Archive for the 'Bad Probability' category

Back to an old topic: Bad Vaccine Math

Jan 25 2013 Published by under Bad Math, Bad Probability, Bad Statistics

The very first Good Math/Bad Math post ever was about an idiotic bit of antivaccine rubbish. I haven't dealt with antivaccine stuff much since then, because the bulk of the antivaccine idiocy has nothing to do with math. But the other day, a reader sent me a really interesting link from what my friend Orac calls a "wretched hive of scum and quackery",, in which they try to argue that the whooping cough vaccine is an epic failure:

(NaturalNews) The utter failure of the whooping cough (pertussis) vaccine to provide any real protection against disease is once again on display for the world to see, as yet another major outbreak of the condition has spread primarily throughout the vaccinated community. As it turns out, 90 percent of those affected by an ongoing whooping cough epidemic that was officially declared in the state of Vermont on December 13, 2012, were vaccinated against the condition -- and some of these were vaccinated two or more times in accordance with official government recommendations.

As reported by the Burlington Free Press, at least 522 cases of whooping cough were confirmed by Vermont authorities last month, which was about 10 times the normal amount from previous years. Since that time, nearly 100 more cases have been confirmed, bringing the official total as of January 15, 2013, to 612 cases. The majority of those affected, according to Vermont state epidemiologist Patsy Kelso, are in the 10-14-year-old age group, and 90 percent of those confirmed have already been vaccinated one or more times for pertussis.

Even so, Kelso and others are still urging both adults and children to get a free pertussis shot at one of the free clinics set up throughout the state, insisting that both the vaccine and the Tdap booster for adults "are 80 to 90 percent effective." Clearly this is not the case, as evidenced by the fact that those most affected in the outbreak have already been vaccinated, but officials are apparently hoping that the public is too naive or disengaged to notice this glaring disparity between what is being said and what is actually occurring.

It continues in that vein. The gist of the argument is:

  1. We say everyone needs to be vaccinated, which will protect them from getting the whooping cough.
  2. The whooping cough vaccine is, allagedly, 80 to 90% effective.
  3. 90% of the people who caught whooping cough were properly vaccinated.
  4. Therefore the vaccine can't possibly work.

What they want you to do is look at that 80 to 90 percent effective rate, and see that only 10-20% of vaccinated people should be succeptible to the whooping cough, and compare that 10-20% to the 90% of actual infected people that were vaccinated. 20% (the upper bound of the succeptible portion of vaccinated people according to the quoted statistic) is clearly much smaller than 90% - therefore it's obvious that the vaccine doesn't work.

Of course, this is rubbish. It's a classic apple to orange-grove comparison. You're comparing percentages, when those percentages are measuring different groups - groups with wildly difference sizes.

Take a pool of 1000 people, and suppose that 95% are properly vaccinated (the current DTAP vaccination rate in the US is around 95%). That gives you 950 vaccinated people and 50 unvaccinated people who are unvaccinated.

In the vaccinated pool, let's assume that the vaccine was fully effective on 90% of them (that's the highest estimate of effectiveness, which will result in the lowest number of succeptible vaccinated - aka the best possible scenario for the anti-vaxers). That gives us 95 vaccinated people who are succeptible to the whooping cough.

There's the root of the problem. Using numbers that are ridiculously friendly to the anti-vaxers, we've still got a population of twice as many succeptible vaccinated people as unvaccinated. so we'd expect, right out of the box, that better than 2/3rds of the cases of whooping cough would be among the vaccinated people.

In reality, the numbers are much worse for the antivax case. The percentage of people who were ever vaccinated is around 95%, because you need the vaccination to go to school. But that's just the childhood dose. DTAP is a vaccination that needs to be periodically boosted or the immunity wanes. And the percentage of people who've had boosters is extremely low. Among adolescents, according to the CDC, only a bit more than half have had DTAP boosters; among adults, less that 10% have had a booster within the last 5 years.

What's your succeptibility if you've gone more than 5 years without vaccination? Somewhere 40% of people who didn't have boosters in the last five years are succeptible.

So let's just play with those numbers a bit. Assume, for simplicity, than 50% of the people are adults, and 50% children, and assume that all of the children are fully up-to-date on the vaccine. Then you've got 10% of the children (10% of 475), 10% of the adults that are up-to-date (10% of 10% of 475), and 40% of the adults that aren't up-to-date (40% of 90% of 475) is the succeptible population. That works out to 266 succeptible people among the vaccinated, which is 85%: so you'd expect 85% of the actual cases of whooping cough to be among people who'd been vaccinated. Suddenly, the antivaxers case doesn't look so good, does it?

Consider, for a moment, what you'd expect among a non-vaccinated population. Pertussis is highly contagious. If someone in your household has pertussis, and you're succeptible, you've got a better than 90% chance of catching it. It's that contagious. Routine exposure - not sharing a household, but going to work, to the store, etc., with people who are infected still gives you about a 50% chance of infection if you're succeptible.

In the state of Vermont, where NaturalNews is claiming that the evidence shows that the vaccine doesn't work, how many cases of Pertussis have they seen? Around 600, out of a state population of 600,000 - an infection rate of one tenth of one percent. 0.1 percent, from a virulently contagious disease.

That's the highest level of Pertussis that we've seen in the US in a long time. But at the same time, it's really a very low number for something so contagious. To compare for a moment: there's been a huge outbreak of Norovirus in the UK this year. Overall, more than one million people have caught it so far this winter, out of a total population of 62 million, for a rate of about 1.6% or sixteen times the rate of infection of pertussis.

Why is the rate of infection with this virulently contagious disease so different from the rate of infection with that other virulently contagious disease? Vaccines are a big part of it.

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Big Number Bogosity from a Christian College Kid

May 04 2010 Published by under Bad Probability, Big Numbers

I know that I just posted a link to a stupid religious argument, but I was sent a link to
another one, which I can't resist mocking.

As I've written about quite often, we humans really stink at
understanding big numbers, and how things scale. This
is an example of that. We've got a jerk who's about to graduate from a dinky
christian college, who believes that there must be something special
about the moral atmosphere at his college, because in his four years at the
school, there hasn't been a single murder.

Yeah, seriously. He really believes that his school is special, because it's gone four whole
years without a murder:

Considering that the USA Today calculated 857 college student deaths from 2000
to 2005, how does one school manage to escape unscathed? It's certainly not
chance or luck. For Patrick Henry College, it's in our Christian culture.

Critics mock us for our strict rules - like no dancing or drinking on campus,
no members of the opposite sex permitted in your dorm room, nightly curfew
hours - and the lack of a social atmosphere it creates. We have been the
subject of books (God's Harvard), television shows, op-eds, and countless
blogs who rant against our brand of overbearing right-wing Christianity that
poisons society's freedom.

Yet, what is the cost of students being able to "express" themselves? Is that
freedom worth the cost of drunk driving deaths, drug related violence, and
love affairs turned fatal?

There were 857 college student deaths in the five-year period from 2000 to 2005! Therefore,
any college where there weren't any murders in that period must be something really
special. That christian culture must be making a really big difference, right?

Well, no.

to Google Answers
, the US Census Department reports that there are 2363
four year colleges in the US. So, assuming the widest possible distribution of
student deaths, there were 1506 colleges with no student deaths in a five-year
period. Or, put another way, more than 60% of colleges in the US went that five-year period
without any violent student deaths.

Or, let's try looking at it another way. According to the census, there are 15.9 million
people currently enrolled in college. The school that, according to the author, is so
remarkable for going without any murders in the last four years? It has 325 students. Not
325 per class - 325 total.

In other words, among a group making up less than 2/1000ths of one percent of the college
population, there were no murders. Assuming that the distribution of violent deaths is perfectly
uniform (which it obviously isn't; but let's just keep things simple), given that there were
857 violent deaths in the student population as a whole, how many violent deaths
would you expect among the student body at his dinky christian college?

That would be a big, fat zero.

The fact that there were no violent deaths at his school isn't remarkable,
not at all. But to a twit who's incapable of actually understanding what
numbers mean, that's not the conclusion to be drawn. It's also not that the
violent death among college students is actually remarkably rare. Nor is it
that most college students will go through college without any
violent deaths on campus. No - according to a twit, with 857 violent
campus deaths over five years, the only reasonable conclusion is that
there must be something special about the ridiculous religious rules at his college
that prevented the great rampaging plague of violence from touching the students
at his school.

I actually spent five years as an undergraduate at Rutgers University in NJ. During that
time, there were no violent student deaths. (There was one death by alchohol poisoning; and there
was one drunk driving accident that killed four students.) But zero violent deaths.
Gosh, Rutgers must have been an absolutely amazingly moral university! And gosh, we had
all of those horrible sinful things, like dancing, and co-ed dorms!
How did we manage to go all that time with no violence?

It must have been the prayers of the very nice Rabbi at the Chabad house
on campus. Yeah, that must be it! Couldn't just be random chance, right?

Ok, now let me stop being quite so pettily snide for a moment.

What's going on here is really simple. We hear a whole lot about violence
on campus. And when you hear about eight-hundred and some-odd violent deaths on campus,
it sounds like a lot. So, intuitively, it sure seems like there must be a whole
lot of violence on campus, and it must be really common. So if you can go through your
whole time in college without having any violence occur on campus, it seems
like it must be unusual.

That's because, as usual, we really suck at understanding big numbers and scale. 800 sounds
like a lot. The idea that there are nearly sixteen million college students is just
not something that we understand on an intuitive level. The idea that nearly a thousand
deaths could be a tiny drop in the bucket - that it really amounts to just one death
per 100,000 students per year - it just doesn't make sense to us. A number like 800 is,
just barely, intuitively meaningful to us. One million isn't. Fifteen million isn't. And a ratio with a
number that we can't really grasp intuitively on the bottom? That's not going to be meaningful

Bozo-boy is making an extremely common mistake. He's just simply failing
to comprehend how numbers scale; he's not understanding what big numbers really mean.

67 responses so far

Big Numbers and Air Travel

Jan 04 2010 Published by under Bad Probability, Big Numbers

As you've surely heard by now, on christmas day, some idiot attempted to
blow up an airplane by stuffing his underwear full of explosives and then
lighting his crotch on fire. There's been a ton of coverage of this - most of
which takes the form of people running around wetting their pants in terror.

One thing which I've noticed, though, is that one aspect of this whole mess
ties in to one of my personal obsessions: scale. We humans are really,
really lousy at dealing with big numbers. We just absolutely
have a piss-poor ability to really comprehend numbers, or to take what we
know, and put it together in a quantitative way.

Continue Reading »

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I am the antichrist. No, really!

Aug 03 2009 Published by under Bad Probability, fundamentalism

I normally try to ignore things like this, but this is just too funny.

In general, I find arguments like this to be extremely silly. This is, basically, like
playing with gematria - only instead of doing real gematria (which can be quite silly enough),
it's like our friend "Gotcha" - mixing systems and screwing things up until you get the results
you want.

Lots of the particularly crazy strain of Christians really, desperately want to believe
that Barack Obama is the antichrist. They want an explanation for how this black man with
a muslim name could possible have actually been elected - they don't believe it could possibly
have happened honestly. And their doctrine requires the antichrist to come soon. Combine
those two, and you've got what, for them, is a sort of perfect storm.

Which gives us things like this. For more mockery, see beneath the fold.

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94 responses so far

Moronic Probability and Stupid Physics

May 03 2009 Published by under Bad Physics, Bad Probability

Via the Bad Astronomer comes one of the most pathetic abuses of
probability that I've ever seen. I'm simply amazed that this idiot was willing
to go on television and say this.

The Daily Show With Jon Stewart M - Th 11p / 10c
Large Hadron Collider
Daily Show
Full Episodes
Economic Crisis First 100 Days

The crank in question is Walter Wagner, the moron who tried to use a lawsuit
to stop the LHC from being activated. (Just that much, already, is amazingly silly;
he sued in Hawaii, but the LHC is in Geneva, Switzerland. How does a Hawaiian court
have any jurisdiction?)

Anyway... Wagner claims that the LHC could destroy the earth. See, there's a tiny theoretical chance that the right collision in the LHC could create a microscopic black hole. According to Wagner, if that happens, the black hole will swallow the entire earth.

That claim is, itself, based on some pretty bad math. The only theory that predicts
that it's possible to create a microscopic black hole also predicts that such a black
hole would evaporate - that is, would completely disappear in a burst of energy - immediately. The
exact same math that predicts that you could create a black hole in a high-energy collision also
predicts that the hole would be destroyed before it had time to do any damage. If you tweak it so that the black hole lasts longer, the energy requirements change so that it's no longer possible to create it in the LHC. To make the black hole last a microsecond is absolutely beyond the
energy of any collider that we could ever build on the earth.

But let's skip that - demonstrating that is pretty complicated. To get an idea of
the level of understanding of the guy who claims that there's a real danger, let's just
take a look at what he says.

When asked what the probability of the LHC destroying the earth is, he says 50%. Why?
Because either it could happen, or it couldn't - therefore, there's a 50% chance of it happening.

You could argue that that's naive Bayesian reasoning - but if you did, you'd be an idiot. Classic Bayesian arguments about stuff like this would say that you use 50/50 as an initial prior in the absence of any other information; then you adjust that based on whatever
other information you have available. For Mr. Wagner's stupid argument, it's based on
a complex physical theory - a complex physical theory which provides lots of information
which you can use to update your probability estimate.

Mr. Wagner's 50/50 claim is based on the fact that he's absolutely clueless about how any of
this stuff works. He clearly doesn't understand probability, and he clearly doesn't understand

But he's awfully funny.

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Lottery Probabilities and Clueless Reporters

Jan 23 2009 Published by under Bad Probability

A simple, silly, but entertaining example of mathematical illiteracy by way of the Associated Press:

OMAHA, Neb. (AP) -- The odds are against something this odd. But a Nebraska Lottery official says there was no mistake: The same three numbers in Nebraska's Pick 3 lottery were drawn two nights in a row this week.

Lottery spokesman Brian Rockey said one of two lottery computers that randomly generate numbers produced the numbers 1, 9 and 6 -- in that order -- for Monday night's Pick 3 drawing. Rockey says the next night, the lottery's other computer produced the same three numbers in the same sequence.

The odds of such an occurrence? One in a million.

Close... Only off by three orders of magnitude...

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If you measure the wrong thing, you get the wrong answer: Down's syndrome in Britain

Dec 01 2008 Published by under Bad Probability

One of the blogs I read regularly is Ben Goldacre's "Bad Science". I recommend
it highly. (Which reminds me that I really need to find some time to update my blogroll!) In saturday's entry, he discussed a BBC Radio documentary that described how Britain is becoming a much more welcoming place for Down's syndrome babies.

Ben did a good job of shredding it. But I also wanted to take a stab, focusing on
the mathematical problem that underlies it, because it's a great example of two very
common errors - first, the familiar confusing correlation and causation, and
second, using incorrect metrics.

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Astrology and the Olympics

Aug 22 2008 Published by under Bad Probability

An alert reader sent me link to a stupid
article published by Reuters about the Olympics and Astrology.

It's a classic kind of crackpot silliness, which I've described
in numerous articles before. It's yet another example of pareidolia - that is, seeing patterns where there aren't any.

When we look at large quantities of data, there are bound
to be things that look like patterns. In fact, it would be
surprising if there weren't apparent parents for us to find. That's
just the nature of large quantities of data.

In this case, it's an astrologer claiming to have found
astrological correlations in who wins olympic competitions:

Something fishy is happening at the Olympic Games in Beijing. Put it all down to the stars.

Forget training, dedication and determination. An athlete's star sign could be the secret to Olympic gold.

After comparing the birthdates of every Olympic winner since the modern Games began in 1896, British statistician Kenneth Mitchell discovered gold medals really are written in the stars.

He found athletes born in certain months were more likely to thrive in particular events.

Mitchell dubbed the phenomenon "The Pisces Effect" (pisces is Latin for fish) after finding that athletes born under the sign received around 30 percent more medals than any other star sign in events like swimming and water polo.

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19 responses so far

Nonsense Pretending: Probability as a Disguise

Jul 31 2008 Published by under Bad Physics, Bad Probability, Debunking Creationism

Once again, you, my readers, have come through with some really high-grade crackpottery. This one was actually sent to me by its author, but I didn't really look at it until several readers sent me the same link because they thought it was my kind of material. With your recommendations, I took a look, and was rewarded. In a moment of hubris, the author titled it A Possible Proof of God's Existence from Multiverse Assumptions.

This article is basically a version of the classic big-numbers probabilistic argument for God. What makes this different is that it doesn't line up a bunch of fake numbers and saying "Presto! Look at that great big probability: that means that it's impossible for the universe/life/everything to exist without God!". Instead, it takes a more scientific looking approach. It dresses the probability argument up using lots of terms and ideas from modern physics, and presents it as "If we knew the values of these variables, we could compute the probability" - with a clear bias towards the idea that the unvalued variables must have values that produced the desired result of this being a created universe.

Aside from being an indirect version of the big-numbers argument, this is also a nice example of what I call obfuscatory mathematics. See, you want to make some argument. You're dead sure that it's right. But it doesn't sound convincing. So you dress it up. Don't just assume your axioms - make up explanations for them in terms of math, so that it sounds all formal and mathy. Then your crappy assumptions will look convincing!

With that said, on to his argument!

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More Bad Bayesians: No ETs!

Apr 22 2008 Published by under Bad Probability

Remember when I talked about the problems with Bayesian probability? As you'll probably recall, one of the things that drives me crazy about Bayesianism is that you get a constant stream of crackpots abusing it. Since the basic assumption of Bayesian probability is that you can always use it, you'll constantly get people abusing it.

Christopher Mims, who was one of the people running ScienceBlogs when I first signed on, sent me a classic example. A professor has published a paper in a journal called "Astrobiology", arguing that there's an exceedingly low probability of intelligent life elsewhere in the Universe.

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