WSJ Statistical Bait and Switch

The Wall Street Journal ran a piece today about how the young folks are excited about Obama, but might not actually vote for him. The piece is based on a poll by conducted by the Wall Street Journal, NBC News and MySpace. Two interesting things about how the poll results are spun. First the lede:

This year's flood of newly registered voters heavily favor Sen. Barack Obama in the presidential contest, but they won't necessarily show up to support him on Election Day, a new survey indicates.

OK, so what's the evidence that new voters won't support Obama on election day?

The first bit of evidence comes from , a completely different poll asking a completely different question:

When asked to rank their interest in the Nov. 4 election, just 49% said they were "very interested." By comparison, 70% of voters of all age groups said they were "very interested," according to a separate Journal/NBC News national poll taken a week ago.

It's not obvious that disinterest in the election translates to not voting.

Second, the actual poll that they are talking aboutreports that

54% of the new voters said they would definitely vote Nov. 4.

That does seem low. And would be cause for alarm, if it were close to true.

But, WSJ does something stoopid--they link to the actual poll results! Here we find, that it's really 84% of responders that are likely to vote on November 4th.

Using a ten-point scale, please tell me how likely you are to vote in the November fourth elections for president and Congress. If you are certain that you will vote, pick a number closer to "eight," "nine," or "ten." If it is less likely that you will vote, use a number closer to "one," "two," or "three." You may choose any number from one to ten.

10, definitely vote 54 [142-143]
9 17
8 13
7 4
6 2
5 4
4 -
3 1
2 2
1, definitely NOT vote 3
Not sure -

Sure, if you only look at the people who responded with a 10, then it's 54%. But the instructions put the cutoff at 8. If you count 8 through 10, it's 84%!

When the poll results weren't interesting enough, the WSJ simply distracted us with the answer to a different question and then cherry-picked the data they were going to show us. Don't be too worried about first time voters showing up on the 4th.

Mathematics Awareness Month

April is Mathematics Awareness Month.

The American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics announce that the theme for Mathematics Awareness Month 2008 is Math and Voting.

You can try out different voting methods on the site.

How to lie--with statistics!

What I'm reading

A couple of posts from Med Journal Watch on science reporting and statistical obfuscation:

Medical Study Concluding for Dummies

The Art of Lying With Statistics

A discussion of Brian May's Dissertation at Bad Astronomy.

A post on reactionary rhetoric at Ecological Economics.

Is there a common thread?

It's like a disease

This is the chart I thought I was looking at in the first place. It plots the total amount of energy used as the number of uses increases. The number of uses along the bottom are in factors of 10. So it goes out to 1500 uses.



Somewhere around 700 uses, the foam cup starts to be more expensive than the ceramic.

I swear, I'm done with this.

I can't leave this alone

Ok, just two points.

1) Of course using foam cups incurs variable energy costs. Every time you throw one away, it has to be carried to the dump. I don't know anything about MJs. And maybe the energy cost of taking one foam cup on a garbage truck is so tiny that it doesn't matter. But look what happens when you assume that the energy cost is 1/10,000th of an MJ.



See the way that line starts to grow? At 1,500 uses, you're almost at twice the Average Total Cost than one use. That's the power of big numbers.

2) You could cut the energy use in the foam option significantly by simply reusing foam cups. If you use the same cup twice before throwing it out, you cut the already low energy use in half, making it a much more attractive option.

Eco-update

Here's an update to my previous post, explaining some of the things I left out.
I assume that Hockett used the formula for the Average Total Cost to create the graphs in the original graph. I used the formula found at about.com:

Average Total Cost = Fixed Costs/Quantity + Variable Costs

In the case of the ceramic mug, that would be AC = 14/Quantity + 0.18 since each mug costs 14 mj to make and 0.18 mj to clean after each use. Here are the other formulas I used to recreate the graph:

Foam: AC = .2 (There are no variable costs, and a new foam cup is used every time)
Paper: AC = .55 (See foam.)
Glass: AC = 5.5/Quantity + 0.18
Plastic: AC = 6.3/Quantity + 0.18

To find the area under the curve for, I used an Excel plug in from Boomer.org--scroll down to "PK Functions for Microsoft Excel".

You can use the area under the curve numbers to calculate just how many mjs you would save by using ceramic, glass, or plastic instead of foam or paper.



Using a ceramic mug twice a day for about 2 years will save 1,639 MJ over using foam cups. That's a savings of 8,195 foam cups (1639/.2)! Still, your better bet is the plastic coffee mug which saves you 13,112 MJ over those 2 years--65,560 foam cups!

See Peter's correction in the comments!

Binary search at home

Saturday I had to figure out which fuse to throw to cut the power to my upstairs bathroom. So I turned to a binary search algorithm.
After doing an exhaustive search of the right side of the panel and coming up with butkiss, I moved to the left panel. To minimize the number of basement to 2nd floor trips (I was alone), I threw the first 6 switches--exactly half of the total 12 switches. I ran up stairs and saw that that had done the trick. So I reset switches 4, 5, and 6. The light was still out in the bathroom. I was down to 3 switches in 2 tries!

Now came the tricky part. Do I reset 1 or 2 switches? Either way I figured I would have to make 2 more choices. So I did one. The light stayed out. On the next try I got lucky and reset the right switch. At worst I would have had one more resetting.

That's a total of 4 tries to find the right switch out of 12 possibilities. I wish I had thought of that when I was doing the right panel.

The scale of the accidental gap issue

To get a number of possible words in English, we'd have to count all the possible combinations of consonants and vowels that could be created from the set of English sounds. This is kinda hard to do, but we can get a pretty good approximation.

The simplest word is made up of one syllable. Fortunately, English, like all languages, has rules about what can and cannot be a syllable. In English, A syllable consists of at least a vowel (V) which is preceded or followed by one or more consonants. Consonants at the start of the syllable are called onsets (O) and the ones at the end are called codas (C).

If we ignore all the onsets and codas with more than one consonant for simplicity, one syllable template for English looks like (O)V(C). The parentheses around the O and C indicate that the consonants are optional. This template gives us words like

eye (V)

me (CV)

on (VC)

cat (CVC)


There are about 23 different consonants that can be an onset to a syllable. And about 21 consonants that can be a coda to a syllable. There is also the possibility that the syllable has no onset or coda. That gives at total of 24 possible Onsets and 22 possible Codas (assuming 0 is an option).

Vowels are a little simpler. There are about 7 so-called long vowels that can be in a syllable with or without a coda. English has another 7 or so so-called short-vowels that have to be in a syllable with a coda. For simplicity I'm going to ignore the short vowels.

So the number of possible single syllable words is more than 3,381.

(O) V (C)
23 x 7 x 21 = 3,381

I say more because, we're ignoring the words that you can make with a short vowel in a closed syllable and any word with more than one cononant in the onset or coda.

If we further assume that two syllable words can be formed by putting any two single syllables together, the number of those would be 3,381 x 3,381. That's over 11 million! Can that be right?

One estimate I found for the number of words in English is roughly 1 million. And that's including multi-syllabic scientific words. Oxford Dictionaries estimates the number to be only around 1/4 of a million.

Could we really be using around 1/10th of the possible words? If so, there is an incredible amount of word space we can use and there should be no need for homonymy.

There and back again

Anyone who is serious about walking in Manhattan knows that if you're going diagonally across and either up or down, there's one rule you must obey: always go with the light.

If you don't know, the streets of Manhattan are laid out in a grid. So getting going up or down town is easy--a straight line. Same with going cross town. But if you need to get across and either up or down, you've got to zig-zag. And this zig-zagging gives you a whole bunch of route choices. Do I head east first? Do I go down a block and then over? The rule makes the choices for you. You go where the green lights lead you.

This is the situation I face about twice a day as I make my way from Penn Station at 33rd and 7th to my office at 42nd and 2nd and then back again. So everyday I put the rule to the test. And everyday, I get a sneaking feeling that the rule is wrong. Sometimes the rule forces me into one side of the box that circumscribes my diagonal. I may end up on 42nd and Park with no choice but to continue straight down 42nd. More often I get to 2nd ave. at around 38th, so it's up 2nd to 42nd.

When I get into these forced choices and then get stuck at a long light, the question starts to nag. If I had just waited at that light back there could I be still making progress here? The rule works on maximizing the local choices. But it can't look ahead at the whole range of choices. And therein lies the rub.

There must be a mathematical proof whether the rule actually is the best way to get around Manhattan or not. During my walk I sometimes imagine creating a computer simulation of my walk and running different versions of the rule a bunch of times to compare their outcomes. Then I remember I'm not a computer scientist and I've got too much to do anyway.

Maybe someone has already done this. Any mathematicians out there want to comment?

Accidental what now?

A little while ago, my friend Frank asked me what I thought the coolest thing in linguistics was. Another friend, Pedro, suggested accidental gaps. At the time I dismissed them as pedestrian. I mean really, so languages have extra words lying around. Big deal. But accidental gaps have gotten under my skin. Now I'm starting to think they are a big deal.

Here's why.

It's pretty clear that synonymy is rare in human language. That means people don't like to have two words that mean the same thing. Obviously, synonymy avoidance puts pressure on the speaker to have a lot of different, distinct words. Especially if you have to develop a specialized vocabulary and make fine-grained distinctions, like artists do with colors.

Given this pressure, accidental gaps seem like an anomaly. We have a desperate need for words to distinguish actions, events, things, etc. And yet here are perfectly good words like wurp and troot going unused.

Oddly enough, we think nothing of having two words that are pronounced exactly the same. In fact, homonymy seems pretty rampant. So we have words like read and reed or the two meanings of mouse, etc. We're doubling up on many words and letting others go unused.

So now I'm thinking, "Yeah accidental gaps are weird!"

There are probably a number of reasons why language is this way. It may be simply a result of evolution. It's pretty common for evolved systems to be poorly designed since natural selection is restricted to the history of the organism. It can only produce variation of what has come before; it can't redesign from scratch. Another possibility is that the two tendencies, synonymy avoidance and homonymy are design features that address two different usage pressures: production and perception.

Whatever the reason, I'm glad I rethought accidental gaps