There’s one piece of bad math that I’ve encountered relatively frequently in conversations. It’s
incredibly frustrating to me, because it’s just so crazy – but the way we teach math and physics, far to many people just don’t have enough of a clue to see how foolish it really is.

This comes up in conversations with lay-people whenever a new space probe is launched. It’s generally presented in the form of a question; something like “That TV announcer said something about a point between the earth and the moon where gravity cancels, so there’s no gravitational pull towards either the earth or the moon. How can the moon cause tides if its gravity is cancelled all the way out there?”

I’ve never found a form of this that was sufficiently mockable – in general, people who ask the question know that there’s something wrong with the question; they know that it’s stupid, but they don’t know why. I don’t like to make fun of that: people who ask a question because they know that their ignorant about something, and they’re trying to fix that patch of ignorance – they don’t deserve to be mocked. So I’ve avoided this. Until now: I’ve found the perfect mockable presentation of this problem. And wait till you see the wonderfully insane form I found it in!

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Yesterday’s Wall Street Journal has a *spectacular* example of really bad math.

The WSJ is, in general, an excellent paper with really high quality coverage of economic
issues. But their editorials page has long been a haven for some of the most idiotic
reactionary conservative nonsense this side of Fox News. But this latest piece takes the
cake. They claim that this figure is an accurately derived Laffer curve describing the relationship
between tax rates and tax revenues for different countries; and that the US has the highest corporate tax
rates in the world.

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In the comments on my DMCA post, a reader asked me to comment on this piece of silliness. I try not to disappoint my readers, so here’s my take. It’s a pile of silliness with the distinct aroma of astrotur – silliness mixed with a bit of deliberate stupidity in order to obscure things.

The basic idea of it is: how dare we complain about the idea of copyrighting numbers! After all, everything you can do on a computer is ultimately stored in a form that can be interpreted as a great big number! So we’re always copyrighting numbers: every book, every article, every poem, every story that’s ever been copyrighted is really just a number. So why should we start complaining now unless we’re just a bunch or dirty anticorporate hippies who are complaining because we want to stick it to the movie companies?

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As I mentioned a while back, I was loaned the Library of Congress discard of George
Shollenberger’s book. Since he’s made such a big deal about how unfair I’ve been by
not reading and considering his argument, I’ve actually forced myself to read it.
(See what I’m willing to do for you, my faithful readers?)

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My fellow SBer Craig Hilberth at the Cheerful Oncologist writes about a
meta-analysis that purports to show the positive effect of intercessory prayer. Neither Craig
nor I have access to the full paper. But what we know is that the claim is that the meta-analysis
shows a result of g=-0.171, p=0.015.

This really ticks me off. Why? because g=-0.17 is not significant. Meta-analysis generally considers g=0.20 to be the minimum cutoff for statistical significance.

Briefly, what is meta-analysis? The idea of it is, suppose you’ve got a bunch of studies of the same topic. Meta-analysis lets you take data from all of the studies in the group, and attempt to combine them. What you can do is get aggregate means and standard deviations, and measures of the significance and reliability of the aggregate measures.

Meta-analysis is a useful technique, but it’s very prone to a number of errors. It’s very easy to manipulate a meta-analysis to make it say whatever you want; and even if you’re being
scrupulously honest, it’s prone to sampling bias. After all, since meta-analysis is based on
combining the results of multiple published studies, the sample is only drawn from the studies that were published. And one thing that we know is that in most fields, it’s much harder to publish negative results than positive ones. So the published data that’s used as input to meta-analysis tends to incorporate a positive bias. There are techniques to try to work around
that, but it’s hard to accurately correct for bias in data when you have no actual measurements
to tell you how biased your data os.

So getting back to the meta-analysis results that they cited, what’s g? g, also called “Hedges g”, is a measure of how much the overall data set of the combined studies differs from the individual data sets means. G is a measure of the significance
of any aggregate result from combining the studies. The idea is, you’ve got a bunch of studies, each of which has a control group and a study group. You compute aggregate mean for both the study and control groups, take the difference, and divide it by the aggregate standard deviation. That’s g. Along with G, you compute a P-value, which essentially measures the reliability of the g-figure computed from the aggregate data.

Assuming a fixed events model – that is, that the studies are essentially compatible, and all measuring the same basic events – the minimum level at which g is considered significant is |g|=0.2, with a minimum p value of 0.05.

This meta-analysis has |g|=0.17, with a p-value of 0.015. So they’re well-below the minimum level of statistical significance for a fixed events model meta-analysis, and their P-value is less than one third of the level at which a |g|=0.2 would be considered significant.

So – what it comes down to is, they did a meta-analysis which produced no meaningful results, and they’re trying to spin it as a “small but statistically significant result”. In other words, they’re misrepresenting their results to try to claim that they say what they wanted them to say.

Many of my fellow SBers have been mocking the recently unveiled Conservapedia. Conservapedia claims to be a reaction to the liberal bias of Wikipedia. Ed, PZ, Afarensis, Tim, John, and Orac have all piled on already. But why should they get to have all the fun?

Conservapedia has an extensive list of what they claim to be examples of the liberal bias of Wikipedia. My SciBlings have already covered most of the nonsense to be found within, but one point is clearly mine to mock: grievance number 16:

Wikipedia has many entries on mathematical concepts, but lacks any entry on the basic concept of an elementary proof. Elementary proofs require a rigor lacking in many mathematical claims promoted on Wikipedia.

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This was posted on slashdot, and forwarded to me by several readers. It’s worth listening to the first few minutes to get an idea of just how pathetically inummerate many people are. It might also help convince you to stay the hell away from *any* service provided by Verizon; my experience with them suggests that this is absolutely typical.
The basic story is that the guy who recorded this took a trip to Canada. Before he left, he checked with Verizon about how much it would cost him to use his cellphone for internet access during his trip, and was told that it cost 0.002 *cents* per kilobyte. But when the bill arrived, they charged him 0.002 *dollars* per kilobyte – 100 times the quoted rate. He then embarked on an odyssey of stupidity, trying to get someone at Verizon to acknowledge the fact that there is a *difference* between 0.002 dollars, and 0.002 cents.
[Go. Listen. Be amazed.][verizon]
[verizon]:http://www.youtube.com/watch?v=Gp0HyxQv97Q&eurl=

One thing I’ve been hearing a lot lately is discussions about Ethanol, and it’s been
really pissing me off. Can ethanol be a serious replacement for oil as a source of energy? I don’t know. Because *both* sides are using really bad math to make their arguments.
There are two fundamental questions about ethanol as fuel where the bad math comes in:
1. How much energy does it cost to *produce* ethanol compared to the amount of
energy released by *consuming* ethanol?
2. How much pollution is generated by the process of producing ethanol?
There are numerous reports or studies from both sides of the political spectrum that quote the
supposed “fact” that ethanol product consumes more energy than can be produced by burning ethanol. But that fact dates back to a single study, which is at best misleading, and at worst, deliberately deceptive.

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