Chapter 7 Proportional Symbol Mapping - Slocum

1. Chapter 7 Proportional Symbol Mapping - Slocum Graduated symbol map Two point data: true point and conceptual point Two kinds of symbols - geometric and pictographic Scaling - math. perceptual and range-graded Problems of legends

2. Selecting Appropriate Data (fig 7.1, 7.2) • True point data - data collected at true location • Conceptual point data - data collected over an area but use one point to represent the area data • City data is considered true point conventionally. • Data standardization works for point data • Choropleth map is more appropriate for showing the area than symbol maps.

3. Kinds of Proportional Symbols • Geometric symbols • circles, squares, spheres, and cubes • Circles is most commonly used symbols due to a) visually stable b) users prefers circle than others c) circles conserve map space d) size reflecting data is easy to be seen e) easy to construct. • Pictographic symbols • heads of wheat, caricatures of people, diagrams of barns, beers.. • clip arts and customized pictures available • problems : a) overlap causing problems (fig 7.3) b) hard to judge difference

4. Scaling proportional symbols • Mathematical Scaling: size is directly proportional to the data • where ri = radius of the circle to be drawn, • rL = radius of the largest circle on the map • vi = data value for the circle to be drawn • vL = data value associated with the largest circle • Formulas for other types of symbols are listed on page 123 • These methods are for unclassed maps. • Classed map can be presented after the classes are assigned and size. • If specifying smallest and largest sizes then the formula on page 123 will produce an unclassed map • most people will underestimate larger symbols

5. Perceptual Scaling: corrected mathematical scaling - account for underestimation. • R= response (perceived size) • S = stimulus (actual size) • c = constant • n = an exponent • actual and perceived size in power function • R = cSn • if size is estimated correctly, n 1 • underestimate, then n < 1 • overestimate, n > 1 • finally, we have the following formula for circle with correction • for square: • ri= radius of the circle to be drawn • rL = radius of the largest circle on the map • ri = data value for the circle to be drawn • vL = data value associated with the largest circle

6. Problems in applying the formula • 1) exponent affected by various experimental factors • 2) using single exponent is not realistic due to variations • 3) fails to account for the spatial context within which symbols are estimated • 4) experimental studies for deriving exponents have dealt only with acquiring specific map information Experimental factors affecting the exponent • Ratio estimation - comparing two symbols on a map, this method produce exponent of 0.87 for circles • Magnitude estimation - comparing symbols on the map to the size of the specific symbols on the legend to get the idea of the size on the map. This produced an exponent of 0.73 for circles. • Exponent increases while size of standard symbol increases

7. Improvement from different methods • No correction and use three circle legend to improve the exponent to 0.94 (Chang) • Training would improve exponents • Ebbinghaus illusion (fig 7.7), circle surrounded by larger circles appear smaller, vice versa. • Fig 7.8 shows the little effect from perceptual scaling while the largest circle is the same size on both maps.

8. Range-Graded Scaling • Data classified to groups and then use sized symbols to represent each class. • Three decision for deciding the sizes: • the number of classes • method of classification • symbol sizes • Advantages: • Readers are easy to match map and legend • Contrast in circle size may enhance the map pattern • good for pictographic symbols • Disadvantage: • careless readers might interpret scale wrong • patterns created by this is somewhat misleading.

9. Legend Design • Two problems: • how to arrange symbols • which symbols to include • Symbols Arrangements • nested-legend:save space • linear-legend: permits solid fill. Display from small to large (from left to right), Space consideration (e.g. Fig 7.12) might alter this arrangement. Largest on top (From top to bottom)

10. Which Symbols to Include • Range-graded Scaling: show class symbols • Math. and Perceptual Scaling: two methods • include smallest and largest symbol and interpolate several intermediate-sized symbols • use Jenks method to class data and use the median (mean) to construct legend symbols

11. Handling Symbol Overlap • Large symbols cause overlap, two questions: 1)how much overlap should, and 2)how the overlap should be symbolized. • 1) - dependent upon whether data is for communication or for data exploration. • if for communication, purpose matters (see 7.15C andD) • 2) Transparent or opaque symbols - color is flexible for displaying symbols (outline, fill different colors). Transparent allows background features show. Opaque enhances figure-ground contrast because the proportional symbols tend to appear as a feature; this is most apparent for the gray and black symbols. Opaque symbol appears above other features.

12. Transparent or Opaque • Transparent provides max info. • Gray and black is good for fill transp. symbols • Black is the best for filling opaque symbols • Transparent is more accurately estimated than opaque • Inset maps to enlarge congested area. • Move symbols slightly away from the center of congested areas Redundant Symbols • Use size and value (shading) • Easier to discriminate symbols on the basis of two visual variables than one. • More appropriate in data exploration environment. • Redundant for acquiring specific information and nonredundant symbols for acquiring general information.