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STATISTICAL ACCURACY
Let's say you hear someone declare, "70 percent of all Americans like astronomy." The first question to ask is, how did we get that number, 70 percent? Perhaps the person took a poll. What if another pollster, however, said, "80% of all Americans like astronomy?" Then which number is right, 70% or 80%? If you found out that Pollster One asked 50 people and 35 of them said they like astronomy, whereas Pollster Two asked 400 people and 320 of them said they like astronomy, your common sense would suggest that Pollster Two's result is more likely to be accurate. Why? Well, you think, she asked a lot more people, so her result is more believable. The quantitative way to express this "gut feeling" is with statistics. If you're counting up data points, you can use something called "counting statistics" or "Poisson statistics," named after a French guy named Poisson. In this case, you're counting up answers to a question; you could also count up marbles in a bag, or photons (light "particles") collected by your telescope - anything you're trying to get a sum total or "count" of. In this case, your accuracy is determined by the number of counts you have. With Poisson statistics, the ERROR in your measurement is the square root of the total number of counts. Thus Pollster One's error is sqrt(50), or about 7, and Pollster Two's error is sqrt(400), or 20. The MARGIN OF ERROR in your measurement would be the fraction or percentage of the total count number that the error is. So Pollster One has a margin of error of sqrt(50) -------- = margin of error = 0.14, or 14% 50 whereas Pollster Two has a margin of error of sqrt(400) --------- = margin of error = 0.05, or 5% 400 So Pollster One's value of 70% of Americans liking astronomy is really "70% plus or minus 14%"; similarly, Pollster Two's result is "80% plus or minus 5%" - much more accurate. |