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Samples and Sampling Surveys Sampling Bias Experiments and Observational Studies Statistical Significance Completely Randomized Design Matched Pairs Design Blocking
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121
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122 U Step 4 Review the Knowledge You Need to Score High
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In the previous two chapters we concentrated on the analysis of data at hand we didn t worry much about how the data came into our possession The last part of this book deals with statistical inference making statements about a population based on samples drawn from the population In both data analysis and inference, we would like to believe that our analyses, or inferences, are meaningful If we make a claim about a population based on a sample, we want that claim to be true Our ability to do meaningful analyses and make reliable inferences is a function of the data we collect To the extent that the sample data we deal with are representative of the population of interest, we are on solid ground No interpretation of data that are poorly collected or systematically biased will be meaningful We need to understand how to gather quality data before proceeding on to inference In this chapter, we study techniques for gathering data so that we have reasonable confidence that they are representative of our population of interest
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The alternative to sampling to gather data about a population is to conduct a census, a procedure by which every member of a population is selected for study Doing a census, especially when the population of interest is quite large, is often impractical, too time consuming, or too expensive Interestingly enough, relatively small samples can give quite good estimates of population values if the samples are selected properly For example, it can be shown that approximately 1500 randomly selected voters can give reliable information about the entire voting population of the United States The goal of sampling is to produce a representative sample, one that has the essential characteristics of the population being studied and is free of any type of systematic bias We can never be certain that our sample has the characteristics of the population from which it was drawn Our best chance of making a sample representative is to use some sort of random process in selecting it
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Probability Sample
A list of all members of the population from which we can draw a sample is called a sampling frame A sampling frame may or may not be the same set of individuals we are studying A probability sample is one in which each member of the population has a known probability of being in the sample Each member of the population may or may not have an equal chance of being selected Probability samples are used to avoid the bias that can arise in a nonprobability sample (such as when a researcher selects the subjects she will use) Probability samples use some sort of random mechanism to choose the members of the sample The following list includes some types of probability samples random sample: Each member of the population is equally likely to be included simple random sample (SRS): A sample of a given size is chosen in such a way that every possible sample of that size is equally likely to be chosen Note that a sample can be a random sample and not be a simple random sample (SRS) For example, suppose you want a sample of 64 NFL football players One way to produce a random sample would be to randomly select two players from each of the 32 teams This is a random sample but not a simple random sample because not all possible samples of size 64 are possible systematic sample: The first member of the sample is chosen according to some random procedure, and then the rest are chosen according to some well-defined pattern For example, if you wanted 100 people in your sample to be chosen from a list of 10,000 people, you could randomly select one of the first 100 people and then select every 100th name on the list after that
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