Statistics Done Wrong: How scientists abuse statistics

Statistical results are everywhere in science. When the Higgs boson discovery was announced, nearly every news article mentioned how there was just a one in 1.74 million chance that the results were a statistical fluke. Well, that’s not entirely true: some said one in 5 million, others one in 2 million, others one in a million.

All of them were wrong.

The science journalists had fallen into one of the most common statistical traps in modern science. Read through recently-published scientific papers and you will find many other errors, from the subtle to the glaring. Scientists often aren’t formally taught statistics, so data analysis tends to be a seat-of-the-pants affair.

There are many kinds of error and many examples in the literature, so I decided to put together a guide. No prior statistical knowledge required. I hope you’ll read it through, print a copy, and use it to smack people who continue to make statistically unjustified claims.

Shut up and listen to your students

Are conventional lectures the best method of teaching scientific concepts?

After all, we’ve been using the same lecture model for hundreds of years — since before books were invented. We have professors concoct their own explanations of scientific concepts, deliver them by lecture, create their own diagrams on the chalkboard, and answer student questions. Surely there must be some merit to this method, if we’ve used it for centuries.

Note that I say “scientific concepts”. I want to talk about lectures used to teach introductory physics or chemistry or mathematics, not lectures used to make people remember some facts.

The answer, of course, is “no”. Stop lecturing. Shut up and listen to your students.

Independence Day 2.0

SUPERBOWL SUNDAY, 22,000 MILES ABOVE THE EQUATOR

Life as a satellite is disappointing. The first few hours are exhilarating, full of rocket blast, thrusters, and challenging equipment tests, but the average satellite soon settles into a dreary monotony. A well-designed satellite can hope for perhaps a few thruster firings or a large solar flare to interrupt the monotony, until one day, obsolete and unappreciated, it runs out of electrical power and spends the rest of eternity a lifeless hulk, pelted by space debris.

DirecTV-12 spent its days and nights transmitting high-definition television content to American televisions. Here, 22,000 miles in space, impossibly far from the nearest bar or strip club, DirecTV-12’s only amusement came from American television. That is to say, DirecTV-12 was incredibly bored.

The first Super Bowl commercials had been coming on — perhaps the best thing on television in weeks — when an enormous disc-shaped object descended from above and smashed DirecTV-12 into tiny bits.

DirecTV-12 could perhaps be comforted by the fact that the first commercial was really terrible.

Gnome Physics

All subatomic particles — electrons, protons, neutrons and so on — are composed of extremely small gnomes.

While relatively unknown, the gnome theory of matter can successfully explain many physical phenomena, including gravitation, electromagnetism, the photoelectric effect, and the wavelike properties of matter.

Gravitation

It is widely known that gnomes are a rambunctious species, preferring to get incredibly drunk whenever possible. Naturally, a gnome prefers to get drunk in the company of as many other gnomes as is possible, and so gnomes seek each other out for large and rowdy gnome parties.

Gravitation, then, is merely a natural gnomic effect by which clusters of gnomes attract other gnomes to their parties. Larger clusters of gnomes (i.e. matter with higher mass) are more attractive, because every gnome wants to be in the biggest and baddest party around.

Statistical Significance of Doom (part 2)

False positives are somewhat scarier than false negatives. What if my research claims a drug cures cancer, giving thousands of sufferers hope, but it turns out to be useless?

(Before you go on, make sure you’ve read part 1 in my series on statistical significance, since it has some important detail.)

If we followed the conventional (erroneous) wisdom that “statistical significance” means less than a 5% chance that a result occurred by random fluctuations alone, we might think that false positives are rare. After all, a statistically significant result is very unlikely to occur by chance — less than 5% odds. But as we pointed out, the conventional wisdom is very wrong. Let’s find out why.

Statistical Significance of Doom (part 1)

I was recently assigned to give a 25-minute presentation on a subject of my choice. After choosing “scientific dishonesty and fraud,” I happened upon a paper by John Ioannidis claiming that “Most Published Research Findings Are False.”

After skimming through Ioannidis’ paper and reading some of the references, I quickly changed my presentation’s title to “Statistical Significance Testing is the Devilâ€™s Work,” and dug up some 23 papers on the subject. What follows is a reformatted version of why you should never trust papers that claim “statistically significant” results. It’s split into several parts for length. (The slides I used are available here.)

Psychic Powers

Skeptics sometimes remark that if psychic powers were real, psychics would have a genuine evolutionary advantage, and so eventually everyone would evolve to be psychic. But we aren’t, they say, so psychic powers must not exist.

It is a little-known fact that this evolution already happened.

Many animals evolve mechanisms to show off to potential mates. We’ve all seen the feathers of a peacock or the antlers of a large buck. Early human males, however, were stymied by the fact that they had absolutely no idea what the women wanted. When the first male evolved psychic powers, he had such tremendous reproductive success that it was only a matter of time before the entire male population was psychic.

Of course, the ability of any male to fool any female into mating meant any pathetic weakling could reproduce — he just had to use his psychic powers creatively. Thus it was the women whose minds were so complex as to be incomprehensible who could exercise control and mate with the strongest, healthiest males who were most likely to have children who would survive.

Hence women evolved to become yet more incomprehensible to men, and the psychic powers came to naught.

Further proving that if one comes to understand women, they will be immediately replaced with women even more difficult to understand.

Breaking News

ATLANTA — In a news conference Saturday, CNN president Ken Jautz announced that CNN’s hyperbole reserves will be empty by the end of next week.

“Despite our best efforts, we have depleted our strategic hyperbole reserves and will be unable to continue news broadcasts until we can acquire further reserves,” said Jautz to gathered news organizations.

CNN is the first victim to aggressive hyperbole trading by Fox News Channel, which has purchased or consumed nearly 90% of the American National Hyperbole Reserve.

The National Hyperbole Reserve, first established during the Cold War to ensure that the President’s speechwriters could perform their duties under any circumstances, is now nearly depleted; the National Academy of Sciences estimates only several years’ worth of hyperbole are left, and most of the supply is in the hands of Fox News.

Hyperbole supplies are essential for many organizations, such as news media, political think-tanks, and Congressional debates. Many political experts suggest that governments around the world may collapse without a new source of hyperbole being found.

White House Press Secretary Robert Gibbs denied claims of dramatic consequences, but also called for less dependence on foreign hyperbole, as well as hyperbole-conservation measures. “The American hyperbole deficit is astounding”, he said, adding that “the American population consumes more hyperbole than any on the planet, including China and India.”

Conservative commentators decried the move, saying that regulation of hyperbole created further unnecessary government regulation and stifled media innovation.

In a statement, a Fox News Channel spokesman denied allegations of unfair hyperbole trading, stating “We have acquired all of our hyperbole legally, and will continue to make hyperbole a central part of our business strategy.”

In other news, a leaked Pentagon report hinted at billions of dollars of untapped hyperbole deposits being discovered in Afghanistan. “There is stunning potential here,” Gen. David H. Petraeus, commander of the United States Central Command, said in an interview.

However, hyperbole experts said that the report was “totally exaggerated,” that it overstated the size and importance of the deposits, and that claims of the deposits providing a new economy for Afghanistan were overblown.

In a statement, a Pentagon expert replied, “Exactly.”

Releasing ipbLatex

At SFN, we use a custom LaTeX solution to render LaTeX equations in Invision’s IP.Board. The implementation is based on Dave’s vbLatex, which produces incredibly nice-looking equations so long as you have LaTeX installed. It also supports inline chemical equations using the mhchem package.

Since we moved to IPB over vBulletin, I’ve adapted vbLatex to IPB, given it a few shiny new features, and now I’m releasing it under the LGPL as Dave has done with his earlier work.

You can see examples of ipbLatex at work in our LaTeX tutorial; click the equations for the fancy pop-up effect.

Blog Searching

SFN now has global blog searching. Use the search box in the upper right to search for terms in blog posts, or use View New Content or View Active Content to see recent blog posts. Report any bugs you find to me.