A good illustration of margins of error:

Apropos my criticism of CNN’s poll reporting, here’s a great item from Mickey Kaus (Slate), quoting a reader e-mail:

Rasmussen numbers [though this applies to any poll numbers] are going to change even if the underlying facts they are polling do not change. To illustrate this I created an excel file in which mimicked the polling of 500 people per day and repeated this for 100 days. During this 100 day period, the underlying “facts” did not change: 45% of people supported bush, 45% of people supported kerry and 10% were other or undecided. Let me emphasize: this never changed during the 100 days: I know this because it’s how the excel file was programmed.

Despite the fact that there was no change in the actual situation, the polling results did change: one day Bush outpolled Kerry 50-40; on another day Kerry outpolled Bush 49-42; and on another day it was Kerry 50-44.

Rasmussen evens out these one day jumps by reporting three day moving averages. But those also move around, though not as much. Let’s look at the 3-day averages for one five day period in my simulation:

Monday: Bush 48 Kerry 41

Tuesday: Bush 46 Kerry 43

Wednesday: Bush 45 Kerry 45

Thursday: Bush 43 Kerry 47

Friday: Bush 43 Kerry 47

That’s what the margin of error (+/-4.5% for 500 respondents, +/-2.5% for 1500, which means that 19 times out of 20 the true numbers will be within the stated percentage of the reported numbers) reflects: You can expect the numbers to vary by quite a bit from poll to poll, even if the underlying reality doesn’t change at all.

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