There is little stranger than watching an argument where neither side knows what they are talking about. Today I’m going to interject myself into such a discussion and try to clarify some things. The subject is Michael Mann’s infamous hockey stick graph, and the Wegman Report which criticized it.
I decided to write this after reading two comments by the user Kevin O’Neill at Judith Curry’s blog. The comments had a lot of incorrect, and even stupid, stuff in them, but the parts that stood out the most to me were:
Wegman deceptively displayed only upward-pointing ‘hockey sticks’ – though half of them would have had to be downward pointing.
And while Wegman in the text acknowledges that half the results will be downward sloping all of his results show upward sloping hockey sticks. Why? Pretty obvious that a downward sloping hockey stick wouldn’t look like MBH.
These remarks originate from a blog post written by Nick Stokes. Stokes discusses criticisms of Mann’s hockey stick which said his implementation of Principal Component Analysis (PCA) was biased toward selecting hockey stick shapes. The Wegman Report showed an image like this showing such a bias:
Stokes claims this is wrong, and the graph ought to look like this:
As you can see, the two are very different. The most glaring difference is some of the hockey sticks in Stokes’s version are upside down. Stokes and O’Neill claim it is dishonest to not show these. However, Stokes also says this in his post:
Now we see that there is still some tendency to HS shape, but much less. It can go either way, as expected. In the PCA analysis, sign doesn’t matter,
If the sign doesn’t matter in PCA, why would we need to show upside down hockey sticks? As Stokes acknowledges, upside down and right-side up hockey sticks are equivalent in PCA. Why should we need to add a large visual discrepancy to our images just to show something which “doesn’t matter”?
Neither Stokes nor O’Neill has ever answered that question. Neither has explained why the image above is “honest” while this version would be “dishonest”:
The “honest” version favors Stokes and O’Neill’s views because it gives them ammunition to attack the Wegman Report, but the “dishonest” version is functionally equivalent. Aside from looking for a reason to attack the Wegman Report, there is no reason to prefer the “honest” version which adds huge visual discrepancies for no purpose.
For those who want to better understand why the orientation of these graphs doesn’t matter, the key is in how Michael Mann combined his proxies (which include those output by his PCA implementation). Series created by PCA are in arbitrary units. To plot them as temperatures, Mann had to convert them into temperatures. He did this by scaling his proxies to match the instrumental record.
You can think of it like multiplying each series by a number. If you multiply a series by 2, the figure will look the same but the scale will change. If you multiply that figure by -2 instead, the figure will flip upside down. The absolute magnitudes in the figure will be identical, but the orientation will be reversed.
Since the instrumental record goes up, all rescaled proxies would have to go up as well. Any proxies which originally had negatively oriented hockey sticks would be multiplied by some negative value, flipping them right-side up. That means every proxy could have an upside down hockey stick in it, and the resulting reconstruction would still be a right-side up hockey stick.
I apologize if this post is unclear. I’m writing it at 3AM in a hotel room after a sizable dart tournament. If you need anything clarified, feel free to ask.