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In statistics, a simple random sample (or SRS) is a subset of individuals (a sample) chosen from a larger set (a population) in which a subset of individuals are chosen randomly, all with the same probability. It is a process of selecting a sample in a random way.
In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. The subset is meant to reflect the whole population, and statisticians attempt to collect ...
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. In complex studies ...
Consider a simple yes/no poll as a sample of respondents drawn from a population , reporting the percentage of yes responses. We would like to know how close p {\displaystyle p} is to the true result of a survey of the entire population N {\displaystyle N} , without having to conduct one.
The sample mean and sample covariance are not robust statistics, meaning that they are sensitive to outliers. As robustness is often a desired trait, particularly in real-world applications, robust alternatives may prove desirable, notably quantile-based statistics such as the sample median for location, [4] and interquartile range (IQR) for ...
Given an r-sample statistic, one can create an n-sample statistic by something similar to bootstrapping (taking the average of the statistic over all subsamples of size r). This procedure is known to have certain good properties and the result is a U-statistic. The sample mean and sample variance are of this form, for r = 1 and r = 2.
Fay's method is a generalization of BRR. Instead of simply taking half-size samples, we use the full sample every time but with unequal weighting: k for units outside the half-sample and 2 − k for units inside it. (BRR is the case k = 0.) The variance estimate is then V/(1 − k) 2, where V is the estimate given by the BRR formula above.
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.For an arbitrarily large number of samples where each sample, involving multiple observations (data points), is separately used to compute one value of a statistic (for example, the sample mean or sample variance) per sample, the sampling distribution is ...