Written by **Rick Kubina**

The amount of statistical graphics generated worldwide staggers the mind. In his breakout book, *The Visual Display of Quantitative Information* (1983), Tufte reported between 900 billion and 2 trillion images of statistical graphics appear in print each year. Tufte reported the information in 1983; imagine the number in 2015!

A large majority of statistical graphics fall under the category of a “line graph.” Line graphs, or linear graphs, represent the most popular type of graphs encountered in print and visual media. Line graphs show time series data, namely, data that occur across a unit of time.

Many disciplines of science, and even popular culture, make use of line graphs to show data marching through time. For example, a 2008 Gallup poll examined the self-reported alcoholic beverages of choice for 30 to 49-year-olds. As the line graph below shows, beer still reigns as the king. Wine has made some significant inroads through time but still remains in the backseat. And liquor preferences have demonstrated a stable trend since 1993.

Figure 1. A line graph showing beer, wine, and liquor preferences of 30 to 49 year-olds across time.

Behavior analysts, therapists, speech and language pathologists, teachers, and a host of other people rely on line graphs to make important decisions. Decision making fueled by line graphs can range from moving a learner on in a curriculum sequence to aiding the determination of whether a learner qualifies for important services (e.g., special education or in-home hours).

Yet both practitioners and consumers of visualization must remain vigilant when viewing graphs. Making a significant clinical decisions (and don’t they all qualify as worthy of attention?) based on a line graph of poor scientific quality seems particularly troubling.

With the proliferation of graphing websites and programs such as Microsoft Excel, anyone with access to a computer can produce a line graph. Gone are the days when a drafter would create a line graph following specific rules with exacting detail.

But rules, indeed standards, for producing a line graph have existed for years. As an example, the Joint Committee on Standards for Graphic Presentation shared a set of rules to help guide anyone construct a proper line graph in 1915. And in 1938 the American Society of Mechanical Engineers shared principles of graphic presentation so line graphs (1) truthfully represent the facts, (2) have a design that attracts and holds the graph viewer’s attention, and (3) possess clarity facilitating easy decoding of the information.

The standards shared in 1915 and 1938 still apply today. Knowing some of the fundamental design rules to line graphs helps guard against the uncritical acceptance of graphs with misleading or deceptive information.

**Rule #1- The Proportional Construction Rule **

The proportional construction rule refers to the physical proportion of the vertical to the horizontal axis. Published recommendations suggest a ratio of vertical to horizontal axis ranges of 5:8 to 2:3, with a maximum of 3:4 (American National Standards Institute & American Society of Mechanical Engineers, 1960, 1979; Bowen, 1992; Cooper et al., 2007; Department of the Army, 2010; Johnston & Pennypacker, 1980; Schmid, 1992).

Notice the two graphs below that violate the proportional construction rule. As a result, the slope of the line and the variability of the data will change. In one case the data will become exaggerated (the first stretched out vertical axis on the left) and in the other compressed (the compacted vertical axis on the right).

Figure 2. Two line graphs violating the proportional construction rule

If you see graphs that disregard the proportional construction rule, and sadly you will see many, exercise caution in interpreting the claims. Visual analysis relies on well-formed graphs with the correct proportion of the vertical to the horizontal axis. As Schmid (1992) reminds us “…grid proportions are of pronounced significance as the determinants of the visual impression conveyed” (p. 28).

**Rule #2: Label and scale the horizontal axis with a unit of time. **

Time-series line graphs must have a unit of time on the horizontal axis (Robbins, 2005). Examples of units of time range from seconds and hours to days and years. Unfortunately, many people use “sessions” on the horizontal axis.

Figure 3. Graph with a non-time unit session.

How long did an intervention take? With sessions we have no idea. Do the data ascend or descend because the session length increased or decreased? In other words, did the timing length increase or decrease resulting in more or less data simply due to the artifact in the length of the observation/recording time. Graph readers have absolutely no idea of what went on during a recorded “session.” And if someone writes an article and does keep track of time but uses sessions as a label, then the person committed a labeling error by not using an accepted unit of time.

The National Institute of Standards and Technology (2014) defines time units as minutes, hours, days, weeks, and years based on the second. Sessions doesn’t represent a unit of time. Remain wary line graphs labeled with the non-time unit sessions; sessions offer no advantages for visually analyzing behavior and instead impede the accurate and efficient portrayal of behavioral data.

**Rule #3. Tick marks have labels. **

To decode information, a core feature of a line graph entails the labeling of ticks. The horizontal axis for a time series graph will display some unit of time. The vertical axis must have a quantitative value showing the measure of interest. Yet graphs appear in print and on websites without containing one or both axes’ tick marks with labels.

Figure 4. A line graph missing tick mark labels.

Can you figure out what happened in the graph above? No one can, except for the maybe the author who created the now information-veiled line graph. Whether tick mark labels don’t show up due to someone forgetting or willfully ignoring the quality feature standards of the line graph, the end result is the same – valuable information diminishes significantly.

Side note: Other problems include line graphs with no tick marks or quantitative labels that do not properly align to the tick mark. Tick marks matter!

**Rule #4. Data points clearly visible. **

Rule #4 seems a no-brainer; difficulty seeing the data means graph readers have struggle to detect trends and emerging patterns. The figure below shows very small data points, to illustrate the point.

Figure 5. A line graph with hard to see data points.

**Conclusion**

Violations of the 4 rules of line graph construction signal potential hazards – look out for these warning signs. Line graphs require adherence to construction features for showing data with clarity, legibility, and graphic integrity.Line graphs with design flaws do not inspire confidence and can negatively affect students whose academic and cognitive growth rely on effective decision making. Finding a graph lacking one or more quality features should alert the graph reader to potential inaccuracies or exaggerations in the stated conclusions.

**References**

American National Standards Institute & American Society of Mechanical Engineers (1960). Time-series charts. New York: American Society of Mechanical Engineers.

American National Standards Institute & American Society of Mechanical Engineers (1979). American national standard: Time-series charts. New York: American Society of Mechanical Engineers.

American Society of Mechanical Engineers. (1938). Time series charts: a manual of design and construction. New York: Committee on Standard for Graphic Presentation, American Society of Mechanical Engineers.

Bowen, R. (1992). Graph it! How to make, read, and interpret graphs. Englewood Cliffs, NJ: Prentice-Hall.

Cooper, J. O., Heron, T. E., & Heward, W. L. (2007). Applied behavior analysis (2nd ed.). Upper Saddle River, NJ: Pearson Prentice Hall.

Department of the Army (2010). Standards of statistical presentation. Washington DC: Department of the Army.

Joint Committee on Standards for Graphic Presentation. Publications of the American Statistical Association, Vol. 14, No. 112 (Dec., 1915), pp. 790-797. Published by: Taylor & Francis, Ltd. on behalf of the American Statistical Association. Article DOI: 10.2307/2965153. Article Stable URL: http://www.jstor.org/stable/2965153

Johnston, J. M., & Pennypacker, H. S. (1980). Strategies and tactics of human behavioral research. Hillsdale, NJ: Erlbaum.

National Institute of Standards and Technology (2014, June 2). Unit of time (second). Retrieved from http://physics.nist.gov/cuu/Units/second.html

Robbins, N. B. (2005). Creating more effective graphs. New York: John Wiley & Sons.

Schmid, C. F. (1992). Statistical graphics: Design principles and practices. New York: John Wiley & Sons.

Tufte, E.R. (1983). The visual display of quantitative information. Cheshire, CT: Graphics Press.