Abstract

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.

Objective

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).

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? 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

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

Position Along Identical, but Non-Aligned 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.

Length

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.

Angle

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

Slope

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.

Area

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.

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.

Suggestions

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

Experimental Procedure

Variations

Careers

If you like this project, you might enjoy exploring these related careers:

Related Links

• Science Fair Project Guide
• Other Ideas Like This
• Human Behavior Project Ideas
• My Favorites

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