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Unformatted text preview: STAT 200, Lang Wu 1 Chapter 3. Producing Data 3.1. Some Concepts In practice, data are often obtained either in designed experiments or in observa tional studies (including survey). In this chapter, we will discuss some concepts which are among the most important in statistics. Let’s first consider a simple example to illustrate the basic idea. Suppose that a doctor wants to know if a drug (or treatment) is effective for reducing blood pressure. The doctor then designs an experiment to collect data, analyze the data using statistical methods, and then draw conclusions about the effec tiveness of the drug or treatment. A typical design is as follows. The doctor would randomly select (say) 40 patients with high blood pressures, and then he would assign the patients randomly into two groups: • Treatment group: patients in this group receives the drug (treatment), • Control group: patients in this group receives a placebo (a dummy pill that looks and tastes like the drug but has no active ingredient). Then, the doctor measures the reductions in blood pressures in both groups and analyzes the resulting data using statistical methods to see if the difference between the two groups is statistically significant. STAT 200, Lang Wu 2 In the above experiment, there are two processes involving randomness: first, the 40 patients are randomly selected; second, the 40 patients are randomly assigned into two groups. The first process ensures that the 40 patients are representative for all patients. The second process is called randomization , which is important since it can eliminate any biases, so that any differences between the two groups are due to the drug (or treatment), not other factors (such as gender or age). The above example contains many important concepts, as described below. Population, sample, parameter, statistics, and inference Some very important general concepts in statistics can be illustrated using the above example: • population : all individuals of interest (a population may contain many individuals), e.g., all patients with high blood pressures in the example. • sample : the individuals from whom data are collected (these individuals are often a random subset of the population representing the population), e.g., the 40 randomly selected patients in the example. • parameters : the unknown population characteristics which are of main interest (such as the population mean and population standard deviation), e.g., the true (but unknown) mean reduction in blood pressure for all patients in the population and the associated standard deviation in the example. • statistics : the known sample characteristics corresponding to the popu STAT 200, Lang Wu 3 lation characteristics of interest (such as the sample mean and sample standard deviation), e.g., the average reductions in blood pressure in each group in the sample and the associated sample standard deviation in the example – both numbers can be computed from the data....
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 Spring '11
 David
 Statistics, Standard Deviation

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