In statistics, a misleading graph, also known as a distorted graph, is a graph which misrepresents data, constituting a misuse of statistics and with the result that an incorrect conclusion may be derived from it. Graphs may be misleading through being excessively complex or poorly constructed. Even when well-constructed to accurately display the characteristics of their data, graphs can be subject to different interpretation.
Misleading graphs may be created intentionally to hinder the proper interpretation of data, but can be also created accidentally by users for a variety of reasons including unfamiliarity with the graphing software, the misinterpretation of the data, or because the data cannot be accurately conveyed. Misleading graphs are often used in false advertising. One of the first authors to write about misleading graphs was Darrell Huff, who published the best-selling book How to Lie With Statistics in 1954. It is still in print.
The field of data visualization describes ways to present information that avoids creating misleading graphs.
- 1 Misleading graph methods
- 2 Measuring distortion
- 3 Usage in finance and corporate reports
- 4 Academia
- 5 See also
- 6 References
- 7 Further reading
- 8 External links
Misleading graph methods
There are numerous ways in which a misleading graph may be constructed.
The use of graphs where they are not needed can lead to unnecessary confusion/interpretation. Generally, the more explanation a graph needs, the less the graph itself is needed. Graphs do not always convey information better than tables.
- Comparing pie charts of different sizes could be misleading as people cannot accurately read the comparative area of circles.
- The usage of thin slices which are hard to discern may be difficult to interpret.
- The usage of percentages as labels on a pie chart can be misleading when the sample size is small.
- Making a pie chart 3D or adding a slant will make interpretation difficult due distorted effect of perspective. Bar-charted pie graphs in which the height of the slices is varied may confuse the reader.
3D Pie chart slice perspective
A perspective (3D) pie chart is used to give the chart a 3D look. Often used for aesthetic reasons, the third dimension does not improve the reading of the data; on the contrary, these plots are difficult to interpret because of the distorted effect of perspective associated with the third dimension. The use of superfluous dimensions not used to display the data of interest is discouraged for charts in general, not only for pie charts. In a 3D pie chart, the slices that are closer to the reader appear to be larger than those in the back due to the angle at which they're presented.
|Misleading Pie Chart||Regular Pie Chart|
|In the misleading pie chart, Item C appears to be at least as large as Item A, whereas in actuality,
it is less than half as large.
Tables are preferable to graphics for many small data sets. A table is nearly always better than a dumb pie chart; the only thing worse than a pie chart is several of them, for then the viewer is asked to compare quantities located in spatial disarray both within and between pies - Given their low data-density and failure to order numbers along a visual dimension, pie charts should never be used.
When using pictogram in bar graphs, they should not be scaled uniformly as this creates a perceptually misleading comparison. The area of the pictogram is interpreted instead of only its height or width. This causes the scaling to make the difference appear to be squared.
|Note how in the improperly scaled pictogram bar graph, the image for B is actually 9 times as large as A.|
|Note how the perceived size increases when scaling.|
The effect of improper scaling of pictogram is further exemplified when the pictogram has 3 dimensions, in which case the effect is cubed.
|Note how the usage of improper scaling of a three-dimensional pictogram in this fictitious graph. It appears that home sales have gone up significantly in 2001 over the previous year. Additionally, because no frequency axis is supplied, readers are unable to quantify the change, and are only left with a misleading perception of the change. The scaling, which is 2x, causes the change to appear to be or 8 times as large.|
Additionally, an improperly scaled pictogram may leave the reader with the sense that the item itself has actually changed in size.
|Assuming the pictures represent equivalent quantities, note how in the misleading graph, there appears to be more bananas
because the bananas occupy the most area and are furthest to the right.
A truncated graph (also known as a torn graph) has a y-axis that does not start at 0. These graphs can create the impression of important change where there is relatively little change.
Truncated graphs are useful in illustrating small differences. Graphs may also be truncated to save space. Commercial software such as MS Excel will tend to truncate graphs by default if the values are all within a narrow range, as in this example.
|There are several ways to indicate a y-axis break.|
|Original graph||Half width, twice height||Twice width, half height|
|Changing the ratio of a graph's dimensions will affect how the graph appears.|
|Less difference||More difference|
|Note the lack of a starting value for the y-axis, which makes it unclear if the graph is truncated. Additionally, note the lack of tick marks which prevents the reader from determining if the graph bars are properly scaled. Without a scale, the visual difference between the bars can be easily manipulated.|
|Volatility||Steady, fast growth||Slow growth|
|Though all three graphs share the same data, and hence the actual slope of the (x,y) data is the same, the way that the data is plotted can change the visual appearance of the angle made by the line on the graph. This is because each plot has different scale on its vertical axis. Because the scale is not shown, these graphs can be misleading.|
The intervals and units used in a graph may be manipulated to create or mitigate the expression of change.
Graphs created with omitted data remove information from which to base a conclusion.
|Scatter plot with missing categories||Regular scatter plot|
|Note how in the scatter plot with missing categories on the left,
the growth appears to be more linear with less variation.
In financial reports, negative returns, or data which does not correlate a positive outlook may be excluded to create a more favorable visual impression.
Graphs based on other graphs should be representative in their presentation.
Extraction has valid uses when searching for anomalies.
|Original Graph||Extracted Graph|
|Note how the extracted graph does not accurately represent the original graph.|
The use of a superfluous third dimension which does not contain information is strongly discouraged as it may confuse the reader.
The third dimension may confuse readers.
Graphs are designed to allow for easier interpretation of statistical data. However, graphs with excessive complexity can obfuscate the data and make interpretation difficult.
Poorly constructed graphs can make data difficult to discern and thus interpret.
A graph with a high lie factor (>1) would exaggerate change in the data it represents, while one with a small lie factor (>0, <1) would obscure change in the data. A perfectly accurate graph would exhibit a lie factor of 1.0.
Graph discrepancy index
The graph discrepancy index also known as the graph distortion index (GDI) was originally proposed by Paul John Steinbart in 1998. GDI is calculated as a percentage ranging from -100% to positive infinity with zero percent indicating that the graph has been properly constructed and anything outside the ±5% margin is considered to be distorted. Research into the usage of GDI as a measure of graphics distortion has found it to be inconsistent and discontinuous making the usage of GDI as a measurement for comparisons difficult.
The data-ink ratio should be relatively high, otherwise the chart may have unnecessary graphics.
The data density should be relatively high, otherwise a table may be better suited for displaying the data.
Usage in finance and corporate reports
Graphs are useful in the summary and interpretation of financial data. Graphs allow for trends in large data sets to be seen while also allowing the data to be interpreted by non-specialists.
Graphs are often used in corporate annual reports as a form of impression management. In the United States, graphs do not have to be audited as they fall under AU Section 550 Other Information in Documents Containing Audited Financial Statements.
Several published studies have looked at the usage of graphs in corporate reports for different corporations in different countries and have found frequent usage of improper design, selectivity, and measurement distortion within these reports. The presence of misleading graphs in annual reports have led to requests for standards to be set.
Research has found that while readers with poor levels of financial understanding have a greater chance of being misinformed by misleading graphs, even those with financial understanding, such as loan officers, may be misled.
- Kirk, p. 52
- Huff, p. 63
- Nolan, pp. 49–52
- "Methodology Manual: Data Analysis: Displaying Data - Deception with Graphs". Texas State Auditor's Office. Jan 4, 1996. Retrieved 19 July 2012.
- Keller, p. 84
- Whitbread, p. 150
- Whitbread, p. 151
- Few, Stephen (August 2007). "Save the Pies for Dessert". Visual Business Intelligence Newsletter. Perceptual Edge. Retrieved 28 June 2012.
- Rumsey, p. 156
- Tufte, Edward R. (2006). The visual display of quantitative information (2nd ed., 4th print. ed.). Cheshire, Conn.: Graphics Press. p. 178. ISBN 9780961392147.
- Weiss, p. 60
- Utts, pp. 146-147
- Hurley, pp. 565-566
- Huff, p. 72
- Rensberger, Boyce (May 10, 1995). "Slanting The Slope of Graphs". The Washington Post. Retrieved 9 July 2012.(subscription required)
- Smith, Karl J. (1 January 2012). Mathematics: Its Power and Utility. Cengage Learning. p. 472. ISBN 978-1-111-57742-1. Retrieved 24 July 2012.
- Moore, David S.; Notz, William (9 November 2005). Statistics: Concepts And Controversies. Macmillan. pp. 189–190. ISBN 978-0-7167-8636-8. Retrieved 24 July 2012.
- Burgess, Deanna Oxender; William N. Dilla, Paul John Steinbart, Todd M. Shank (May 2008). "Does Graph Design Matter To CPAs And Financial Statement Readers?". Journal of Business & Economics Research 6 (5).
- Wainer, p. 51-53
- Robison, Wade (2002). "Representation and misrepresentation: Tufte and the Morton Thiokol engineers on the Challenger". Science and Engineering Ethics 8 (1): 59–81. doi:10.1007/s11948-002-0033-2.
- Visual Explanations, p. 38-53
- Mather, Dineli R.; Mather, Paul R.; Ramsay, Alan L. (July 2003). "Is the Graph Discrepancy Index (GDI) a Robust Measure?". SSRN Electronic Journal. doi:10.2139/ssrn.556833.
- Mather, Dineli; Mather, Paul; Ramsay, Alan (1 June 2005). "An investigation into the measurement of graph distortion in financial reports". Accounting and Business Research 35 (2): 147–160. doi:10.1080/00014788.2005.9729670.
- Craven, Tim (November 6, 2000). "LIS 504 - Graphic displays of data". Faculty of Information and Media Studies. London, Ontario: University of Western Ontario. Retrieved 9 July 2012.
- Fulkerson, Cheryl Linthicum; Marshall K. Pitman, Cynthia Frownfelter-Lohrke (June 1999). "PREPARING FINANCIAL GRAPHICS". The CPA Journal.
- McNelis, L. Kevin (June 1, 2000). "Graphs, An Underused Information Presentation Technique.". The National Public Accountant.(subscription required)
- Beattie, Viviene; Jones, Mike (June 1, 1999). "Financial graphs: True and Fair?". Intheblack. (subscription required)
- Beattie, Vivien; Jones, Michael John (1 September 1992). "The Use and Abuse of Graphs in Annual Reports: Theoretical Framework and Empirical Study". Accounting and Business Research 22 (88): 291–303. doi:10.1080/00014788.1992.9729446.
- Penrose, J. M. (1 April 2008). "Annual Report Graphic Use: A Review of the Literature". Journal of Business Communication 45 (2): 158–180. doi:10.1177/0021943607313990.
- Frownfelter-Lohrke, Cynthia; Fulkerson, C. L. (1 July 2001). "The Incidence and Quality of Graphics in Annual Reports: An International Comparison". Journal of Business Communication 38 (3): 337–357. doi:10.1177/002194360103800308.
- Isa, Rosiatimah Mohd (2006). "The incidence and faithful representation of graphical information in corporate annual report:a study of Malaysian companies". Technical Report. Institute of Research, Development and Commercialization, Universiti Teknologi MARA. Retrieved 9 July 2012.
- Beattie, Vivien; Jones, Michael John (1 March 1997). "A Comparative Study of the Use of Financial Graphs in the Corporate Annual Reports of Major U.S. and U.K. Companies". Journal of International Financial Management and Accounting 8 (1): 33–68. doi:10.1111/1467-646X.00016.
- Beattie, V.; Jones, M (2008). "Corporate reporting using graphs: a review and synthesis". Journal of Accounting Literature, 27 . pp. ISSN 27: 71–110. ISSN 0737-4607.
- Christensen, David S.; Albert Larkin (Spring 1992). "Criteria For High Integrity Graphics". Journal of Managerial Issues (Pittsburg State University) 4 (1): 130–153.
- Eakin, Cynthia Firey; Timothy Louwers, Stephen Wheeler (2009). "The Role of the Auditor in Managing Public Disclosures: Potentially Misleading Information in Documents Containing Audited Financial Statements". Journal of Forensic & Investigative Accounting 1 (2).
- Steinbart, P. (September 1989). "The Auditor’s Responsibility for the Accuracy of Graphs in Annual Reports: Some Evidence for the Need for Additional Guidance". Accounting Horizons: 60–70.
- Beattie, Vivien; Jones, Michael John (1 January 2002). "Measurement distortion of graphs in corporate reports: an experimental study". Accounting, Auditing & Accountability Journal 15 (4): 546–564. doi:10.1108/09513570210440595.
- Frees, Edward W; Robert B Miller (Jan 1998). "Designing Effective Graphs". North American Actuarial Journal 2 (2): 53–76.
- Huff, Darrell (1954). How to lie with statistics. pictures by Irving Geis (1st ed. ed.). New York: Norton. ISBN 0393052648.
- Hurley, Patrick J. (2000). A Concise Introduction to Logic. Wadsworth Publishing. ISBN 9780534520069.
- Keller, Gerald. Statistics for Management and Economics, abbreviated (9th ed., abbreviated ed. ed.). Mason, OH: South-Western. ISBN 1111527326.
- Kirk, Roger E. (23 February 2007). Statistics: An Introduction. Cengage Learning. ISBN 978-0-534-56478-0. Retrieved 28 June 2012.
- Nolan, Susan; Heinzen, Thomas (1 February 2011). Statistics for the Behavioral Sciences. Macmillan. ISBN 978-1-4292-3265-4. Retrieved 28 June 2012.
- Rumsey, Deborah (17 May 2010). Statistics Essentials For Dummies. John Wiley & Sons. ISBN 978-0-470-61839-4. Retrieved 28 June 2012.
- Weiss, Neil A. (1993). Elementary statistics. Addison-Wesley. ISBN 978-0-201-56640-6. Retrieved 28 June 2012.
- Tufte, Edward (1997). Visual Explanations: Images and Quantities, Evidence and Narrative. Cheshire, CT: Graphics Press.
- Utts, Jessica M. (2005). Seeing through statistics (3rd ed. ed.). Belmont: Thomson, Brooks/Cole. ISBN 9780534394028.
- Wainer, Howard (1 July 2000). Visual Revelations: Graphical Tales of Fate and Deception From Napoleon Bonaparte To Ross Perot. Psychology Press. ISBN 978-0-8058-3878-7. Retrieved 19 July 2012.
- Whitbread, David (2001). The design manual (2nd ed. ed.). Sydney: University of New South Wales Press. ISBN 0868406589.
- A discussion of misleading graphs, Mark Harbison, Sacramento City College
- Robbins, Naomi B. (2005). Creating more effective graphs. Hoboken, N.J.: Wiley-Interscience. ISBN 9780471698180.
- Durbin CG, Jr (October 2004). "Effective use of tables and figures in abstracts, presentations, and papers.". Respiratory care 49 (10): 1233–7. PMID 15447809.
- Goundar, Nadesa (2009). "Impression Management in Financial Reports Surrounding CEO Turnover". Masters Dissertation. Unitec Institute of Technology. Retrieved 9 July 2012.
- Huff, Darrell; Geis, Irving (17 October 1993). How to Lie With Statistics. W. W. Norton & Company. ISBN 978-0-393-31072-6. Retrieved 28 June 2012.
- Bracey, Gerald (2003). "Seeing Through Graphs". Understanding and using education statistics : it's easier than you think. Educational Research Service. ISBN 9781931762267.
- Harvey, J. Motulsky (June 2009). "The Use and Abuse of Logarithmic Axes". GraphPad Software Inc.
- Chandar, N.; Collier, D.; Miranti, P. (15 February 2012). "Graph standardization and management accounting at AT&T during the 1920s". Accounting History 17 (1): 35–62. doi:10.1177/1032373211424889.
- Mather, Paul; Ramsay, Alan; Steen, Adam (1 January 2000). "The use and representational faithfulness of graphs in Australian IPO prospectuses". Accounting, Auditing & Accountability Journal 13 (1): 65–83. doi:10.1108/09513570010316144.
- Beattie, Vivien; Jones, Michale John (1996). Financial graphs in corporate annual reports : a review of practice in six countries. London: Institute of Chartered Accounants in England and Wales. ISBN 9781853557071.
- Galliat, Tobias (Summer 2005). "Visualisierung von Informationsräumen". Fachhochschule Köln, University of Applied Sciences Cologne. Archived from the original on 2006-01-04. Retrieved 9 July 2012.
- Carvalho, Clark R.; McMillan, Michael D. (September 1992). "Graphic Representation in Managerial Decision Making: The Effect of Scale Break on the Dependent Axis". AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH.
- Johnson, R. Rice; Roemmich, R. (October 1980). "Pictures that Lie: The Abuse of Graphs in Annual Reports". Management Accounting: 50–56.
- Davis, Alan J. (1 August 1999). "Bad graphs, good lessons". ACM SIGGRAPH Computer Graphics 33 (3): 35–38. doi:10.1145/330572.330586.
- Louwers, T.; Radtke, R; Pitman, M. (May–June 1999). "Please Pass the Salt: A Look at Creative Reporting in Annual Reports". Today's CPA: 20–23.
- Beattie, Vivien; Jones, Michael John (May 2001). "A six-country comparison of the use of graphs in annual reports". The International Journal of Accounting 36 (2): 195–222. doi:10.1016/S0020-7063(01)00094-2.
- Wainer, Howard (1984). "How to Display Data Badly". The American Statistician 38 (2): 137–147.
- Lane, David M.; Sándor, Anikó (1 January 2009). "Designing better graphs by including distributional information and integrating words, numbers, and images.". Psychological Methods 14 (3): 239–257. doi:10.1037/a0016620.
- Campbell, Mary Pat (Feb 2010). "Spreadsheet Issues: Pitfalls, Best Practices, and Practical Tips". Actuarial Practice Forum.
- Arocha, Carlos (May 2011). "Words or Graphs?". The Stepping Stone.
- Raschke, Robyn L.; Steinbart, Paul John (1 September 2008). "Mitigating the Effects of Misleading Graphs on Decisions by Educating Users about the Principles of Graph Design". Journal of Information Systems 22 (2): 23–52. doi:10.2308/jis.2008.22.2.23.