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Politics : PRESIDENT GEORGE W. BUSH -- Ignore unavailable to you. Want to Upgrade?

To: nihil who wrote (37012)	9/15/2000 7:30:56 AM
From: Neocon	Read Replies (1) \| Respond to of 769667

Margin of Error deserves better than the throw-away line it gets in the bottom of stories about polling data. Writers who don't understand margin of error, and its importance in interpreting scientific research, can easily embarrass themselves and their news organizations. Check out the following story that moved in the summer of 1996 on a major news wire: WASHINGTON (Reuter) - President Clinton, hit by bad publicity recently over FBI files and a derogatory book, has slipped against Bob Dole in a new poll released Monday but still maintains a 15 percentage point lead. The CNN/USA Today/Gallup poll taken June 27-30 of 818 registered voters showed Clinton would beat his Republican challenger if the election were held now, 54 to 39 percent, with seven percent undecided. The poll had a margin of error of plus or minus four percentage points. A similar poll June 18-19 had Clinton 57 to 38 percent over Dole. Unfortunately for the readers of this story, it is wrong. There is no statistical basis for claiming that Clinton's lead over Dole has slipped. Why? The margin of error. In this case, the CNN et al. poll had a four percent margin of error. That means that if you asked a question from this poll 100 times, 95 of those times the percentage of people giving a particular answer would be within 4 points of the percentage who gave that same answer in this poll. (WARNING: Math Geek Stuff!) Why 95 times out of 100? In reality, the margin of error is what statisticians call a confidence interval. The math behind it is much like the math behind the standard deviation. So you can think of the margin of error at the 95 percent confidence interval as being equal to two standard deviations in your polling sample. Occasionally you will see surveys with a 99 percent confidence interval, which would correspond to 3 standard deviations and a much larger margin of error. (End of Math Geek Stuff!) So let's look at this particular week's poll as a repeat of the previous week's (which it was). The percentage of people who say they support Clinton is within 4 points of the percentage who said they supported Clinton the previous week (54 percent this week to 57 last week). Same goes for Dole. So statistically, there is no change from the previous week's poll. Dole has made up no measurable ground on Clinton. And reporting anything different is just plain wrong. Don't overlook that fact that the margin of error is a 95 percent confidence interval, either. That means that for every 20 times you repeat this poll, statistics say that one time you'll get an answer that is completely off the wall. You might remember that just after Dole resigned from the U.S. Senate, the CNN et al. poll had Clinton's lead down to six points. Reports attributed this surge by Dole to positive public reaction to his resignation. But the next week, Dole's surge was gone. Perhaps there never was a surge. It very well could be that that week's poll was the one in 20 where the results lie outside the margin of error. Who knows? Just remember to never place to much faith in one week's poll or survey. No matter what you are writing about, only by looking at many surveys can you get an accurate look at what is going on. robertniles.com

To: nihil who wrote (37012)	9/15/2000 7:32:49 AM
From: Neocon	Respond to of 769667

So How Come a Survey of 1,600 People Can Tell Me What 250 Million Are Thinking? The best way to figure this one out is to think about it backwards. Let's say you picked a specific number of people in the United States at random. What then is the chance that the people you picked do not accurately represent the U.S. population as a whole? For example, what is the chance that the percentage of those people you picked who said their favorite color was blue does not match the percentage of people in the entire U.S. who like blue best? (Of course, our little mental exercise here assumes you didn't do anything sneaky like phrase your question in a way to make people more or less likely to pick blue as their favorite color. Like, say, telling people "You know, the color blue has been linked to cancer. Now that I've told you that, what is your favorite color?" That's called a leading question, and it's a big no-no in surveying.) Common sense will tell you (if you listen...) that the chance that your sample is off the mark will decrease as you add more people to your sample. In other words, the more people you ask, the more likely you are to get a representative sample. This is easy so far, right? Okay, enough with the common sense. It's time for some math. (insert smirk here) The formula that describes the relationship I just mentioned is basically this: The margin of error in a sample = 1 divided by the square root of the number of people in the sample How did someone come up with that formula, you ask? Like most formulas in statistics, this one can trace it roots back to pathetic gamblers who were so desperate to hit the jackpot that they'd even stoop to mathematics for an "edge." If you really want to know the gory details, the formula is derived from the standard deviation of the proportion of times that a researcher gets a sample "right," given a whole bunch of samples. Which is mathematical jargon for..."Trust me. It works, okay?" So a sample of 1,600 people gives you a margin of error of 2.5 percent, which is pretty darn good for a poll. (See Margin of Error for more details on that term, and on polls in general.) Now, remember that the size of the entire population doesn't matter here. You could have a nation of 250,000 people or 250 million and that won't affect how big your sample needs to be to come within your desired margin of error. The Math Gods just don't care. Of course, sometimes you'll see polls with anywhere from 600 to 1,800 people, all promising the same margin of error. That's because often pollsters want to break down their poll results by the gender, age, race or income of the people in the sample. To do that, the pollster needs to have enough women, for example, in the overall sample to ensure a reasonable margin or error among just the women. And the same goes for young adults, retirees, rich people, poor people, etc. That means that in order to have a poll with a margin of error of five percent among many different subgroups, a survey will need to include many more than the minimum 400 people in the overall sample. robertniles.com

To: nihil who wrote (37012)	9/15/2000 7:52:12 AM
From: Neocon	Read Replies (1) \| Respond to of 769667

statistics Estimation of a population mean When the sample mean is used as a point estimate of the population mean, some error can be expected owing to the fact that a sample, or subset of the population, is used to compute the point estimate....The standard deviation of a sampling distribution is called the standard error.... In the large-sample case, a 95% confidence interval estimate for the population mean is given by +/- 1.96/n, (where n equals the sample size).....The quantity 1.96/n is often called the margin of error for the estimate. ....The interpretation of a 95% confidence interval is that 95% of the intervals constructed in this manner will contain the population mean. Thus, any interval computed in this manner has a 95% confidence of containing the population mean. By changing the constant from 1.96 to 1.645, a 90% confidence interval can be obtained. It should be noted from the formula for an interval estimate that a 90% confidence interval is narrower than a 95% confidence interval and as such has a slightly smaller confidence of including the population mean. Lower levels of confidence lead to even more narrow intervals. In practice, a 95% confidence interval is the most widely used. ....the sample size affects the margin of error. Larger sample sizes lead to smaller margins of error. This observation forms the basis for procedures used to select the sample size. Sample sizes can be chosen such that the confidence interval satisfies any desired requirements about the size of the margin of error. britannica.com