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Rudimentary Statistics (2004)
Jeez. How many times does this have to be explained?
TtoG, quoting the L.A. Times:
"'Fifty-three percent of respondents said the situation in Iraq did not merit war, while 43 percent said war was justified. When the same question was asked for Times polls in March and November, the numbers were precisely reversed. . . The poll, which was conducted from Saturday to Tuesday, surveyed 1,230 registered voters nationwide. It had a margin of error of plus or minus three percentage points.'"
TtoG:
"The U.S. population is estimated at close to 300 million right now, and we're supposed to get worked up over what 1,230 people who are registered voters have to say? Hell, I only just registered yesterday, so I would've been ineligible. And if the margin of error is plus or minus 3%, and 53% of these 1,230 people thought war was not necessary, then perhaps only 615 people in the whole USA said this."
OK, kiddies, let's do this one more time:
First of all, Mr/Ms Trying, comparing the 300 million population with the number of registered voters is incorrect. I don't know what the number of registered voters is, but figure: just over 100 million voted in the 2000 election, and turnout was pretty good. Ballpark it at 160-170 million R.V.s.
But that's not really important. Flip a coin once, or ask a "yes-no" question of one poll respondent, call "heads" or "yes" 1 and the other thing zero, and you have defined a random variable, usually called a "Bernoulli trial." At any given moment, a fixed (but unknown) proportion of American voters can answer "yes" to the poll question. Call this proportion p. If the pollster samples from the population at random, the probability that any individual pollee says "yes" is also p. To the pollster, p is unknown. The standard deviation of a Bernoulli random variable, evaluated at the null hypothesis p = 0.5, is 0.5. If you ask N people the same question, the percentage of "yes" answers gives an estimate of p; call it p^ (when possible, put the caret over the p). This estimate is "unbiased," but I stress that "unbiased" is a statistical term of art unrelated to political or other everyday biases. It also approximately obeys the normal distribution; the bigger the N, the better the approximation.
The standard deviation of p^ is, still under the 50-50 null, 0.5/sqrt(N). From this you can construct, for any chosen level of "confidence" or "statistical significance," a "confidence interval." A 95% (for example) confidence interval is interpreted as saying: If I went around repeating the experiment, each time asking the question of N people, the confidence intervals I calculated for each repetition would cover the true value of p 95% of the time.
For the 95% level, for the normal distribution, the "critical value" is about 1.96. So, we are 95% confident that the interval
covers the true p.
For p^ = 0.53 and N = 1230, this works out to
0.53 +/- 0.0279, i.e. the interval (0.502, 0.558).
Thus, the sample data permits us to reject, at the 95% confidence level, the 50-50 null hypothesis in favor of the alternative, "a majority of registered voters now believes that the situation in Iraq does not merit war." The LA Times also points out that these figures were reversed in November and March; assuming the sample sizes were similar, at those times we would have rejected the null in favor of the alternative "a majority of registered voters believes that the Iraq was was justified."
Even if all this is too technical for you, think about this. Assuming the Times's pollsters followed the same methodology in November, March, and June, the shift of a statistically significant majority from supporting the war to opposing the war tells us something. Even if you buy into the variations on the tune "how can 1200 sample respondents represent all the millions of voters in this great U.S. of A.!!!" (which is what I just tried to explain), the rapid change in the sentiment of pollees is informative, possibly importantly so, about the attitudes of a large number of voters.
People do, eventually, come to their senses. Some say it's like a fever that must "run its course." Ask Attorney General Palmer, Joe McCarthy, Lyndon Johnson. As Honest Abe Lincoln said, "You can fool all of the people some of time, and a few hard-core Republicans all of the time, and 53% of the people once in a while."
(my thanks to Yoram Gat for helpful suggestions)
16 Mar 06. On the "approval" data graphics I combined CNN/Time (up through 2004) with Time (2004-present) into one symbol and discarded TIPP, which has not been published since 2004.
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