Abstract: This chapter will show you how random sampling ensures a representative sample (on average) and makes it possible for you to describe (approximately) how different your results (from the sample) are from the (unknown) characteristics of the population. By using a random sample, your survey results will be approximately correct (compared with what you would find by interviewing all customers), and you will know if your results are close enough for comfort. The language we use when sampling helps us distinguish the population (that we wish to know about) from the sample (that we have selected to observe). A population is any collection of units that you are interested in knowing about. A sample is a smaller collection of units selected from the population. A sample is representative if characteristics arise with the same percentages in the sample as in the population. A biased sample is not representative in an important way. A sampling frame gives you access to the population units so that a random sample can be chosen. A sample statistic is any number computed from your sample data. A population parameter is any number computed for the entire population. An estimator is a description of a sample statistic used as a guess for the value of a population parameter, and the actual number computed from the data is called an estimate. The error of estimation is the estimator (or estimate) minus the population parameter and is usually unknown. An unbiased estimator is correct on average (neither systematically too high nor too low). A pilot study is a small-scale version of a study, designed to help you identify problems and fix them before the real study is run. A random sample consists of independently chosen units where each population unit has equal probability of being chosen. The central limit theorem is an amazing mathematical fact about random sampling that tells you that the average of the sample values follows a distribution that becomes more normal-shaped as the sample size grows, tells you that the mean of the sample average is the population mean, and tells you that the standard deviation of the sample average (which indicates the quality of the sample information) is the population standard deviation divided by the square root of the sample size. The standard error of a sample statistic indicates approximately how far the statistic is from its population value. The standard error of the average tells approximately how far the sample average is from the unknown population mean.
Publication Year: 2016
Publication Date: 2016-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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