Every day or more, one of the news aggregator robots gets both my attention and my goat. Here’s one of today’s missiles: “CDC: Most Teens Choose to Abstain,” at cbn.com. The first paragraph:

A recent study shows that most teenagers are virgins, contradicting claims from family planning groups that most young people do not abstain from sex and more sex ed should be taught in schools.

Image by Kelley Boone, some rights reserved (CC-BY-SA 2.0)

This kind of blabbery drives me nuts. They might has well have said, “A recent study shows that the earth is flat, contradicting claims from Unitarians that the planets revolve around the sun and astronomy should be taught in schools instead of the Bible,” when in fact a recent study showed no such thing, and even if it had, it wouldn’t contradict what the Unitarians supposedly said. Maybe if I’d been on the debate team I’d know how to respond more effectively.

If I were a fundamentalist Christian who wanted to justify abstinence education, I wouldn’t quote or misquote studies, nor would I attempt to use logic. I’d be honest: “According to my church, the world is flat, most young people abstain from sex, and abstinence should be taught in schools right after study hall and before creationism. That’s what I believe, because faith in the church is my guiding light.”

Studies be damned, science be damned, the church is the ultimate authority. I might have more respect if they put it that way more often. (I would still object if it got to the point of the Constitution be damned and laws be damned.) Why should fundamentalists care a whit about the fact that science is consistent, well-founded, and predictive? Why should they care about evidence from studies and measurements, if faith, not intelligence, is their life’s compass? I can disagree, disapprove, and be dismayed, but I have no appeal. We live on different planets; we grew up in different universes.

Anyway, for readers who might appreciate facts and figures, let me explain the CBN’s vulpigeration.

What is “sex,” anyway? For its study, the CDC defined “sex” to be heterosexual vaginal sexual intercourse¹ only (though the boy need not stay on top). Many English speakers would call a bunch of other things people do naked with others sex, but the CDC’s restrictive definition should suit the Christian Broadcasting Network in two ways. First, this definition doesn’t infringe on the way CBN might define another word, “sodomy.” They might prefer it for that bunch of other things people do naked with each other. Second, it yields higher virgin percentages. As far as the CDC and CBN.com are concerned, you’re a virgin if you haven’t been part of any penis-in-vagina hanky-panky, even if you’ve gotten plenty naked and nasty with one or more hims or hers.

Fact: Most young people do not abstain from sex. (Or “sex.”) Not during their entire youth, which is what CBN.com suggested. According to the CDC study, most (65% of) boys aged 18-19 and most (60% of) girls in the same age group have had heterosexual vaginal sexual intercourse. The CDC numbers suggest that most young people do abstain from sex “sex” until about age 17 or 18, but abstaining until you stop abstaining is not the same thing as abstaining. Using the CBN.com logic, you could say that all people abstain from sex, ’cuz they all do — until they stop, and most stop, as we know from all the babies being born and abortions being performed. Few babies (or aborted fetuses) are incarnate nowadays.

¹ Additional information available on the internet.

According to the abstract,

Our findings suggest that men experience a conflict between their relatively intrinsic preferences and gender norms and that they tend to forgo their intrinsic preferences to conform to a masculine gender identity (when they have sufficient resources to incorporate gender norm information in their choices). Women, on the other hand, appear to be less concerned with making gender-congruent choices.

The authors found that men, when asked to choose between two foods, one with a straight macho masculine description corresponding to American societal “norms” for guy food and the other that was gay sissy feminine more what Americans might think of as girly food, they picked the guy item almost two-thirds of the time. If, that is, they had plenty of time to ponder their choice. If they were rushed to decide, though, they picked girl food choices more often — about 55% of the time, on average. Women, on the other hand, choose girl food about two-thirds of the time, regardless of whether they’re rushed to decide.

The authors conclude (in more precise language than my paraphrase) that men, unlike women, are cognitively self-regulating their decisions according to societal norms of gender expression. In other words, while men like girly food as much as girls, they’ll decide not to order it (forgoing food they like in order to look like “real men”) if they have time to think things through.

It doesn’t surprise me that men put energy into “behaving like men,” even when it sometimes conflicts with their intrinsic desire. (I’m not so convinced that men are as unlike women as the authors say.¹)

The authors describe the effect they saw as “making gender-congruent choices,” but I might envision it another way: men put a lot of energy into avoiding anything they think will make them look gay. How different is what the authors call “threats associated with gender-norm transgression” from fear of being labeled a fag?

In any case, special thanks to the authors for their menu of “feminine” and “masculine” menu items, which was half the fun of the paper. Here are a few selections. I want all of them, but hold the shredded American cheese.

• Martha’s Vineyard Salad Mixed baby greens and fresh spinach with toasted pine nuts, dried cranberries, cucumber, red onion, and a warm Vermont goat cheese crouton with a balsamic vinaigrette
• Chunky Fudge Cake Ice Cream Vanilla ice cream, smothered in hot fudge with chunks of chocolate fudge cake, whipped cream, and peanuts
• Vitello Carciofi and Asparagus Beef medallions sautéed with asparagus and artichoke in a light demi-glace sauce
• Damon’s Specialty Pizza Ground hamburger, red onions, roasted peppers, and mozzarella cheese
• Western Salad Chunks of barbequed chicken with shredded American cheese served on greens with a side of Ranch dressing

¹ The authors’ findings suggest that men do this, but women don’t (or do to a much smaller extent). But the authors only studied university undergraduates at (I assume from their affiliation) a largish private Midwestern university. For that population, it’s fairly reasonable to generalize, and perhaps for that population this in fact is a guy-only thing. I’d speculate, but with no support from the study, that the effect is present among men across most segments of the U.S. population. But it wouldn’t surprise me to find the “I better order something gender-appropriate” effect in women, too, in some places (richer white populations in the South?). Studies in populations other than undergraduates would be nice to see.

The danger in generalizing from undergraduates, who are readily available to university researchers, to the general population, has fortunately been getting some press lately. It’s a real danger.

There are plenty of other interesting angles to explore. To what extent this effect is expressed ought to depend on the environment. Do men (with time to think) pick guy foods more frequently when they’re dining with several guys as opposed to when dining with a single woman? (I’d put money on yes.) Are there differences between straight men and gay men? (I’m not sure I’d bet on this one.)

I learned about Zelazny’s desecration here, though Andrew Abela, who reported it, failed to call it that. “Zelazny notes that the graphic is difficult to read, and proposes that there might be better ways to convey the same information.”

Sure, there might be, just like there might be better ways to decorate the ceiling of the Sistine Chapel, but what Zelazny offers is an epic numerical fail, because IT NOT ONLY DEPICTS DIFFERENT (AS IN WRONG) INFORMATION, IT ALSO DEPICTS THE WRONG INFORMATION BADLY (as in we can’t even tell what wrong numbers he wants us to find and what they are supposed to quantify).

Zelazny might as well propose that “there might be better ways to clean up the Gulf of Mexico,” trot out a broken doorknob and a bent bicycle tire, and ask us to wonder with him. Ugh, ugh, ugh. And ugh.

Here are a few of the gory details (of which there can be but few, given how little actual stuff there is in Zelazny’s chart).

Ok, so the spirit levels in the cutesy clipart thermometers don’t match the numbers, only their absolute values (sort of).  But the numbers are wrong, too. Five of Zelazny’s six data points are wrong — misread from Minard’s original. Five out of six. That’s almost all wrong, for those of you who aren’t counting. Badly, differently, and horrifyingly wrong.

Minard reports that there was rain on October 24, and that the temperature was about zero*. Zelazny misread the day of the month (24) as a temperature, then used the only other written figure at that spot on Minard’s chart (8^bre, for octobre) for both the month and the day. No explanation short of “Who gives a fuck?” works for this slop.

*Minard’s figures give the Réaumur scale temperature, which detail Minard, lest future readers misconstrue his chart, tells us. Minard cared deeply about communicating. (Zelazny’s figures are wrong in every known temperature scale. He cares less. Much less, like not at all.)

Remarkably or not, almost nothing is correct in Zelazny’s “presentation.” The border between Poland and Russia is misplaced, and all the graphical scales are wrong. I’m no PowerPoint guru, but I assume you have to work very hard to incorporate numbers into a slide this wrongly (as was famously done here, and better).

Even Zelazny’s title is wrong.

Things got bad on the retreat from Moscow. And it’s not clear how many died. Minard charted the number of troops, not deaths. Some who didn’t return were captured. Others may have deserted. And the overall message isn’t “the colder … the more.” The biggest declines were early in the campaign, when the temperatures aren’t given. So the title is all wrong, but hell, IT FIT ON TWO LINES. Shit like this matters. It’s our planet’s fucking history.

Sure, Minard’s correct title (Carte figurative des pertes successives en hommes de l’ Armée Française…, and penned more beautifully than any web typography can be rendered) won’t work projected at WXGA resolution or on your favorite eReader or phone.

THIS IS WHY WE PRINT STUFF ON PAPER. If you don’t have a copy of Minard’s chart, buy yourself one. Fuck, if you’re one of the first five people to ask me, I’ll buy you one.

Now turn off your computer and pick up a beautiful book. Or go to the library. Or write. On paper. Thanks for listening.

Example 1. MathWorld explains here that “The numbers of palindromic numbers less than a given number are illustrated in the plot [below].”

So the left plot tells us that there are about 100 palindromes less than or equal to 20. But there are only 21 nonnegative integers less than or equal to 20, so there can’t be 100 palindromes among them. In fact, there are 11 palindromes less than or equal to 20: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 11. My guess is that the left plot illustrates the n-th palindromic number as a function of n. In any case, it’s not what MathWorld describes.

MathWorld begins its list of the “first few palindromic numbers” with 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 (these 10 numbers are palindromes and are all less than 10), but in the next paragraph, MathWorld states that the number of palindromic numbers less than 10 is 9. There are 9 if you don’t count zero for some strange reason, but if you don’t intend to, give a definition that excludes it (MathWorld’s definition is less than clear), and then don’t list it.

Still confused? Read the Wikipedia article.

Example 2. Pascal’s Triangle shouldn’t be hard to screw up, right? Wrong. Here’s MathWorld’s Pascal’s Triangle:

This triangle needs to go to the shop for an alignment. The numbers are neither lined up in columns nor staggered (the latter being the usual presentation). What are the numbers in the column containing the rightmost 4? What numbers are along the diagonal through the top? (1, 1, 1, 1, 1, 5, 6?) As shown, MathWorld’s anyway-ill-worded “each subsequent row is obtained by adding the two entries diagonally above” is meaningless.

Example 3. In its article on Mersenne numbers (numbers that are one less than a power of two), MathWorld attempts to explain why “[i]n order for the Mersenne number [2ⁿ-1] to be prime, n must be prime.” MathWorld’s justification: “This is true since for composite n with factors r and s, n = rs. Therefore, 2ⁿ-1 can be written as 2^rs-1, which is a binomial number and can be factored.” That’s sloppy to say the least. First, if a composite number n has factors r and s, it’s not necessarily the case that n = rs. Furthermore, the fact that a number can be factored doesn’t prove it’s composite. Every Mersenne number 2ⁿ-1 can be factored. It’s just that when n is composite, there’s definitely a factorization into positive integers neither of which equals 1. Explaining it isn’t hard: In order for 2ⁿ-1 to be prime, n must be prime. For if not, n = rs where r and s are integers greater than 1 and less than n; then 2ⁿ-1 = 2^rs-1 has a factor between 1 and 2ⁿ-1, namely 2^r-1.

Example 4. MathWorld describes prime numbers as “numbers that cannot be factored.” Prime numbers, like all integers, however, can be factored, and elsewhere, MathWorld gives the factorization of several prime numbers, such as 7: 7 = 7×1.

Example 5. Any of MathWorld’s articles on statistics.

In the article on the Central Limit Theorem, what is lowercase n? What is f? The “limiting cumulative distribution function” of X_norm is limiting in the sense of what approaching what? (It’s not clear to me that MathWorld’s statement of the theorem is even correct, but it’s clearly unclear.)

The article “explaining” the p-value has perhaps the worst definition of p-value I’ve ever seen when not grading exams. MathWorld says it’s “[t]he probability that a variate would assume a value greater than or equal to the observed value strictly by chance: P(z > z_observed)” (wrong). Wikipedia says “In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true” (right).

“We’re surprised, but we’re still forecasting a positive outlook for the year,” said Trend Analytics’ Sandeep Singh. “Don’t forget that increasing optimism, though off its January peak, remains strong.” In his widely-read newsletter, “Pulses,” Singh calls for renewed concern to drop by 10-15% in Q2 and for increasing optimism to remain steady.

The Los Angeles Times was one of the first to pick up on the scare. They interviewed the article’s lead author, Edmond J. Byrnes, III for their report. In PLoS Pathogens, Byrnes and his coauthors described an “increasingly fatal fungal outbreak” in their discussion, without providing statistical support or an inline reference. The Times knows what readers will glom onto, however, and they devoted a couple of paragraphs to this “more lethal” angle.

The spread is also a concern because the strain of the fungus that moved into the United States in 2004 has mutated to become more lethal than the original strain that invaded British Columbia in 1999.

Five of the 21 people who contracted the fungus in the United States have died (about 25%), compared with 8.7% of the 218 infected people in Canada. The fungus has also infected many different species of mammals.

These details aren’t in today’s PLoS Pathogens article. Today’s article focuses on the molecular biology of C. gattii, not its epidemiology. My admittedly cursory search for the source of the Times’s numbers turned up one mention of an “over 25%” U.S. fatality rate. That was in a previous article of Byrnes’s, where he referenced the figure as the “unpublished observations” of two other scientists. But let’s give Byrnes and the Times the benefit of the doubt and suppose the numbers are reliable.

Math time. If you know only a handful of small numbers about a disease, drawing any epidemiological conclusions — especially alarmist ones that might be misconstrued — is risky, but mathematics can still help us evaluate the numbers. There will be lots of ifs, but that’s to be expected when you have limited data. The standard way to proceed is to ask the following question: If in fact nothing scary is happening (meaning that the infections in the U.S. are not more deadly than they are in Canada), might we really see as many as five deaths in 21 cases?

Under the probabilistic assumptions of this kind of analysis, getting infected with C. gattii is treated like a crap shoot as to whether you die or not; you die with probability 8.7%, the Canadian fatality rate. If 21 people get infected and for each one God rolls the dice to see who dies, what’s the likelihood at least five of them will succumb? Well, it’s around 3%. To put that in context, imagine that tomorrow’s traffic is terrible, like once-a-month terrible. Would you chalk it up to bad luck or a real change in traffic congestion? I’d chalk it up to bad luck and assume a real change only if traffic was similarly terrible again tomorrow or maybe next week. (Even then I would probably look for other explanations, like an announced construction project or a visiting dignitary.)

Other factors should be considered when comparing fatality rates to test the hypothesis of increasing deadliness, particularly with such small numbers of cases. Were the U.S. persons infected by C. gattii diagnosed as promptly (or not) as the Canadians and given identical treatments? If not, the higher U.S. fatality rate could be due to late diagnosis or ineffective treatment. Were the U.S. persons infected or killed similar to the Canadians in age, general health, and other factors known to be independent predictors of mortality from disease? If not, the higher U.S. mortality might not be due to greater virulence.

PLoS Pathogens is a peer-reviewed journal, and that provides some assurance that the scientific conclusions were based on accepted scientific practices. Unfortunately, published science has the potential to affect society and policy via the popular press, and reviewers need to think about how a publication might be construed by a journalist.

To Byrnes’s credit and the Times’s, readers who ventured a few paragraphs past the alarming headline will read this more moderate assessment of the situation: “Overall, I don’t think it is a large threat at this time. But the fact that it is continuing to spread geographically and the number of cases is rising makes it a concern.”

Whether or not Byrnes et al. were more justified than I can tell in calling this a “increasingly fatal fungal outbreak,” sure, this could be the next black plague. So could any number of currently very rare or unknown pathogens. But based on the science I’ve seen, you shouldn’t be any more worried about C. gattii today than you were last week, when I’m guessing you’d never heard of it.

References

• PLoS: Emergence and Pathogenicity of Highly Virulent Cryptococcus gattii Genotypes in the Northwest United States
• LA Times: Potentially lethal fungus moves south from Canada

Updated at 2010-04-22 at 23:28. I added the words Deadly and Fungus to the post title hoping to get more play. A list of headlines on this story follows.

One rebuttal of the alarm: Ore. DHS questions article statements about deadly fungus
(DHS is Department of Human Services, not Homeland Security)

Alarm and alarm in all the other headlines, though.

• Airborne fungus claiming lives
• New strain of virulent airborne fungi, unique to Oregon, is set to spread
• New Deadly Fungus Found in US, Has Already Killed Six
• Potentially Lethal Airborne Fungus May Spread to California
• Deadly Oregon fungus may spread on West Coast
• Deadly airborne fungus in Oregon set to spread
• Killer fungus seen in Pacific Northwest
• Potentially deadly fungus spreading in US and Canada
• Deadly Oregon fungus may spread on West Coast
• Deadly Fungus In Oregon: New Strain Of Fungus Killed 6 in Oregon
• Fungus Cryptococcus gatti Threat to Healthy People
• New Likely Deadly Fungus Invading US & Canada – Signs & Symptoms
• Emerging Northwest fungal disease develops virulent Oregon strain
• Oregon Fungus Spreading South
• Toxic Airborne Fungus From Oregon Spreading Across West Coast
• New Concerns About Deadly Fungus Found in Oregon
• Deadly strain of airborne fungus spreading among healthy people and animals
• Life threatening tropical fungus seen in Pacific Northwest
• Fungus Spreading Throughout US, Canada
• Killer Fungus Migrates To The US
• Killer Lung Fungus Hits Northwest
• ‘Highly Virulent’ Strain of Killer Fungus Found in Ore

Looks like a typo to me. At a glance, the breakdown by age seems inconsistent with the aggregate result.

Most (about 85%) of the survey participants fell into one of the three oldest age groups, all of which favored gay marriage at a lower rate than the general population. The 65+ crowd, numbering 507, favored gay marriage at a rate a full 17 points lower than the rate for all ages combined. Although young’ens favor allowing Adam¹ and me (or Autumn and Eve) to get married legally, and they smile with approval at a rate almost 20 points higher than the rate for all ages combined, there are too few of them (only 283) to balance out the manier² old grumps and middle-aged semigrumps.

I have no reason to suspect the Pew folks of vulpigeration, so I tried to find an honest basis for these apparently contradictory figures.

Pew’s full report on survey question Q146a revealed one potential source of slop: the number under “Favor” seems be the sum of two individually rounded percentages: one for “Favor” and one for “Strongly Favor.” The actual survey instrument included both possible answers. Therefore, 39% could mean anything between 38% and 40%. Survey percentages are routinely rounded, but one expects 39% to mean somewhere between 38.5% and 39.5%.

Even allowing for extra slop, the numbers don’t agree. Here’s a tabulation (using the increased slop allowance) that gives the minimum and maximum numbers of favorers in each age group and (by summing) the minimum and maximum number of favorers among those in any age category.

According to these numbers, between 34.8% and 36.8% of 1,980 respondents would be cool with my marrying Adam legally.

According to Pew’s summary chart (at the top), though, between 38% and 40% of 2,010 responses, or between 764 and 804 people, answered “Favor.” That’s quite a bit higher than the breakdown figures show, and even if the 30 people in no age category (who presumably withheld their age or were under 18) all favored gay marriage, the maximum (and an unlikely maximum, because it would require all the rounding and missing information to be skewed favorably) number of favorers is 759.

As another plausible scenario, I calculated a Total percentage based on the age breakdown but weighted according to the actual histogram of age in the U.S. Still no dice. If anyone has an idea, let me know.

¹ For the record, I’m currently Adamless and available

² manier, adjective. Comparative of many; more numerous. To be coined presently. Many and numerous are synonyms; if things can be more numerous, I see no reason they can’t also be more many, or manier.

Here’s an illumination, as MapPoint is my amanuensis. Click to embiggen.

Explanation: Pie areas are proportional to the number of deaths; the yellow slice is cremations, the red non-cremations.

Pies for our nation’s two newest states are not shown. Alaska’s looks like a two-thirds size Vermont pie; Hawai’i’s looks like a one-third size Oregon pie.

Contralateral prophylactic mastectomy lowers post-mastectomy five-year death rate by 30%

The five-year death rate after mastectomy was 11.5% for women who had both breasts removed. It was 16.3% for those who only had the cancerous breast removed. Adding a contralateral prophylactic mastectomy to the original surgery therefore reduced the five-year death rate from 16.3% to 11.5%. Almost a third fewer mastectomy patients died within 5 years when the had chosen to remove the second (healthy) breast, compared to mastectomy patients who had not chosen to remove the second breast. The bilateral mastectomy decreased the 5-year death rate by 29.4%.

This strikes me as a significant benefit. Suppose I have breast cancer and need a mastectomy. I can choose a single mastectomy and have a one-in-6 chance of dying in five years, or I can choose a double mastectomy and have a one-in-9 chance of dying in five years. One-in-9 sounds quite a bit better to me. If 100,000 women with unilateral cancer need mastectomies, performing 100,000 double mastectomies instead of 100,000 unilateral mastectomies will reduce the number of deaths in the first five years from 16,300 to 11,500. About 4,800 fewer women will die within five years.

Contralateral prophylactic mastectomy benefits only 5% of mastectomy patients.

The reporting of this study takes a very different viewpoint. It compares the survival rate, not the death rate, and notes that the bilateral prophylactic mastectomy increases the survival rate from 83.7% to 88.5%, “a difference of less than 5%.” Five percent sounds like a small number, but 5,000 lives saved sounds like a large number.

Point of view

Both statements (lowers by 30%; benefits only 5%) are the same. Only the intent to communicate is different. Whether prophylactic mastectomy is good practice depends not only on the change in five-year survival rate, and I don’t have more information.. For example, how does a double mastectomy (which for 95,000 of the women will not change the five-year death rate outcome) affect a woman’s well-being and general health over time? What is the cost to save these 5,000 lives, and how will the disparity of death rates change more than five years after surgery?

Good news

There is a good piece of news in the study: The study data identified a subgroup of women for whom double mastectomy had an even greater benefit: women 50 and younger with early stage estrogen receptor negative cancer. Removing the second breast had no benefit for women 60 and older, and the benefit for women in their 50s was uncertain, presumably because of the small number of bilateral mastectomies in the sample.

The journalists writing about this study generally downplayed the benefits. It would have been better for them to downplay the benefits on most of the women, but hype the discovery that there is a subgroup of women who might get a substantial benefit from this procedure. If you read the study, or find better summaries of it, you may find that this study can help patients and doctors make wise treatment choices (contralateral mastectomy sometimes among them). With luck and more studies like this, prophylactic mastectomies might in the future go only to those women whom they might help. With even more luck, we’ll improve our diagnosis and prevention of breast cancer and the number of mastectomies will go down.

Today, researchers and others are expressing surprise that just-in real crash data doesn’t support what they don’t realize the earlier research didn’t show in the first place. For example:

• Results of Study on Cellphone Use Surprise Researchers
• Cell phone bans do little to reduce crashes, study finds

If researchers (or journalists) are surprised by today’s news, they probably didn’t examine the research very closely. They may have believed the misleading headlines instead.

Disclaimers: I haven’t read all the research, and some studies might have in fact shown an increased crash risk, unlike the one I mentioned. That might be reason for real surprise. In addition, today’s data doesn’t specifically show that less phone use means no fewer accidents, because laws don’t always change behavior. But some of the reports I read did suggest that there was less phone use, yet no lower crash rate, in places that instituted bans.

Ironically, the crash data out today could make things worse. If drivers think phone use while driving is not as unsafe as previously thought, they might be less careful when using a phone while driving, and phone-related crashes might increase. Common sense suggests that multitasking requires greater concentration. If you do use a phone while driving, drive with even more care than usual. In other words, this might be one situation where being wary might have benefits, even when its not warranted by the facts – especially because being somewhat over-cautious while driving has no serious down side, it seems to me. (It’s not like it infringes upon hundreds of millions of people’s civil rights, like acting on other unwarranted fears can and does…)