manipulative representations

Here is yet another visual manipulation of statistical figures. This time it is done by J.P.Morgan. Forget objective analyses of financial information... These guys can not even visually present raw data without letting their sentiments shine through!

Have a look at the circles that are drawn to depict 2.Quarter (2007) and October (2008) market values of Goldman Sachs. It seems as if the area corresponding to "100" is more than two times the area corresponding to "56". The visual representation is clearly misleading.

What J.P.Morgan did was to take a circle with radius of x and place it inside a circle with radius y. The resulting area difference between the two circles is as follows:

[π*(x^2)]-[π*(y^2)] = π*[(x^2)-(y^2)] = π*(x-y)*(x+y)

To understand how this deceitful mechanism works, compare the circles of Morgan Stanley to those of J.P.Morgan. The market value of Morgan Stanley decreased from $49 billions to $21 billions and that of J.P.Morgan decreased from $165 billions to $147 billions. In percentage terms the market value of Morgan Stanley fell more than the market value of J.P.Morgan did. But the difference is not as much as the visual representation suggests:

Real Percentage difference = [(49-21)/49] - [(165-147)/165] = 0.571 - 0.109 = 0.462 = 46.2%

Visual Percentage difference = [[π*(49-21)*(49+21)]/[π*(49^2)]] - [[π*(165-147)*(165+147)]/[π*(165^2)]] = 0.816 - 0.206 = 0.610 = 61%