a closer look at the LD time skew

What follows is an analysis of particular empirical evidence for the fabled "time skew" in Lincoln-Douglas debate.



The Context
I've heard several theory shells that rely heavily on time skew arguments, all sharing the same warrants. For the uninitiated, "time skew" is the idea that in LD, the Negative has an unfair time advantage in the 1NR--7 minutes to run all sorts of attacks, disads, theory shells, meta-ethics, a prioris, interpretive dances, killer bee swarms, whatever--that the Aff simply can't respond to in the 4 minute spittlefest known as the 1AR. Compound this with the 6 minute 2NR, and the measly 3-minute 2AR in response, and the modern LDer feels significantly cramped while affirming.

Often, the "fairness" portion of the shell's standard appeals to an empirical fact: at the Tournament of Champions in LD, the Negative has won over 50% of the ballots.

This, of course, raises all sorts of questions.

* Is this a historical trend, or the result from one tournament?
* If one, what was the resolution? Would its own presumptions and associated judge biases cause the skewed results?
* If it's an identifiable trend at the TOC, what is the root cause?
* Do judges have a contrarian bias that favors the Neg? (Good luck answering this one in a mere blog post.)
* What if it's abusive tactics that actually create the problem?

These questions, of course, presume that the statistic is true. Is it?

To find out, I crunched the numbers myself, because I'm the fact-checking sort.


Methodology
I used the 2011-2013 LD results, based on the first six rounds, presuming that this would provide an even number of Aff-Neg opportunities for each individual debater, with the exception of 2011, which had 8 rounds for each. I counted each by hand, double-checked, and then ran the results through a spreadsheet. I eliminated two 2013 ballots, as they were both forfeits, one on each side, which doesn't significantly alter the results or the conclusions. Of course, I didn't count byes.


Results
Out of 772 preliminary round ballots in the past 3 years of competition, 345 went for the Aff, or 44.7%. Negs took 427 ballots, or 55.4%.

Before we declare the skew to be real, we have to account for the margin of error. For a sample of this size, at a 99% confidence interval (i.e., only 1 in 100 results could be explained by pure chance), we would expect an error margin of +/- 4.57%.

Thus, the lowest "expected value" for the Aff is 368 ballots, or 47.7% of the total, while the highest is 404, or 52.3%. Any result within this range isn't far enough away to be anything but intriguing.

But the actual total, 345, is well below the range. Even being optimistic, the Aff has won only 94% of the times they "should have" won, while, at worst, they've won only 85% of the times they "should have" won at the TOC. (Consider also that the skew would be stronger in the 2012-13 tournaments, which went 7 rounds in prelims, as roughly half of the debaters had one extra round on the Neg.)


Interpretation
The time skew is statistically significant. The numbers indicate that at the TOC, the Neg picks up at anywhere from 1 to 3 extra ballots per round.

What causes the skew, though? The simplistic answer is the seeming structural disadvantage of the 1AR, described above. But this is a bit like saying, "Honda Civics built in the mid-1990s spend more time in the shop than other similar makes from that era, and are thus defective," when an equally plausible explanation is that that Honda Civics are preferred wheels for crazy drivers who YOLO their way through life / the Interstate Highway System.

In other words, the TOC's emphasis on progressive, spread-based tactics has potentially created the skew, whereas it may not be a problem in a more traditional form of LD.

We might be on firmer ground if we compared results to NFL tournament preliminary rounds to draw firmer conclusions. (Maybe that'll be the subject of a future post.)


Takeaways
First, never uncritically accept a statistic, even one as potentially intuitive as this one.

Second, if the timeskew is inherent--or, as TOC tactics are now mainstream in many regions, will eventually become ubiquitous, which at that point may as well mean it's inherent--then I propose a solution: 6 3 7 3 5 6 2. Give the Aff an extra minute to work with in the 1AR, and turn the 2AR into a voters-only speech. I think it's elegant, workable, and fair. (I typically have a high opinion of my own ideas.) I'd love to hear of a tournament trying it, and getting enough data to draw meaningful conclusions.

Third, if you're running a theory shell using the TOC data, here's an easy citation.

ANDERSON: "In the past three years, over 55% of TOC elimination-round LD ballots went to the Neg, a statistically significant advantage."

Fourth, if you're running against a similar theory shell, and wish to debate the point, here's another easy citation.

ANDERSON: "It is possible, and even likely, that spread tactics themselves are the root cause of the skew, which may not exist in more traditional LD clashes."

Hint: don't run this if you're the one who started the ruckus by spreading.

Meanwhile, I'll be speeding down the freeway in my tricked-out Civic. Or in the shop getting it fixed.

#YOLO?

the greatest television audience that wasn't

Was Super Bowl XLV the most-watched television event in U.S. history?

Sure.

The Nielsen Co. said Monday that an estimated 111 million people watched the Green Bay Packers outlast the Pittsburgh Steelers in professional football's ultimate game. That tops the 106.5 million who watched the 2010 game between New Orleans and Indianapolis.

The series finale of "M*A*S*H" had held the title of the most-watched TV show in the United States for 27 years. It is now No. 3.

On the other hand, not really.

You see, there's this little thing called "population growth." M*A*S*H's finale had a remarkable 105.9 million viewers in 1983--back when the U.S. held about 233 million residents--meaning that over 45% of the U.S. watched that episode. In contrast, only 36% saw yesterday's surrealist hootenanny.

Now, to be fair, it's possible that the Nielsen ratings system in 1983 lacked today's sophistication and nuance, so the estimate is overgenerous. Furthermore, in today's fragmented media landscape--where we have 500 channels instead of 5, plus an Internet that didn't even exist in 1983--simultaneously capturing a hundred million Americans' attention for longer than 15 seconds is an achievement worth celebrating.

Just not with a Fergie / Slash duet.

Vlatko Vedral decodes reality

According to Vlatko Vedral (who's been mentioned here before), the universe is a quantum computer.

Over the last two decades, a flourishing field of quantum information and computation has generated a wealth of experimental and theoretical tests of information processing at the quantum scale. Vedral is one of the luminaries in this field.

In Decoding Reality, Vedral argues that we should regard the entire universe as a gigantic quantum computer. Wacky as that may sound, it is backed up by hard science. The laws of physics show that it is not only possible for electrons to store and flip bits: it is mandatory. For more than a decade, quantum-information scientists have been working to determine just how the universe processes information at the most microscopic scale.

Combine this with Nick Bostrom's "simulation argument," and, like Hamlet, you start wondering which level you're on, and if there will be any continues when the game ends. (At least I think that's what Hamlet was on about.)

never bet against a pigeon

Add this to the list of things that make humans exceptional: we are exceptionally bad at probability. Worse than pigeons, in fact.

your homework, due April 4th

Baseball websites are bursting at the seams with statistics of every stripe. (Yes, I went there--twice.) And now, remarkably, you can find a series of the web's best intros to the various methods of sabermetrics all in one place.

Now you have no excuse.



[via Dave Cameron]

math requirements changed again, again

From time to time, this blog deals with the education standards set by the state, particularly those dealing with graduation requirements. After all, they're important.

They're also as confusing as hell.

Actually, more confusing, because in hell, as Gary Larson, cartoonist and theologian, noted, you get your accordion and off you go. As for passing high school in Washington state, should you fail the math WASL*: welcome to hell. Here's your flow chart.

Which is now obsolete, with yet another in a long line of changes to the math requirements. The Seattle Times explains:

The board decided earlier that beginning with the class of 2013, high-school students will be required to earn three credits of math to earn a diploma.

When the requirement was changed, the state rule said students who took a high-school-level math class without credit as an eighth-grader were required to repeat that same course for credit in high school.

The state board decided Friday that students can choose to start with a different math class in high school and don't have to repeat the eighth-grade class if they don't want to.

Hurrah for flexibility, I suppose. And, hopefully, someday, hurrah for clarity.

Someday.

Until then, here's your accordion.



*Which won't be the WASL for long. Progress!

I read it, but I don't get it

The title of this post is stolen from one of the best books any English teacher (or any secondary teacher, for that matter) can buy. I thought of Tovani's classic while attempting to read this paper [pdf], offered as "homework" by blog-neighbor Mark Olson. Here's a sample:

If either one of these functions, say θF/a , is influenced by some information that is free in the above sense (i.e., not a function of A’s choice of directions and events F-earlier than that choice),then there must be an an earliest (“infimum”) F-time t0 after which all such information is available to a. Since the non-free information is also available at t0, all these information bits, free and non-free, must have a value 0 or 1 to enter as arguments in the function θF/a . So we regard a’s response as having started at t0.

You can be the world's most competent reader--me--and still have no idea what you're reading, if you lack the requisite background knowledge.

symplectic camels and quantum uncertainty

I'll let the science writer explain a potential challenge to the Heisenberg Uncertainty Principle:

Maurice de Gosson at the University of Vienna in Austria thinks that the inability to pin a particle down is due to something called symplectic geometry, not quantum weirdness.

De Gosson realised that a theorem in symplectic geometry had parallels with the uncertainty principle. The concept is known as the symplectic camel after the biblical suggestion that it is easier for a camel to pass through the eye of a needle than for a rich man to get into heaven.

De Gosson imagined that a ball represents a cloud of possible positions for a quantum particle. He found that such a ball cannot be squeezed down to the size of one particle to fit through a hole in a plane, because its geometry resists this in some way. The inability to squeeze the ball is analogous to singling out one particle and measuring its position and momentum exactly. De Gosson reckons this geometrical resistance creates the uncertainty in measurement, not quantum fuzziness (Foundations of Physics, vol 39 p 194).

I just wanted to point out the word: symplectic. In my imagination, it is a super-adjective combining the meanings of sympathy and apoplexy.

fighting crime with math

Could we cut crime without resort to drama, political posturing, or needless injury and death? Cue mathematics [sub. req.]:

One of the earliest studies using this approach was led by Michael Batty of University College London. Since its inception in 1964, the Notting Hill carnival in London has grown to attract more than a million visitors each year. With vast crowds jammed into narrow streets, crime is inevitable - anything from pickpocketing and shoplifting to violent assault and worse. After three people were murdered at the event in 2000, the Greater London Authority commissioned a review of public safety and asked Batty to create a computer model of people's movements in an attempt to identify better crowd-management strategies. "We simulated the crowd movement around the parade and the exhibits," says Batty, "and used the model to test 'what if' scenarios for changing the parade route, or closing particular streets."

This led to the discovery that altering the parade route could significantly reduce the density of the crowds. "The circular parade route didn't let people easily cross it," says Batty. "This was the problem, as all the events were inside the route." Enlightened carnival organisers adopted the straighter route suggested by the computer analysis, and subsequent carnivals registered a big drop in both maximum crowd densities and the number of crimes committed.

Bowers's finding that burglaries spread like communicable diseases is another example of the power of computer modelling. It first emerged from work with her colleague Shane Johnson, completed four years ago. They studied data from the Merseyside region of the UK, containing information on locations and times of residential burglaries committed over 14 months within an area of about 26 square kilometres. This revealed that, following a given burglary, the likelihood of another was increased for the next two weeks for any house within about 200 metres, though the probability tailed off at greater distances and after that time had elapsed. This pattern of communicability of crime strongly mirrors the patterns that epidemiologists find with diseases that spread from one person to another. In the case of crime, Bowers and Johnson suspect, communicability arises simply because burglars have routines, and after one success they often continue in familiar territory nearby.

Seems a lot smarter than this approach.

time to throw concrete math instruction out the window?

This... could hurt.

In the first experiment, involving 80 students, some participants were given one concrete example before testing on the children’s game, while some were given two or three examples. One group only learned the generic symbols.

When tested on the children’s game, the group that learned the generic symbols got nearly 80 percent of the questions right. Those who learned one, two or even three concrete examples did no better than chance in selecting the right answers.

“They were just guessing,” Kaminski said.

In a second experiment, the researchers gave 20 participants two concrete examples and explained how they were alike. Surprisingly, this still did not help students apply the concept any better and they still did no better than chance when tested later about the game.

In a third experiment, the researchers presented 20 students with two concrete examples and then asked them to compare the two examples and write down any similarities they saw. After this experiment, about 44 percent of the students performed well on the test concerning the children’s game, while the remainder still did not perform better than chance.

This suggests that only some students, not all, benefit from direct comparison of learned concrete examples.

Finally, in a fourth experiment involving 40 students, some learned the concrete example first followed by the generic symbols, while others learned only the generic symbols. The thought here was that the concrete example would engage the students in the learning process while the generic symbols would promote transfer of that knowledge.

But even in this experiment, students who learned only the generic symbols performed better on subsequent testing than those who learned the concept using the concrete example and then the generic symbols.

The authors said that students seem to learn concepts quickly when they are presented with familiar real objects such as marbles or containers of liquid, and so it is easy to see why many advocate this approach. “But it turns out there is no true insight there. They can’t move beyond these real objects to apply that knowledge,” said Sloutsky.

Compare that with, say, the recent math-athon in the North Thurston district.

Pre-calculus students at North Thurston High School will show display boards of photographs of everyday objects that are examples of conics — circles, parabolas, ellipses and hyperboles.

“I just wanted them to see real math in the real world,” said their teacher, Julie Cassidy.

Boards showed photographs of nail polish bottles, mustard containers, bicycle racks, basketballs, garden hoses, shoe soles and more.

“I really liked it because it kind of gives you a more hands-on idea of math. I’m the type of person who likes to get out and experience in the world. I can’t sit at a desk and remember it,” said junior Raewyn Heim, 17.

Obviously, further studies are needed to see if Heim has it right. It could be that the hands-on aspect provides greater motivation for learners who aren't already college undergrads, the subjects of the OSU experiment. Also, if Piagetian principles are at play, the older students might just be more facile in the realm of abstraction. Still, as an English teacher, I have to go with this quote by one of the experimenters: "Story problems could be an incredible instrument for testing what was learned. But they are bad instruments for teaching."

Now you have a scientific reason to hate story problems.

I'm not skipping the math WASL

Because I'm proctoring it, I don't have to pass it. Technically, neither do the seniors who'll be retaking it under my watch--but that's only if they're passing their third year of math.

Confused?

You're not alone.

Although there are alternative means for students to achieve the state’s current math standard, such as a “Collection of Evidence” that gathers tests and papers from a student’s high school career to prove mastery of WASL skills, or substituting a college entrance exam score, students still must attempt to pass the math WASL each year.

Two years of high school math are required for graduation. But the state mandates members of the Class of 2008 who did not pass the math WASL to pass a third year of math; members of the Class of 2009 who didn’t meet the math standard must pass two additional years.

Not everyone who is taking those mandatory credits is passing, Caba said, which could affect their graduation. And while some students have submitted a “Collection of Evidence” and others may use college entrance exams, not all of those scores are in.

But even if they are pursuing these options, re-taking the math WASL is mandatory.

Tomorrow's going to be fun.

Monty Hall confounds psychologists

Many experiments testing rational preferences suffer from a flawed perspective of the Monty Hall problem, writes John Tierney of the New York Times.

The Yale psychologists first measured monkeys’ preferences by observing how quickly each monkey sought out different colors of M&Ms. After identifying three colors preferred about equally by a monkey — say, red, blue and green — the researchers gave the monkey a choice between two of them.

If the monkey chose, say, red over blue, it was next given a choice between blue and green. Nearly two-thirds of the time it rejected blue in favor of green, which seemed to jibe with the theory of choice rationalization: Once we reject something, we tell ourselves we never liked it anyway (and thereby spare ourselves the painfully dissonant thought that we made the wrong choice).

But Dr. Chen says that the monkey’s distaste for blue can be completely explained with statistics alone. He says the psychologists wrongly assumed that the monkey began by valuing all three colors equally.

Its relative preferences might have been so slight that they were indiscernible during the preliminary phase of the experiment, Dr. Chen says, but there must have been some tiny differences among its tastes for red, blue and green — some hierarchy of preferences.

If so, then the monkey’s choice of red over blue wasn’t arbitrary. Like Monty Hall’s choice of which door to open to reveal a goat, the monkey’s choice of red over blue discloses information that changes the odds. If you work out the permutations (see illustration), you find that when a monkey favors red over blue, there’s a two-thirds chance that it also started off with a preference for green over blue — which would explain why the monkeys chose green two-thirds of the time in the Yale experiment, Dr. Chen says.

Whether this statistical oddity takes down the entire "free choice paradigm" remains to be seen; not all experiments might have used methodology falling prey to Monty Hall's charms.

(For an explanation of the Monty Hall problem and its counterintuitive solution, see here.)

Gregoire passes end-of-course exams

I'm still a little surprised that she signed a bill to gut the Math WASL, replacing it with end-of-course tests (described earlier). The WASL's been such a fixture on the landscape for so long, and Gregoire had previously been so adamant about preserving high standards.

But no: no more Math WASL.

In 2013, students will have a choice: Pass the math WASL, or two end-of-course exams. In some districts, those exams will be given at the end of Algebra I and Geometry I. In districts that mix those two subjects into "integrated" math classes, there will be end-of-course exams in Integrated Math I and II.

In 2014, the math WASL is scheduled to end all together.

A bill that would have dumped the WASL in favor of end-of-course exams also passed last year, but Gregoire vetoed it, in part because she thought there were too many unanswered questions, said Judy Hartmann, her executive policy adviser for K-12 education.

Since then, however, the state Board of Education commissioned a study that looked at end-of-course exams in other states and concluded that both the math WASL and end-of-course exams can do a good job of assessing students' math skill.

And before you say anything: yes, I realize the title is ambiguous. It's on purpose.

success is arbitrary

A flawed premise, and a little logic, and you can justify giving a student 50% for nothing. Ryan finds it troublesome, and so do I.

However, there's a deeper question: who originally decided that, when it comes to a passing grade, 60% is good enough?

(By the way, success for a National Board candidate is 68.75 percent. I have exactly one week to get the first part of my D+ or better.)

math WASL dumped for end-of-course exams

Hasta la geometría, baby:

Legislators and Gov. Chris Gregoire have decided to phase out the math portion of the Washington Assessment of Student Learning and replace it with end-of-course tests. The final budget announced on Wednesday included $3.2 million toward developing exit tests for each math course. The senior class of 2013 will still be the first group of students who must pass a math test to graduate, but they will be able to pass either the WASL math test or end-of-course exams. And the math WASL likely will be eliminated by 2014....

State Superintendent of Public Instruction Terry Bergeson supports the change, and Steve Mullin, president of the Washington Roundtable business group, said, “We’ve basically received a lot of assurances that while this was a different method, the rigor would be the same or perhaps higher.”

I can see a certain amount of pedagogical sense to the plan, detailed in HB 3166 [pdf]. Not sure it's going to be any less expensive, though.

Over at the Partnership for Learning blog, alisonm goes over the pros and cons. Her final assessment of the assessment:

Offering both tests gives students more options, which can be a good thing. But the reality is, if standards aren't aligned with curriculum taught by high quality teachers to motivated students, the kind of test given to students won't really make much of a difference.

what are the chances?

Chances are, you're bad at probability. Don't fret too much, though--comes with being human. Your emotion overrides your calculation*, and you tend to be very bad at probability quizzes. Try this one:

1. What's more common in the United States, (a) suicide or (b) homicide?
2. What's the more frequent cause of death in the United States, (a) pool drowning or (b) falling out of bed?
3. What are the top five causes of accidental death in America, following motor-vehicle accidents, and which is the biggest one?
4. Of the top two causes of nonaccidental death in America, (a) cancer and (b) heart disease, which kills more women?
5. What are the next three causes of nonaccidental death in the United States?
6. Which has killed more Americans, bird flu or mad cow disease?
7. How many Americans die from AIDS every year, (a) 12,995, (b) 129,950, or (c) 1,299,500?
8. How many Americans die from diabetes every year? (a) 72,820, (b) 728,200, or (c) 7,282,000?
9. Which kills more Americans, (a) appendicitis or (b) salmonella?
10. Which kills more Americans, (a) pregnancy and childbirth or (b) malnutrition?

Answers found at the bottom of the linked page, which goes into great depth explaining just how bad at probability you probably are.

Don't bet on sports.



[via Joe Carter]




*I don't say "reason," because Spock-like, emotionless reason is humanly impossible, as Antonio Damasio's work shows.

the vampire math fallacy in action, again

I don't understand the attraction of "vampire math." It's clearly fallacious, and it leads otherwise reasonable people to make goofy claims. Case in point: Joe Carter.

At first glance this seems so obvious as to be unworthy of notice. Since we humans do, in fact, continue to exist, it shouldn't be surprising that vampires (and other V-class objects) do not exist. But this begs the question of why humans exist and V-class objects do not. Their existence is, after all, as probable (or improbable) as the existence of humans. And the non-existence of any V-class objects is as statistically improbable as the aligning of dozens of independent physical constants that give rise to life.

The anthropic principle could therefore be restated as claiming that the existence of human life requires both (a) the alignment of several cosmological, chemical, and physical constants and (b) the non-existence of all V-class objects. The probability that each of these stochastically independent events could align precisely as they have, without any intervention, is roughly 0 -- in other words, it can't happen. The evidence therefore points to "fine-tuning" of these conditions.

As I point out on Joe's site, the range of conceivable V-class objects is infinite; thus, it's impossible to calculate their probability, or improbability.

Whenever you have the urge to invoke vampire math, resist it. Please.

Monty Hall's evil twin

Fans of the Monty Hall problem who have time to burn should visit Jason Rosenhouse's blog and try their brain at a fresh incarnation.

Moebius transformations visualized in video

I love the Moebius strip. And now I love the Moebius transformations video. [via BoingBoing]

more dubious vampire math

You'd think the editors of Skeptical Inquirer would've seen through this one:

If we factor in the human birthrate into our discussion, we find that, after a few months, the human birthrate is very small compared to the number of deaths due to vampires. This means that ignoring this factor has a negligibly small impact on our conclusion. In our example, the death of humanity would be prolonged by only one month.

Sadly, this argument deserves to be called the Vampire Math Fallacy.

Two words: vampire hunters.