1. From Point to Point: The Proportional Symbol Map SP 240 Cartography Alex Chaucer

2. Spatial Information Technology Center Conceptual Basis for Proportional Point System Mapping Proportional point symbol mapping The method is obvious to the map reader Allows for easy understanding of the quantitative distribution

3. Spatial Information Technology Center When to Select This Method Two common instances: 1.Data occur at points 2.Data are aggregated at points within areas This method works when the map is to show relative magnitude Source: Monmonier

4. Spatial Information Technology Center A Brief History of Proportional Point Symbols Graduated circle A popular form of proportional point symbol; compact and easy to construct William Playfair developed the first use of graduated symbols in 1801 but not on maps Playfair used circles: still the most common shape Playfair scaled the symbol areas (rather than diameters or circumferences) to the data quantities - and this method also persists to date

5. Spatial Information Technology Center History, cont. First use on maps by Henry Harness, August Peterman, and Minard (1850s): Minard Graduated Circle Map (1858) (Source: Robinson)

6. Spatial Information Technology Center A Variety of Choices Circles, Squares, and Triangle are the most common forms of proportional symbols, with the circle being the dominant form.

7. Spatial Information Technology Center Circles are most common, but almost any shape could be used. http://go.owu.edu/~jbkrygie/krygier_html/geog_353/geog_353_lo/geog_353_lo11.html

8. Spatial Information Technology Center Circles have an advantage because: 1. form is compact 2. ease in scaling 3. they are visually stable

9. Spatial Information Technology Center Three-Dimensional Symbols 3D Symbols (sphere, cube, and rectanglar prisms) can offer attractive mapping, though it may be difficult to gauge their scaled values correctly.

10. Spatial Information Technology Center Graduated Bars http://go.owu.edu/~jbkrygie/krygier_html/geog_353/geog_353_lo/geog_353_lo11.html

11. Spatial Information Technology Center http://www.forbes.com/static_html/rich400/2004/distmap/indexFla.shtml

12. Spatial Information Technology Center Proportional Symbol Scaling There have been studies regarding perception of quantitative symbols for several decades. Humans response to symbols and their characteristics are referred to as psychophysical investigations.

13. Spatial Information Technology Center Psychophysical Examination of Quantitative Thematic Map Symbols Apparent Magnitude Scaling Scaling of proportional symbols that incorporates correction factors to compensate for the normal underestimation of a symbol’s area or volume Absolute Scaling Directly proportional scaling or area or volume of symbols to data values Area and Volume are often underestimated in the visual psychophysical world.

14. Spatial Information Technology Center Apparent Magnitude Curves Perceptual scaling: scaling adapted to take into account human perceptual abilities; also called apparent magnitude scaling

15. Spatial Information Technology Center Absolute and Apparent Scaling

16. Spatial Information Technology Center http://faculty.frostburg.edu/geog/kessler/geog 310/CompareCircles.jpghttp://faculty.frostburg.edu/geog/kessler/geog 310/CompareCircles.jpg

17. Spatial Information Technology Center The Proportional Circle what if someone tries to get a value from the map by measuring the circle? need to warn the user if this type of scaling is used further: most computer mapping programs don't incorporate perceptual scaling (but ArcGIS now does!) further: opinions about perceptual scaling have grown increasingly negative so absolute scaling is the norm

18. Spatial Information Technology Center Visual Illusions When a circle is seen among smaller circles, it is perceived as about 13% larger than if the same circle is seen among larger circles. Dent, Figure 9.7

19. Spatial Information Technology Center Perception of Circles among Circles Illusions Can show spatial numerousness Pattern can be important Can aide in memorability Though some overlapping can occur, can show cohesiveness

20. Spatial Information Technology Center Graduated squares are somewhat easier to calculate but are not quite as easy to interpret as circles because they are not as compact squares do not have the perceptual problems of circles people do not underestimate the area of squares as they do with circles The Square Symbol Source: Dent fig. 9.9

21. Spatial Information Technology Center Range Grading: A Probable Solution Adaption Theory In psychological theory, a neutral reference point on which perceived judgments are based; affected by the perceptual anchors from which judgments are made Anchor Effects the size of the visual anchor affects the estimate of magnitude of an unknown symbol; the contrast effect causes estimation to be away from the anchor, and the assimilation effect causes judgments to be toward the anchor.

22. Spatial Information Technology Center Range Grading: A Probable Solution Range Grading: A symbol represents a range of data values; differently sized symbols are chosen for differentiability for each of several ranges in the series of values being mapped.

23. Spatial Information Technology Center Graphic Design Considerations for Proportional Point Symbol Maps Only use when there is good variation in the data; no variation is better represented with another type of map. If the map looks homogeneous, choose another mapping method.

24. Spatial Information Technology Center Overloaded Proportional Point Symbols Don’t try to show too much-you might “overload” the map! Multiple variables quickly lead to complexity and symbol overload.

25. Spatial Information Technology Center Source:Robinson

26. Spatial Information Technology Center Source:Dent

27. Spatial Information Technology Center Eugene Turner

28. Spatial Information Technology Center Graphic Treatment of Proportional Symbols Grey tones can work. Overlap can have questionable results Filled circles better than outlines or transparent Symbols should be clear and not confused with the background.

29. Spatial Information Technology Center Computer Maps Keep design consideration in mind. May not have total control. Some methods are much easier in a computing environment.