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What's the Best Method to Communicate Data Graphically?: An Experiment in Visual Perception

Time Required Long (2-4 weeks)
Prerequisites None
Material Availability Readily available
Cost Very Low (under $20)
Safety No issues


Graphical methods of data presentation are a key feature of scientific communication. This project will get you thinking about how to find the best way to communicate scientific information.


The goal of this project is to investigate the best methods for communicating data graphically. You'll compare how accurately people make different types of visual discriminations which are required for interpreting common graphs (e.g., position along a common scale; position along identical, but non-aligned scales; length; angle; area; slope).


Andrew Olson, Ph.D., Science Buddies


  • Cleveland, W.S., 1985. The Elements of Graphing Data. Monterey, CA: Wadsworth Advanced Books and Software.

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Last edit date: 2012-12-07


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? To answer this question, we'll follow an experiment conducted by William Cleveland and described in his book, The Elements of Graphing Data (Cleveland, 1985, 229–254). We'll provide some examples of different visual discrimination tasks that are required for decoding common types of graphs:

  • position along a common scale,
  • position along identical, but non-aligned scales,
  • length,
  • angle,
  • area,
  • slope.
We'll show you how you can construct comparison tests like Cleveland's to measure people's accuracy at these different kinds of visual discrimination tasks. You can then choose which visual discrimination tasks you want to investigate for your project.

Here are six example graphs, using made-up data, illustrating how each of the visual discrimination tasks listed above can be used in decoding graphical information.

Position Along a Common Scale

Dot plot with common scale.

With the box plot above, comparisons between the different categories are made along a common scale.

Position Along Identical, but Non-Aligned Scales

Three dot plots side-by-side, with identical scales.

With data in multiple groups, such as the three shown above, comparisons between data points in different groups are made along identical, but non-aligned scales.


Scatter plot with error bars indicating 50% and 95% confidence intervals.

In the scatterplot above, the data points are indicated by the solid circles. The vertical lines surrounding each data point show the confidence intervals for each data point. The total length of each line shows the 95% confidence interval (there is 95% probability that the true average for the data point lies within this range). The region between the short horizontal line shows the 50% confidence interval (there is a 50% probability that the true average for the data point lies within this range). When comparing the confidence intervals between the different data points, you are making visual discriminations based on length.


Pie chart.

When comparing the different sections of a pie chart, you are making visual discriminations based on angle.


Line plus symbol graph, showing an irregularly rising curve.

This line-and-symbol graph shows a data set with a rising trend in the y-measurement as the x-measurement increases. When you compare the rate of increase of y at one x-value vs. another, you are making a visual discrimination based on the slope of the connecting line segments.


Scatterplot encoding three values per data point.  One value is shown by position on the x-axis, a second value is shown by position on the y-axis, and a third value is shown by the area of the symbol.

In this scatterplot, each data point encodes three values. The x- and y-positions of the centerpoint encode one value each, while the area of the circle encodes a third value. When you compare this third value between the data points, you are making visual discriminations based on area.

Constructing Comparison Tests

Which of the visual discrimination tasks above do you think is the easiest? Which is the most difficult? In order to find out if your hunches are correct, you can construct some simple visual discrimination tasks and have a group of volunteers take your test. Then you can analyze the test results and see which tasks people perform with lower errors and which with higher errors.

The two illustrations below will give you an idea of how to make your test samples. The first one is an example of comparing position along a common scale, and the second one is an example of comparing position along identical, non-aligned scales. In both cases, the task is the same. You ask your volunteers to use "A" as the reference element. The volunteer is asked to compare each of the other elements ("B", "C" and "D") to "A", and to estimate what percentage of "A" each element is. In all cases, the test elements are less than or equal to the reference element with regard to the attribute being judged, so all answers should be between 0 and 100 percent.

Test sample for comparing position along a common scale.
Test sample for comparing position along a common scale.

Test sample for comparing position along identical, non-aligned scales.
Test sample for comparing position along identical, non-aligned scales.

The error for each estimate is calculated like this:

error = | estimated percent − actual percent | .

You can make similar test samples for the other attributes (length, angle, slope and area). Choose at least three attributes to test, and make at least 10 different test samples for each attribute. Make all of your test samples the same size (e.g., a single sheet of paper). Keep the spacing of your test samples uniform across all of the attributes.


When you do your background research, try to find existing information on how well people can make visual discriminations for the tasks you've chosen. Then make sure that you formulate your tests so that for each task you cover the entire range of difficulty in making comparisons. In other words, make sure that some of the comparisons will be easy, some of the comparisons will be harder, and some of the comparisons will be difficult. The information on Stevens' Power Law should be helpful in this regard.

Terms and Concepts

To do this project, you should do research that enables you to understand the following terms and concepts:

  • visual discrimination:
    • "just noticeable difference,"
    • discrimination threshold,
    • Steven's power law,
    • Weber-Fechner law;
  • statistical analysis:
    • t-test,
    • confidence intervals.


Materials and Equipment

To do this experiment you will need the following materials and equipment:

  • materials for making graph-element tests:
    • blank paper,
    • pencil,
    • ruler,
    • protractor;

    • or computer with graphing or drawing software and printer,
  • binder,
  • clear sheet protectors (at least 30),
  • answer sheets for your volunteers to fill in,
  • calculator (or computer spreadsheet program),
  • a group of volunteers (25–30 people) to take a short test.

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Experimental Procedure

  1. Do your background research so that you are knowledgable about the terms and concepts above.
  2. Pick at least three of the six visual discrimination tasks to test (more is better). The six visual discrimination tasks are:
    1. position along a common scale,
    2. position along identical, but non-aligned scales,
    3. length,
    4. angle,
    5. area,
    6. slope.
  3. For each of the tasks, create a set of at least 10 test samples, as described in the Introduction. Remember to:
    1. Make the test elements (B–D) lesser than the reference element (A) for the attribute being tested.
    2. Use a uniform spacing for the test elements throughout the experiment.
    3. Use a uniform size for the test samples throughout the experiment (a single sheet of paper is suggested).
    4. Number the test samples so that your volunteers will know where to put their estimates on the answer sheet.
  4. Since 25 or 30 people will be taking your test, it would be a good idea to put the test pages into a binder inside sheet protectors.
  5. It's a good idea to run a "pilot" test with small groups (who will not be part of the final test group), to make sure that your instructions are worded clearly, and that people know what to do with each type of test sample. That way you can correct any problems that you find before running the actual experiment.
  6. Optional: you may want to include a space on the answer sheet for the time for each test sheet. This will give you another piece of interesting data to analyze.
  7. Analyze your results. Here are some ideas:
    1. For which attribute were errors smallest?
    2. Which attribute has the biggest variance in error?
    3. If you collect time data, is there a correlation between time taken to answer a question and accuracy? Is the correlation negative or positive?
    4. 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.


    • What do your results tell you about selecting a graph type for displaying data?
    • Do you think people will make better estimates of percentages using a pie chart (angle comparison) or a bar graph (position and length comparison)?

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  • To make this project more advanced, expand it and create test samples for all six of the visual discrimination tasks mentioned above. Can you rank the tasks in order of increasing difficulty? From your data, what recommendations can you make about graph design?
  • Another interesting area to explore is the use of color in graphs. Here are some questions you might try to answer. Is color an effective method for encoding quantitative information? How good are people at decoding such information? Is color an effective method for distinguishing categories within data sets? Can you use color in a graph in such a way that people with color blindness can still distinguish differences in shading?
  • For a more basic project that focuses on comparison of areas vs. bar graphs, see: Interpreting Area Data from Maps vs. Graphs: An Experiment in Visual Perception.

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