An investigation into the measurement of graph distortion in financial reports

Abstract

The Graph Discrepancy Index (GDI), which originates from the lie factor introduced by Tufte (1983).is the mechanism commonly used in the financial graphics literature to determine whether graphs are distorted and to quantify the extent of such distortion. Although the GDI is critical to the financial graphics literature, little or no attention has been paid to its robustness and accuracy. We critically examine the mathematical characteristics of the GDI and show its limitations as a measure of graph distortion. We review a number of cases to demonstrate these limitations and present an alternative measure of graph distortion -the Relative Graph Discrepancy index (RGD). Numerous simulations suggest that the RGD overcomes the problems associated with the GDI. The RGD is also tested on data presented in earlier research and the results are compared to those obtained using the GDI. In comparison with the GDI. we find that the RGD is more consistent and produces slightly stronger results. We stress, however. that this is not a best or definitive measure but is intended to start a research process that leads to a generally accepted measure.

Investigating Presentational Change in U.K. Annual Reports: A Longitudinal Perspective

“…They show that measurement distortion in excess of 10% is just perceptible to users. Since 1992, there have been a succession of financial graphics studies (e.g., Beattie andJones, 2000 and2001;Courtis, 1997;Frownfelter-Lohrke and Fulkerson, 2001;Mather, Ramsay and Serry, 1996;Mather, Ramsay and Steen, 2000;and Mather, Mather and Ramsay, 2005) all of which have developed, and reinforced, the earlier findings of selectivity, measurement distortion and presentational enhancement.…”

Graphical disclosures by charities: clarification or distortion? The case of the Netherlands

“…In this case the GDI would require you to divide by zero, which is not possible. Mather et al (2005) have found a possible solution to overcome this problem with their Relative Graph Discrepancy index (RGD). Even though this measure produces stronger results, their conclusions are only based on one research.…”

“…After all, a favourable distortion of graphs changes users' perception of the charity's performance (Beattie and Jones, 1994;Mather et al, 2005) and affects judgement and decisions (Xu, 2005), e.g. of donors.…”

Impression Management and Retrospective Sense-Making in Corporate Annual Reports: Banks’ Graphical Reporting During the Global Financial Crisis

“…Second, we investigated via t-tests whether during the global financial crisis: unfavourable cross-sectional comparisons were equal or higher than favourable (Hypothesis 3a); time-series portraying a declining trend were equal or higher than those with a rising trend (Hypothesis 3b); and stock market performance graphs which included other bank's indicators portraying a negative performance were equal or higher than those portraying a positive performance (Hypothesis 3c). To test impression management by commission via measurement distortion (Hypothesis 2b), we considered both mandatory and voluntary graphs, but excluded 12 graphs because RGD values were undefined and 5 because the RGD could not be calculated (Mather et al, 2005).…”

“…We considered a cut-off level of +/-2.5% to distinguish between material and non-material distortions (Falschlunger et al, 2015;Mather et al, 2005;Muiño & Trombetta, 2009). Positive and negative values of RGD represent favourable and unfavourable distortions, respectively (Mather et al, 2005). Favourable (unfavourable) distortions overstate (understate) increasing trends or understate (overstate) declining trends.…”