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Unformatted text preview: + + Chapter 12: Describing A Numerical Re sponse So far, the response has been a dichotomy. Now, we consider a response that is a number. There are two ways we get a numerical re sponse: counting and measuring . Suppose the subjects are students in this class. Below are some examples of numerical re sponses. Counting: Number of minuses on homework to date; number of credits this semester; num ber of persons living in current household. Measuring: Height; weight; age. As often happens in life, the boundary be tween these options can be blurry. For exam ple, consider annual income. Literally, annual income is determined by counting the num ber of cents earned in the year, . . . + 197 + + but economists and other researchers tend to treat it as a measurement. The general guideline is that if a count vari able has many many values in a population, and no one value dominates others in terms of frequency, it is usually mathematically more convenient to treat the variable as a measure ment. Two important words are: precise and accu rate Accurate means close to the truth. For ex ample, if I state that my dog Casey lived for 15.5 years, that is accurate. If I state that my grandfather Wardrop lived to be 150, that is highly inaccurate. Precise is most useful for measurements. + 198 + + If I state: Yesterday I ran one mile in 250.376 seconds, this is incredibly precise (to the near est onethousandths of a second), but ridicu lously inaccurate. If I say I ran it In less than one hour it is accurate, but not the least pre cise. The level of precision needed depends on the situation. As children we learn that the dis tance from the sun to the Earth is 93 million miles. I suppose that this is deemed precise enough to get some sense of the size of our solar system, but perhaps not precise enough if you are trying to determine the amount of fuel needed to send a missile into the sun. (I have no idea why anybody would want to do that.) Here is a good general guideline for science: measurements should be precise enough to create variation in our population or subjects of interest, but there is no need to get carried away with it! + 199 + + For example, if I want to measure heights of students in this class, it is dumb to measure height to the nearest mile (we are all 0 miles tall) or even to the nearest five feet (we are all five feet tall). But there seems no reason to try to measure height in millimeters. Precise is somewhat meaningless for counts that take on small values. For example, it is accurate to say that 2 cats live in my house. It is no more precise to say I have 2.000 cats! For large counts, precision does become mean ingful. For example, if forced to guess, I would say that there are 300 million people living in the US. I suspect that this is accurate, but clearly I am not being very precise....
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 Fall '08
 ProfessorWardrop
 Statistics, Counting

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