GEOG 486
Cartography and Visualization

Proportional Symbol, Graduated Symbol, Dot Density Maps


Before you begin the activities in this lesson, let me touch on some important distinctions, both semantic and data-based. The first important point to remember is the difference between discrete (or raw) data values and rates (or ratios). When you look at a weather map of temperatures, you are viewing individual data values placed at locations in space. In contrast, rates and ratios are calculated by normalizing raw counts against some other variable - miles per hour, persons per square mile, percentage of cows per acre. These rates are usually aggregated to some geographic unit - population density by county, for example. The maps you created in lesson 4 were Choropleth maps (maps of rates). In Lesson 5 we will explore some other map representations, some of which are more appropriate for those discrete values (i.e. counts).

As for semantics, we have the terms Graduated and Proportional. In most cartography texts these terms are used interchangeably, implying scaling of symbols based on the nature of the data distribution. Esri uses these terms to describe two different symbolization methods (more on that later). For now, be aware that the terminology used in the Concept Gallery is consistent with the literature and that used in the task instructions coincides with ArcGIS software.

A. Verify crime data is joined to Philadelphia Census Tracts.

The burglaries.xlsx file should still be joined to the attribute table of the tracts2000 shapefile dataset (remember, the Equal_Interval and duplicate layers are based in this shapefile).

  1. In ArcMap, open your lesson4.mxd map document. Then save as lesson5.mxd (so you still have the lesson 4 one in your files).
  2. If necessary, verify that your burglaries.xlsx file is joined to the attribute table of the tracts2000 shapefile by right-clicking on the 2009 Burglary Counts layer (or another map layer that contains crime data) and selecting Properties.
  3. Click the Joins & Relates tab.
  4. The name of the spreedsheet (burglaries_06$) should appear in the Joins window. If it is not there, you can use the Add button next to the Joins window to re-create the join to the 2009 Burglary Counts layer.
  5. Close the Layer Properties window.

note In Parts B - F of this lesson you will add a number of additional layers to your ArcMap document. If your table of contents pane starts to get too cluttered, you can:

  • Delete some of the classification maps from Lesson 4 (i.e. Equal Interval, Quantile, Natural Breaks and Standard Deviations).
  • Click the (-) sign next to a layer name in order to collapse the legend.
  • Turn off unused layers. Here is a keyboard shortcut: Ctrl-click the checkbox of any layer in the Table of Contents to toggle the visibility of all of the layers.

B. A range-graded proportional symbol map

Cartography texts typically use the phrases Proportional Symbol and Graduated Symbol interchangeably. Our Concept Gallery uses Graduated Symbol Maps for that section heading. The GIS software you are using actually distinguishes between the two phrases in order to differentiate the two modes of application of graduated/proportional symbols in thematic mapping. As mentioned in the Concept Gallery, you can create classed graduated symbol maps. These can be referred to as range-graded graduated symbol maps. In the ArcGIS software you will choose Graduated symbols when you want to create this type of map using classes. When you want to create a graduated/proportional symbol map where the data is not classed, but proportional to the data value, you will choose Proportional symbols.

First let's create a classed range-graded symbol map. Or, as the software refers to it, a graduated symbol map.

Concept Gallery

Learn more about establishing graduated and proportional symbols in the Concept Gallery.

Make a copy of the 2009 Burglary Counts layer and paste it into the data frame.

  1. Name this new layer Graduated.
    Recall that we have not actually replicated the dataset by doing this. We are just able to symbolize it in a different way in each layer.
  2. Make this new layer the only one visible.
  3. Open the Layer Properties window for this new layer.
  4. Click the Symbology tab.
  5. In the Show: window, on the left side, click on Quantities.
  6. Under Quantities click on Graduated symbols. You see that the interface looks similar to that of the Graduated colors window that you have already used.
  7. In the Fields: area of the window, the Value: should already be set to the P500_All_2009 field. Keep that as is. Leave the Normalization: setting at None.

    The Symbology properties interface gives you access to:

    • picking a classification method and number of classes, (note: because we are mapping counts we do not need to exclude data that is erroneous)
    • the size range of the symbols (the default size unit is points: a point (pt.) is equal to 1/72 inch)
    • the symbol, and its color (the Template button)
    • the background color of, in this case, the tract polygons (the Background button)

    Spend some time modifying these settings, keeping in mind that:

    • one of the challenges when it comes to proportional/graduated symbol mapping is to create differentiable symbols that do not completely obscure the base map or other symbols
    • you can use a color scheme with the classed graduated symbols as an additional device to create differentiable symbols. That is, vary the symbols by color value (and/or hue) in addition to size. (This should not be used for a multivariate map where color, particularly color value, is being used for a different variable).
    • proportionally sized circles and squares (and triangles) are the symbols most interpretable by the map reader
    • you may need to create a background map that just shows the tracts without data, so that the tracts with zero counts are not just missing. You could give these tracts a special symbol, gray them out or just have the background the same as the others and no symbol in them.

note When you zoom in and zoom out on a map containing graduated or proportional symbols, the symbols by default will retain the size dimension they were assigned when created (unless you have already set a reference scale). If you want the symbols to change scale along with the map, you can right-click on the data frame—either the data frame name in the table of contents, or in the map display area—then go to Reference Scale, and choose Set Reference Scale. You first learned to set the reference scale in Geography 483, to control the scaling of the text, but we also did this in Lessons 2 and 3.

C. A proportional symbol map

Now you will create a map employing proportional/graduated symbols where the data has not been put into classes. The ArcGIS/ArcView software refers to this type of map as a proportional symbol map.

  1. First, in the table of contents pane of your ArcMap window, make another copy of the 2009 Burglary Counts layer  or Graduated layer and paste it back into the table of contents list.
  2. Rename this copy Proportional.
  3. Make this new layer the only visible crime data layer.
  4. Bring up the Symbology properties window for this new layer.
  5. This time, under the Quantities category in the Show: window, click the Proportional symbols entry.
  6. Again, set the Value: to P500_All_2009. Leave the Normalization setting at None.
  7. Examine the interface. Note that you can:
    • exclude values from the display, based on a logical expression (the Exclude button). (Note that with proportional symbols - even though we are still mapping counts - there are times where you may need to exclude data UNDER a certain threshold because of the extreme range in the data. If there is ever a need for that, you can create a constant symbol that represents everything you excluded).
    • the Units button allows you to control the size of the symbols relative to map units. To size the symbols in terms of dimensioned units, the data values should represent a measurement on the map—a distance or an area, (for example area per tract that represents private residences). Otherwise Unknown Units should be specified
    • choose the background polygon fill color and line weight and color (the Background button)
    • specify the properties of the symbol used (the Min Value button)
    • toggle the Flannery scaling factor on and off (see the Concept Gallery)
    • choose the number of symbols that will display in the legend: this is important to the map reader's ability to gauge the meaning of the map symbols

D. Pictographic symbols

Before we leave the topic of proportional symbols, let's experiment with something other than the default circle symbol. The Concept Gallery mentions the subject of pictographic symbols and how they can challenge the perceptual capabilities of the map reader. Let's see.

  1. Make another copy of the 2009 Burglary Counts, Graduated or Proportional layer , naming it Pictographs. Make it visible.
  2. Turn off the display of all crime data layers but this new one.
  3. In the Symbology properties of this new layer, choose to Show: Proportional symbols.
  4. Set the Value: to the P500_All_2009 field.
  5. Now, click the Min Value button.
  6. In the Symbol Selector window that comes up, click on the Style References button. From this list select Crime Analysis. If there is already a check mark next to it, then the symbol set will already be part of the symbols you can scroll through.
  7. One of the symbols in the Crime Analysis set is named Burglary. It looks like a ski mask. It is actually almost circular in shape, so it will work decently as a proportional symbol. In the list of symbols scroll down until you find it. It will be grouped with several other symbols having light yellow colored backgrounds.
    When you locate it, click on it. Notice that its size is 18 (points).
  8. The 18-point symbol, remember, will represent the minimum data value. A height of 18 pts is rather large, considering the minimum data value will be 1 and the symbols need to scale up to represent the maximum value of burglaries in a census tract for 2009.
  9. Still in the Symbol Selector window, change the Size: to 2. (Although you can click on the Edit Symbol button to bring up the Symbol Property Editor window. There you can modify individual layers, the size, the angle, offset, etc. of the symbol.)
  10. Select OK to get to the Layer Properties window, where you can see the maximum size symbol that will be used. Click the Apply button. Symbols or text below 5 or 6 pts in height are often difficult to see/distinguish. If you want, make the minimum size 5, and see what size the largest symbol ends up being. This illustrates one of the challenges when it comes to creating a proportional or graduated symbol map.
  11. Click the OK button to close the property windows.

    Try this (optional)

    If you have been curious enough to zoom in and pan around your Census tract map of Philadelphia in the course of creating the maps in sections B, C and D, you may have come across a situation where a tract polygon has two symbols in it, when each tract polygon should have only a single symbol associated with it. The symbols that you create when you make a proportional symbol map are positioned at the centroid of the respective polygon. Think of the centroid of a polygon as the center of mass of the polygon. If you were to cut the polygon out of cardboard, the centroid would be the point where you could balance the polygon on a pin. Note that the centroid does not necessarily lie on/in the polygon (imagine a donut shape with the centroid in the central hole) so you might need to glue the polygon to a piece of transparent plastic and place the pin on the plastic (after

    1. Choose either one of the proportional symbol map layers you created in sections C or D, and make it visible.
    2. Open its attribute table.
    3. Via the Select By Attribute option, find the Census tract polygon that has a TRT2000 value of 033700.
    4. You should see that this polygon contains two symbols instead of just one (you might have to zoom in to see this, since one symbol will be quite small).
    5. Examine the tract polygon that borders it on the north. Its TRT2000 value is 034300. This is a rather sinuous polygon that bounds a stretch of Pennypack Creek. Can you find a symbol in it? It turns out that its centroid does not fall within the bounds of the polygon. The smaller symbol that you see in the 033700 tract polygon is located at the centroid for the 034300 tract polygon, outside of the polygon that it corresponds to.

      There is at least one other similar occurrence: the centroid for the 012400 tract polygon falls within the 010900 tract polygon. These tract polygons that have an external centroid are characterized by low numbers of burglary incidents, so you could decide to exclude them from map.

    6. Access the Symbology properties of the layer.
    7. Click on the Exclude button. This will bring up the Data Exclusion Properties window. Click the Query tab if it is not already chosen. The interface should look familiar; it is a query builder.
    8. The tract polygons that could be excluded in this case have TRT2000 values of: 009700, 012400, and 034300. Build an expression that will select all of them to be excluded. Note that the data values in the TRT2000 field are of type string, so in the logical expression, quotes around the field name and around each data value are necessary—and it is particular about whether they are single quotes or double quotes.
    9. Use the Verify button to test your syntax. Use the Help button if necessary.
    10. Note that when you perform this Exclude operation successfully, you get rid of not just the symbol, but the entire polygon.
    11. If you don't already have a layer showing the tracts without symbols, create one now to use as a background behind your layer with excluded tracts. Make sure to match the color of the backgrounds.

    I have you performing the Exclude operation on one of the proportional symbol maps. You can also exclude features when you make a graduated symbol map. There is an Exclusion button in the Classify properties window.

E. A dot density map

Concept Gallery

Learn more about establishing dot density maps in the Concept Gallery.

  1. Make one more copy of the 2009 Burglary Counts layer in your table of contents pane. Name it Dot Map. Make it visible.
  2. Turn off the display of all other crime data layers.
  3. Zoom out to full extent.
  4. Open the Layer Properties window for this new layer, and access the Symbology properties.
  5. In the Show: window, under Quantities, choose Dot density.
  6. In the Field Selection window you will see a listing of all of the fields in the tracts2000 attribute table (and any joined fields) that hold numeric data (short integer, double precision, etc.).
  7. For now click on the P500_All_2009 field of burglary data to highlight it, and add it to the Symbol/Field list by clicking the > button.
  8. Click the Apply button.
  9. Depending on the color of the dots and the color of the polygon fill, you may want to change either or both colors. You can change the fill color of the tract polygons via the color palette in the Background area of the properties window. To change the symbol properties of the dots you can either double-click on the dot symbol or the field name in the Symbol/Field list, or click on the Symbol or the Field column headings.
  10. In the Densities area of the properties window you can alter both the size of the dots and the number of burglaries that each dot represents. After altering these settings, hit the Apply button to see the change without having to close the properties window.
    Experiment with these settings, noting the visual effect that your changes have on the map. You can see that there is a component of artistry, or at least subjectivity, to determining the characteristics of a dot density map.
  11. By default the dots will randomly relocate within the polygon they are representative of each time you zoom in or zoom out. This setting is controlled by clicking on the Properties... button, found in the lower left of the Symbology properties window. Go ahead and click on this button. The window that comes up allows you to toggle between fixed and non-fixed dot placement. For now leave it set to Non-fixed Placement.
  12. Also by default the Maintain Density check box is checked. (If it is not checked, please make it so.) With this setting active, as you zoom in or out the relative size of the dots changes to maintain the same visual sense of dot density in the context of the map; the dots decrease in size as you zoom in, and vice versa. This change in dot size is reflected in the table of contents legend, too.
    With both the dot placement setting (see the previous step) and the Maintain Density checkbox in the default settings, click the OK button to close the Layer Properties window. Do some zooming in and out, paying attention to the dot size and the positions of the dots. If, after zooming in, you reopen the Symbology properties window, you will see the enlarged size of the dots reflected in the Dot Size slot.

F. A multivariate dot density map

In the Concept Gallery there is an example of a multivariate dot map, showing Chicago population by race/ethnicity. Theoretically, we could do this with the burglary by year data, to allow the map reader to determine whether or not there is a difference from year to year in the number of burglaries in Philadelphia in a single map. But to be really effective the different classes have to have some spatial variation as they do in the Chicago race/ethnicity dot map. Let's see what it takes to produce a multivariate dot map for our burglary data.

Concept Gallery

Learn more about establishing multivariate symbols in the Concept Gallery.

  1. Access the Symbology properties for the Dot Map layer.
  2. From the list of fields, add two or more of the individual years of the burglary count data fields to the Symbol/Field window. Make certain that they are listed in chronological order. It does not matter if the oldest is on the top or the bottom. Use the arrow buttons, to the right of the list, if you need to reorder the fields.
  3. Click the Apply button.

    It has been my experience that often, after you add to or take away from the list of fields in the Symbol/Field window, the Apply button remains grayed out. I have found that if you simply click on either of the Dot Size or Dot Value slider pointers, without even having to move it, the Apply button will activate.... You can then update the map view without having to click OK, which will update the map view but also close the Layer Properties window.

  4. No matter what the default colors are for the dots from the different years of burglary data, they are apt not to provide a logical scheme to the symbolization of the data (although they may work for qualitative data). Let's see if we can remedy that. You can be the judge of how effective we are.
  5. Expand the color palette/ramp list, and choose one of the color ramps, not the color palettes. The color ramps are characterized by continuous change gradients between hues. Whereas the palettes show blocks of discrete colors. To be able to do what we are attempting we need to select a color ramp from this list.
    A screen shot of the Layer Properties window, from which color ramps may be chosen.
    Figure 5.1.1 Choosing an appropriate color ramp from the Layer Properties box.
    Credit: Adrienne Gruver
    In the Figure 5.1.1, above, I have chosen the color ramp that ranges from green, through yellow, to red. It is about three-fourths of the way down the list of choices. Find the same color ramp and select it.
  6. We could stop here, if you feel the map reader can distinguish relative amounts of greens, yellow-greens, yellow-reds, and reds, and easily equate them to the chronology of the data. There, of course, would be a legend to aid the reader.
    Let's decide that this map is too difficult to read, and attempt a different color scheme.
  7. Right-click on the color ramp itself (not on the dropdown arrow) and choose Properties from the list that appears. This will open an Edit Color Ramp window.
  8. Click-highlight and Remove all but one of the entries that you see in the Color Ramps list.
  9. This should leave you with a single color ramp. If you click on it to highlight it, you can then click the Properties... button and proceed to change the end colors of the ramp. Alter the colors so that the ramp is going from light to dark in a single hue (for example, light pink to dark red), thus creating the potential basis of a sequential color scheme.
  10. Name and save the the new color ramp you create by right-clicking on the color ramp again, and choosing Save to Style. Click OK. You may want to go back and modify it.
  11. Click the Apply button.

    One might think that a qualitative color scheme would/should be used to symbolize temporal data. But in this case we are regarding the succession of time as quantitative and sequential.

    The color of the background can certainly have an effect on how distinguishable the dots are; if the background is dark, then the darker dots may not be as distinguishable, and vise versa if the background color is light.

  12. Spend some time experimenting with changing the dot size, the dot value, the background color, and the color ramp.

G. Save the map document

That is it for the walk-through instructions for Lesson 5. See the Final Tasks page (next) to see what is due.

If you have any questions, feel free to post them to the Lesson 5 Discussion Forum.

Concept Gallery

Learn more map pattern analysis in the Concept Gallery.