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The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power .
Example: Suppose we have six schools with populations of 150, 180, 200, 220, 260, and 490 students respectively (total 1500 students), and we want to use student population as the basis for a PPS sample of size three.
In statistics, a population is a set of similar items or events which is of interest for some question or experiment. [1] A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of ...
Let be the size of the population of interest and let be the sample size of a simple random sample of the population. If N ≥ 10 n {\displaystyle N\geq 10n} , then the data's individual observations are independent of each other.
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.If an arbitrarily large number of samples, each involving multiple observations (data points), were separately used in order to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample, then the sampling ...
If the members of the population come in three kinds, say "blue", "red" and "black", the number of red elements in a sample of given size will vary by sample and hence is a random variable whose distribution can be studied. That distribution depends on the numbers of red and black elements in the full population.
The sampling starts by selecting an element from the list at random and then every k th element in the frame is selected, where k, is the sampling interval (sometimes known as the skip): this is calculated as: [3] = where n is the sample size, and N is the population size.
Where is the sample size, = / is the fraction of the sample from the population, () is the (squared) finite population correction (FPC), is the unbiassed sample variance, and (¯) is some estimator of the variance of the mean under the sampling design. The issue with the above formula is that it is extremely rare to be able to directly estimate ...