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Is the Graph Discrepancy Index (Gdi) a Robust Measure?
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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. Whilst the GDI is critical to the financial graphics literature, little or no attention has been paid to its robustness and accuracy. We examine the mathematical characteristics of the GDI and show that it is inconsistent as a measure of graph distortion. We present a number of cases to demonstrate this inconsistency and show that in many instances the GDI values calculated are not particularly meaningful. We develop and present an alternative measure referred to as the Relative Graph Discrepancy (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. Overall in comparison with the GDI the RGD appears to be more theoretically robust and produces stronger results.
Title: Is the Graph Discrepancy Index (Gdi) a Robust Measure?
Description:
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.
Whilst the GDI is critical to the financial graphics literature, little or no attention has been paid to its robustness and accuracy.
We examine the mathematical characteristics of the GDI and show that it is inconsistent as a measure of graph distortion.
We present a number of cases to demonstrate this inconsistency and show that in many instances the GDI values calculated are not particularly meaningful.
We develop and present an alternative measure referred to as the Relative Graph Discrepancy (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.
Overall in comparison with the GDI the RGD appears to be more theoretically robust and produces stronger results.
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