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Ironically, this graph does an excellent job of showing a correlation that really exists between the two data sets, albeit a non-linear one.

The only misleading thing about this graph is the title, which states a causal link with no evidence of one.



Yeah, I think this is completely off-base in blaming the axes. The axes are perfectly fine in showing the actual correlation that's present here (almost certainly due to a third common causal factor, of course).

There's no really magically "unbiased" way of choosing axes. There seems to be a popular view recently that you should always start your axes at zero, I assume as a backlash to some graphs magnifying very small differences by choosing zoomed-in axis values that visually exaggerate variation. That isn't really an absolute truth either, since interesting data regions are not always near zero. For example, if you graph temperature variation in different cities staring at 0 K, you can make it look like essentially all habitable cities have around the same temperature, somewhere in the range of 250-300 K give or take. Of course 250 K versus 300 K is a huge difference to human perception of temperature, while the entire range 0-200 K is more or less irrelevant when discussing weather, so starting your axis at 0 would be a poor choice. In this case that would be the biased choice, intended to visually minimize actually important variation by choosing an unreasonably low starting point for the Y axis.


> (almost certainly due to a third common causal factor, of course).

..or absolutely certainly associated so remotely that correlation is purely accidental and found only by carefully cherry picking data sources, ranges, functions to massage the data (log with the right base) and axis ranges. To sum up ... not meaningful.

You could find similar correlation between ocean temperatures and lottery numbers but you'd have to precisely adjust so many inputs that the correlation would be not so much found as constructed.


"log with the right base" doesn't make any difference. That's a linear mapping. For instance:

    2log x = log x / log 2 = ln x / ln 2
(With 2log the logarithm in base 2, log and ln the logarithm in bases you pick, but you can think of 10 and e)

See, for example, http://www.purplemath.com/modules/logrules5.htm, or derive it from the axioms.


I think this ln2 factor matters when you are drawing a graph. But I guess that's included in what I called axis range.


Actually, in this case I'd argue that a general/generic measure of "human scientific and technical advancement" is a decent underlying causal factor.

Maybe meaningful, if kind of obvious...




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