In most statistical studies, we wish to quantify something about a population. For example, we may wish to know the prevalence of diabetes in a population, the typical age that teenagers begin to smoke, or the average birthweight of babies born in a particular community. When the population is small, it is sometimes possible to obtain information from the entire population. A study of the entire population is called a census. However, performing a census is usually impractical, expensive and time-consuming, if not downright impossible. Therefore, nearly all statistical studies are based on a subset of the population, which we will call the sample. Show
When selecting a sample, we need to know how many people to study and which people from the population to select. A study's sample size depends on many factors, and will be the topic of future study. Presently, let us consider how to select a valid sample. A valid sample is one that represents the population to which inferences will be made. And although there is no fail-safe way to ensure sample representativeness, much has been learned over the past half century about sampling to maximize a sample's usefulness. One thing that has been learned is that, whenever possible, a probability sample should be used. A probability sample is a sample in which:
(Cochran, 1977, p. 9). This forms the basis by which generalizations about the population can be made. The simplest form of a probability sample is the simple random sample. A simple random sample as a sample in which each member of the population has an equal probability of entering the sample. This ensures that the sample will be:
These are two extremely important features of a simple random sample. In order to select a simple random sample, it is best to start with a sampling frame of all sampling units in which each population member is then assigned an identification number between 1 and N. A random number generator is then used to determine which of the n individuals will be sampled. (Random number generators can be found at www.random.org/nform.html or www.randomizer.org/form.htm). Here, for example, is a list of 10 random numbers between 1 and 600: 35, 37, 43, 143, 321, 329, 337, 492, 494, 546. Let us use these random numbers to select 10 individuals from the population located at www.sjsu.edu/faculty/gerstman/StatPrimer/populati.htm. Notice that this population contains N = 600, with variables AGE, SEX, HIV status, KAPOSISARComa status, REPORTDATE and OPPORTUNIStic infection. Our sample is: (Dots represent missing values.) Let us review our procedure for selecting a simple random sample: (1) A sampling frame of all population members is compiled. Random sampling can be done either with replacement or without replacement. Sampling with replacement is done by "tossing" population member back into the pool after they have been selected. This way, all N members of the population are given an equal chance of being selected at each draw, even if they have already been drawn. Sampling without replacement is done so that once a population member has been drawn, this population member is removed from the pool for all subsequent draws. The ratio of the sample size (n) to population size (N) is called the sampling fraction. Let f represent the sampling fraction, so f = n / N. Notice that, in our illustrative sample, f = 10 / 600 = .0167. When we sample a population with several strata, we generally require that the proportion of each stratum in the sample should be the same as in the population. Stratified sampling techniques are generally used when the population is heterogeneous, or dissimilar, where certain homogeneous, or similar, sub-populations can be isolated (strata). Simple random sampling is most appropriate when the entire population from which the sample is taken is homogeneous. Some reasons for using stratified sampling over simple random sampling are: When everyone in your population has the same chance of being selected?One of the key advantages of probability sampling is that it is the easiest to measure for error. Probability sampling methods include: Random sampling is the truest form of probability sampling. This type of sampling guarantees that each member of a population has an equal chance of being included in the sample.
What is it called when members of the population have a known chance of being selected into the sample?Probability sampling: What it is, Examples & Steps. Imagine you have a population of 100 people. In this scenario, every person would have odds of 1 in 100 for getting selected. Probability sampling gives you the best chance to create a sample representative of the population.
When every member of the population has an equal chance of being selected to participate in the study the researcher is using?If all participants are equally likely to be selected in the study, equiprobabilistic sampling is being used, and the odds of being selected by the research team may be expressed by the formula: P=1/N, where P equals the probability of taking part in the study and N corresponds to the size of the target population.
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