This is an extreme example, but one should consider all potential sources of systematic bias in the sampling process. Selecting every tenth person (or any even-numbered multiple) would result in selecting all males or females depending on the starting point. For example, suppose that the population of interest consisted of married couples and that the sampling frame was set up to list each husband and then his wife. With systematic sampling like this, it is possible to obtain non-representative samples if there is a systematic arrangement of individuals in the population. Once the first person is selected at random, every fifth person is selected from that point on through the end of the list. If the desired sample size is n=175, then the sampling fraction is 1,000/175 = 5.7, so we round this down to five and take every fifth person. The selection process begins by selecting the first person at random from the first ten subjects in the sampling frame using a random number table then 10th subject is selected. For example, if the population size is N=1,000 and a sample size of n=100 is desired, then the sampling interval is 1,000/100 = 10, so every tenth person is selected into the sample. The spacing or interval between selections is determined by the ratio of the population size to the sample size (N/n). However, in systematic sampling, subjects are selected at fixed intervals, e.g., every third or every fifth person is selected. Systematic sampling also begins with the complete sampling frame and assignment of unique identification numbers. Excel, for example, has a built-in function that can be used to generate random numbers. Many introductory statistical textbooks contain tables of random numbers that can be used to ensure random selection, and statistical computing packages can be used to determine random numbers. This sampling strategy is most useful for small populations, because it requires a complete enumeration of the population as a first step. As a result, each element has an equal chance of being selected, and the probability of being selected can be easily computed. Each of these is assigned a unique identification number, and elements are selected at random to determine the individuals to be included in the sample. In simple random sampling, one starts by identifying the sampling frame, i.e., a complete list or enumeration of all of the population elements (e.g., people, houses, phone numbers, etc.). Probability Sampling Simple Random Sampling In non-probability sampling, each member of the population is selected without the use of probability. In probability sampling, each member of the population has a known probability of being selected. There are two types of sampling: probability sampling and non-probability sampling. Consequently, if we were to select a sample from a population in order to estimate the overall prevalence of obesity, we would want the educational level of the sample to be similar to that of the overall population in order to avoid an over- or underestimate of the prevalence of obesity. For example, studies have shown that the prevalence of obesity is inversely related to educational attainment (i.e., persons with higher levels of education are less likely to be obese). When selecting a sample from a population, it is important that the sample is representative of the population, i.e., the sample should be similar to the population with respect to key characteristics. Sampling individuals from a population into a sample is a critically important step in any biostatistical analysis, because we are making generalizations about the population based on that sample.
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