Interpreting Area Data from Maps vs. Graphs: An Experiment in Visual Perception
Abstract
Graphical methods of data presentation are a key feature of scientific communication. This project asks the question, "What's the best way to compare the land area of states: a map or a bar graph?" You'll be measuring performance on two different visual discrimination tasks: comparison of areas vs. comparison of position on a common scale. Which method is more accurate? Which method is faster? This project will get you thinking about how to find the best way to communicate scientific information.Summary
Andrew Olson, Ph.D., Science Buddies
Sources
- Cleveland, W.S., 1985. The Elements of Graphing Data. Monterey, CA: Wadsworth Advanced Books and Software.
Objective
The goal of this project is to compare how accurately people make comparisons of areas using a map vs. a bar graph.
Introduction
This project explores both visual perception and scientific communication. Often, the most efficient way to communicate a scientific result is with a graph that shows the interesting features of the data. We can describe results with words, and we can give averages and other statistics, we can even provide tables of data, but a good graph can convey the "story" of the data more quickly. Furthermore, a good graph lets the reader critically evaluate the data. Is it convincing? Does it really support the conclusions or might there be another interpretation?
So what makes a graph good? Which graphical methods present data most clearly? Which methods are more difficult to decode? There are many possible variations to explore (see the Variations section, below, for some suggestions), but this project will focus on two fairly simple question:
- Is it more accurate to make land area comparisons using a map or a bar graph?
- Is it easier to make land area comparisons using a map or a bar graph?
If you wanted to compare the size of Oklahoma and Kansas, for example, the first thing you'd probably do is to look at a map. If you you just wanted to know which state was bigger, you'd be fairly certain of the answer. Now use a map to compare Kansas to Nebraska, its neighbor to the north. Which is bigger? The difference is much smaller here, and the answer may surprise you.
For this experiment, you will write a short geography test about the land areas of U.S. states. You'll need two groups of volunteers to take the test. One group will be given an outline map for reference while taking the test, the other group will be given a bar graph of state land areas. You can measure both the accuracy and the speed of each group in answering your test questions.
When you do your background research, study up on how well people can make visual discriminations. In the case of the map, you are asking your volunteers to make a visual discrimination by comparing areas with irregular borders. In the case of the bar graph, you are asking your volunteers to make a visual discrimination by comparing position along a common scale. Which task do you think will be easier? Make sure that you formulate your questions so that you cover the entire range of difficulty in making comparisons. In other words, make sure that some of the questions involve easy comparisons (a clear difference in area), some of the questions involve harder comparisons (a moderate difference in area), and some of the questions involve difficult comparisons (nearly equal areas).
Terms and Concepts
To do this project, you should do research that enables you to understand the following terms and concepts:
- land areas of the 48 contiguous states,
- mapping projections,
- visual discrimination:
- "just noticeable difference,"
- discrimination threshold,
- Steven's power law,
- Weber-Fechner law;
- statistical analysis:
- t-test,
- confidence intervals.
Bibliography
- For information on different map projections, see:
Rodrigue, C.M., 2002. Map Projections, Department of Geography, California State University, Long Beach. Retrieved February 28, 2006. - The following are selected references on the Weber-Fechner law and Stevens' power law, both of which describe relationships between the actual physical magnitude of a stimulus and the human perception of that stimulus:
- Wikipedia contributors, 2006. Just noticeable difference, Wikipedia, The Free Encyclopedia. Retrieved February 28, 2006.
- Wikipedia contributors, 2006. Weber-Fechner Law, Wikipedia, The Free Encyclopedia. Retrieved February 28, 2006.
- Wikipedia contributors, 2006. Stevens' Power Law,. Retrieved February 28, 2006.
- Cleveland, W.S., 1985. The Elements of Graphing Data. Monterey, CA: Wadsworth Advanced Books and Software.
Materials and Equipment
To do this experiment you will need the following materials and equipment:
- blank outline map of the continental United States, showing state boundaries,
- U.S. atlas, listing areas of each state,
- graph paper, ruler, and pencil (or computer graphing program),
- calculator (or computer spreadsheet program),
- a list of area comparison questions for your test (about 20 questions),
- two groups of volunteers (25–30 people in each) to take a short test.
Experimental Procedure
- Do your background research so that you are knowledgeable about the terms and concepts.
- For the first test group, make an outline map of the 48 contiguous U.S. states, with each state labeled with its two-letter code. Use the same size label for each state. For small states in the northeast, use a label outside the state with a line pointing to the approximate center of the state.
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Compile a table of the land areas of the 48 contiguous U.S. states. Your data table should include:
- the two-letter abbreviation for each state,
- land area in thousands of square kilometers (km2), and
- the log base 2 of the land area in thousands of square kilometers. (Use a calculator or spreadsheet program.)
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For the second test group, create a bar graph of the land area data. Here are some suggestions:
- Arrange the data from highest to lowest area.
- Label each bar with the two-letter state abbreviation code.
- For interpreting the bar lengths, one axis should be labeled in units of area (1000 km2), the other in units of log base 2 area (log base 2 1000 km2).
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For both test groups, construct a state area quiz to administer to your two groups of volunteers. Here are some ideas for questions and considerations to keep in mind:
- One type of question you can ask is to order a group of neighboring states from highest to lowest area. This will be easier for some groups than for others.
- Make sure that you formulate your questions so that you cover the entire range of difficulty in making comparisons. In other words, make sure that some of the questions involve easy comparisons (a clear difference in area), some of the questions involve harder comparisons (a moderate difference in area), and some of the questions involve difficult comparisons (nearly equal areas). Also, be sure that your test includes multiple comparisons of each of these three types so that you can do statistical analysis on each group of questions.
- Finally, keep in mind that comparing areas becomes more difficult as the distance between the objects increases. For this reason, it is best to restrict your questions to comparisons of groups of neighboring states. If you want to include comparisons of distant states, remember to treat the separation distance as another independent variable in your analysis.
- It's a good idea to run "pilot" tests with small groups (who will not be part of the final test group), to make sure that your instructions, map, graph and test questions are worded clearly. That way you can correct any problems that you find before running the actual experiment.
- Remember to ask your test volunteers to write down the time when they start and when they finish the test. If you want more detailed data, have them fill in the time for each question.
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Analyze your results. Here are some ideas:
- Was one group consistently faster than the other?
- Was one group consistently more accurate?
- Group the test answers according to the relative difference in area required to make the discrimination. How do the two groups compare when you look at the results this way?
- Have a mentor help you with statistical analysis of your results, and see if you can come up with a way to compute confidence intervals for your analyzed results.
Questions
- What do your results tell you about the best way(s) to communicate results that include an area component? Is one method superior in all cases? If not, how can you choose which method to use?
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Variations
- Testing methods of graph construction. Instead of using a map for the first test group, use a second bar graph. For the second bar graph, instead of arranging the states in order by area, randomize the order. How do the results of the two groups compare?
- Make your test questions more quantitative. Instead of simply rank-ordering areas, include more quantitative questions in your test. For example, ask for an estimated ratio of the areas of two states, or ask something like "List the state(s) with about 50% more area than Washington."
- Using tables of numbers. Add a third condition for comparison (you'll need a third group of test volunteers): have the third group use a table of numbers giving the area of the states (arranged in rank order). Do you think this group's answers will be more or less accurate than the group using the map? More or less accurate than the group using the bar graphs? Will they be faster or slower than the other two groups? Try it and find out!
- Comparing areas with regular borders. Maybe you think the map comparison is too difficult. Many of the state borders are irregular, and there is the added variable of making comparisons between neighboring states and distant states. Here's another area comparison experiment you can try. Compile a table showing the population of the 20–30 selected U.S. cities. For ideas on which cities to select, think about the kinds of questions you'd like to ask about the data. Create two graphs of the data: 1) a bar graph (consider using a log scale, as in the map project); 2) a graph that encodes the city populations using the area of a simple geometrical shape (e.g., a square or circle). Create a test of 10–20 questions based on relationships in the data set (e.g., Which city (or cities) have about one-third the population of the most populous city? Which city has about twice the population of _______ ?) Have two groups (at least 30 people each) take your test. Both groups answer the same questions, but one group uses the bar graph and one group uses the area graph to answer the questions. Compare the results. Use statistical analysis to determine how confident you can be in drawing conclusions from your experiment.
- Maybe you're interested in exploring other aspects of map-based data. What are the best methods for conveying information about geographical areas? For example, compare different methods for showing population densities: color-coded map, vs. identically sized "thermometer"-type bars for each area, vs. dot densities representing population. Which method conveys the information most accurately?
- For a project that explores other types of visual discrimination in decoding graphs, see: What's the Best Method to Communicate Data Graphically?: An Experiment in Visual Perception.
Careers
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