 33 43948 2 181028 37 135215 541761935 46 3252627 11 29303132 4201236 4150 38 5 49 475344 2114 22 45 40 51 39 15 - 1731 1732 - 3448 3449 - 5164 5165 - 6881 6882 - 8597

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Equal area Thematic Mapping28 1 23 34 42 7 16 824 33 43948 2 181028 37 135215 541761935 46 3252627 11 29303132 4201236 4150 38 5 49 475344 2114 22 45 40 51 39 Total area = 441 Classes = 5 Area interval = 88.2 15 - 191 204 - 285 286 - 343 369 - 523 618 - 8597

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Quintile Thematic Mapping29 1 23 34 42 7 16 824 33 43948 2 181028 37 135215 541761935 46 3252627 11 29303132 4201236 4150 38 5 49 475344 2114 22 45 40 51 39 Total units = 54 Classes = 5 Unit Interval = 10.8 15 - 243 272 - 404 418 - 1195 1244 - 2883 3719 - 8597

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Standard Dev Thematic Mapping30 1 23 34 42 7 16 824 33 43948 2 181028 37 135215 541761935 46 3252627 11 29303132 4201236 4150 38 5 49 475344 2114 22 45 40 51 39 Mean = 1721.8 Sta Dev = 2169.8 15 - 1692 1981 - 3719 4017 - 5366 7668 - 7954 8957

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Thematic Mapping31 Example: world population density Maximum = 30127 Minimum = 0 Mean = 291.3 Std = 1947.1

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Thematic Mapping32 Natural breaks

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Thematic Mapping33 Equal interval

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Thematic Mapping34 Equal area

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Thematic Mapping35 Quartile

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Thematic Mapping36 Standard deviation Mean = 291.3 SD = 1947.1

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