Statistics

# Homework #1: Answer part I

A couple of days ago I gave out homework. I asked my loyal readers to count how many people walked by them and to keep track of how many of those people wore a thinking-suppression device like an I-pod etc. Like every teacher, my heart soared like a hawk when some of the students actually completed the task. Visit the original thread’s comments to see the “raw” data.

The project was obviously to recreate a survey of the kind which we see daily: e.g. What percent of Americans favor a carbon tax? What fraction of the voters want “change”? How many prefer Brand A? And so on.

Here is how a newspaper might present the results from our survey:

More consumers are endangering their hearing than ever before, according to new research by WMBriggs.com. Over 20% of consumers now never leave the house without an I-pod or I-pod-like device.

“Music is very popular” said Dr Briggs, “And now it’s easier than ever before to listen to it.” This might help explain the rise in tinnitus reports, according to some sources. Dr So Undzo of the Send Us Money to Battle Tinnitus Foundation was quoted as saying, “Blah blah blah.” He also said, “Blah blah blah blah blah.” &tc. &tc.

Despite its farcical nature, this “news” report is no different than the dozens that show up on TV, the radio, and everywhere else. In order to tell a newsworthy story, it extrapolates wildly from the data at hand, it gives you no idea who collected the original data or why (for money? for notoriety?) or how (by observation? by interview?), or of any of the statistical methods used to manipulate the data. In short: it is very nearly worthless. The only advantage a story like this has is that it can be written before any data is actually taken, saving time and money to the news organization issuing it.

But you already knew all that. So let’s talk about the real problem with statistics. Beware, however, that some of this is dull labor, requiring attention to detail, and probably too much work for too little content. However, that’s how the get you, by hoping you pass by quickly and say “close enough.”

We had five to six responses to the homework so far, but we’ll start with the first one from Steve Hempell. He saw `n=41` people and counted `m=1` wearing a thinking-suppression device (TSD). He sat on a bench in a small town during spring break to watch citizens pass by.

The first thing we need to have securely in our minds is what question we want to answer with this data. The obvious one is “How many people regularly wear a TSD?” This innocent query begins our troubles.

What do we mean by “people”? All people? There are a little over 6 billion humans now. Do we want an estimate from that group? What about historical, i.e. dead, people, or those yet to be born? How far back into the future or past do we want to go? Are we talking of people “now”? Maybe, but we still have to define “now”: does it mean in a year or two, or just the day the survey was taken or a few days into the future? Trivial details? Well, we’ll see. Let’s settle on the week after the survey was taken so that our question becomes “How many people in the week after our survey was taken regularly wear a TSD?”

We’re still not done with “people” and haven’t decided whether it was all humans or some subset. The most common subset is “U.S. Americans” (as Miss Teen South Carolina would have phrased it). But all U.S. citizens? Presumably, infants do not wear TSDs, nor do many in nursing homes or in other incarcerations. Were infants even counted in the survey? Older people in general, experience tells us, do not often wear TSDs. As I think about this question, I find myself unable to rigorously quantify the subset of interest. If I say “All U.S. citizens” then my eventual estimate would probably be too high, given this small sample. If I say, “U.S. citizens between the ages of 15 and 55” then I might do better, but the survey is of less interest.

To pick something concrete, we’ll go with “All U.S. citizens” which modifies our question to “How many U.S. citizens in the week after our survey was taken regularly wear a TSD?”

Sigh. Not done yet. We still have to tackle “regularly” and the bigger question of whether or not our sample represents fairly the population we have in mind, and would still leave the largest, most error-prone area: what exactly is an TSD? I-pods were identified, but how about cell phones or Blackberries and on and on? Frankly, however, I am bored.

Like I said, though, boredom is the point. No one wants to invest as much time as we have for this simple survey to each survey they meet. No matter how concrete the appropriate population in a survey seems to you, it can mean something entirely different to somebody else; each person can take away their own definition. This ambiguity, while frustrating to me, is gold to marketers, pollsters, and “researchers.” So vaguely worded are surveys that the reader can supply any meaning they want to its results. Although they usually consciously aware of it, people read surveys like they read horoscopes or psychic readings: they always seem accurate or to confirm people’s worst fears or hopes.

An objection might have occurred to you. “Sure, these complex surveys are ambiguous. But there are simple polls that are easy to understand. The best example is ‘Who will you vote for, Candidate A or B?’ Not much to confuse there.”

You mean, since a poll is a prediction of ballot results, besides trusting that the pollster found a population representative of people who will actually vote on election day? That no event between the time the poll was taken and the election occurs that will cause people to change their minds? And—pay attention here—nobody lied to the pollster?

“Oh, too few people lie to make a difference.” Yeah? Well, I live in New York City and I like to tell the story of the exit polls taken for the presidential race between Kerry and Bush. Those polls had Kerry ahead by about 10 to 1, a non-surprising result, and one which confirmed people’s prior beliefs. The pollsters asked tons of voters and were spread throughout the city in an attempt to obtain the most representative sample they could. Not everybody would answer them, of course, and that is still another problem which is impossible to tackle.

But when the actual results were tallied, Kerry won by only a margin about a little under 5 to 1. Sure, he still won, but the real shocker is that so many people lied to the pollster. And why? Well, this is New York City, and in Manhattan particularly, you just cannot easily admit to being a Bush supporter (then or now). At the least, doing so invites ridicule, and who needs that? Simpler just to lie and say, “I voted for Kerry.”

We have done a lot and we still haven’t answered the question of how to handle the actual data!

Here are the answers to part I of the homework.

1. The applicability of all surveys is conditional on a population which must be, though rarely is, rigorously defined.
2. All surveys have significant measurement error that has nothing to do with the actual numerical data.
3. Because of this, people are too certain when reading or interpreting the results of surveys

In part II, if we are not already worn down, we will learn how to—finally!—handle the data.

Categories: Statistics

### 5 replies »

1. GeorgeM says:

Well, we’re already in trouble with the population criteria. Here in S. Texas this week in any shopping venue, the person passing by is about as likely to be a Mexican shopper as a US citizen, it being Holy Week and all. So what does that do to the statistics?

2. Richard Sharpe says:

I sometimes use a TSD (especially at the Gym) but it has Chinese lessons on it.

3. TCO says:

You do a nice job of showing how brands can misuse surveys for advertising, to an extent, I wasn’t even tuned to. However, I think the more interesting, yet tricky thing is when you really DO WANT the correct answer (say for a business decision) but need to struggle with these methodology issues.

4. Ed Asner says:

My thinking suppression device is actually a thinking amplification device, since I mostly listen to podcasts which address similar concerns to those addressed by this blog. I don’t think I am the only person on earth who does this. . . . . .