12.1 Sampling Techniques and Misuses of Statistics 763 in, a random sample can be expected to produce satisfactory results. For example, consider a large container holding 300 tennis balls that are identical except for color. Onethird of the balls are yellow, one-third are white, and one-third are green. If the balls can be thoroughly mixed between each draw of a tennis ball so that each ball has an equally likely chance of being selected, randomness is not difficult to achieve. However, if the objects or items are not all the same size, shape, or texture, it might be impossible to obtain a random sample by reaching into a container and selecting an object. The best procedure for selecting a random sample is to use a random number generator. A random number generator is a device, usually a calculator or computer program, that produces a list of random numbers. To select a random sample, first assign a number to each element in the population. Numbers are usually assigned in order. Then select the number of random numbers needed, which is determined by the sample size. Each numbered element from the population that corresponds to a selected random number becomes part of the sample. Systematic Sampling A systematic sample is obtained by selecting a random starting point and then selecting every n th item in a population. For example, in a factory producing bicycles using an assembly line, a systematic sample could be obtained by randomly selecting a bicycle and then selecting every 20th bicycle thereafter coming off of the assembly line. It is important that the list from which a systematic sample is chosen includes the entire population being studied. See the Did You Know? called “Don’t Count Your Votes Until They’re Cast” on page 764. Another problem that must be avoided when this method of sampling is used is the constantly recurring characteristic. For example, on an assembly line, every 10th item could be the work of robot X. If only every 10th item is checked for defects, the work of other robots doing the same job may not be checked and may be defective. Cluster Sampling A cluster sample is sometimes referred to as an area sample because it is frequently applied on a geographical basis. Essentially, the sampling consists of a random selection of groups of units. To select a cluster sample, we divide a geographic area into sections. Then we randomly select the sections or clusters. Either each member of the selected cluster is included in the sample or a random sample of the members of each cluster is used. For example, geographically we might randomly select city blocks to use as a sample unit. Then either every member of each selected city block would be used or a random sample from each selected city block would be used. Another example is to select x boxes of screws from a whole order, count the number of defective screws in the x boxes selected, and use this number to determine the expected number of defective screws in the whole order. Stratified Sampling When a population is divided into parts, called strata, for the purpose of drawing a sample, the procedure is known as stratified sampling . Stratified sampling involves dividing the population by characteristics called stratifying factors , such as gender, race, religion, or income. When a population has varied characteristics, it is desirable to separate the population into classes with similar characteristics and then take a random sample from each stratum (or class). For example, we could separate the population of undergraduate college students into strata called freshmen, sophomores, juniors, and seniors. The use of stratified sampling requires some knowledge of the population. For example, to obtain a cross section of voters in a city, we must know where various groups are located and the approximate number of voters in each location. Did You Know? The Birth of Inferential Statistics John Gaunt, a London merchant, is credited with being the first person to make statistical predictions, or inferences, from a set of data rather than basing the predictions simply on the laws of chance. He studied the vital statistics (births, deaths, marriages) contained in the Bills of Mortality published during the years of the Great Plague. He observed that more males were born than females and that women lived longer than men. From these observations, he made predictions about life expectancies. The keeping of mortality statistics was stimulated considerably by the growth of the insurance industry. SPL/Science Source
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