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Theoretical sampling is considered to be purpose driven and it explicitly carries out its function on the basis of an emerging theory. [18] The main focus of theoretical research is to use its development through a constant comparative analysis of data that is gained through theoretical sampling for a better understanding of the theory produced.
Theoretical sampling [18] occurs when samples are selected on the basis of the results of the data collected so far with a goal of developing a deeper understanding of the area or develop theories. An initial, general sample is first collected with the goal of investigating general trends, where further sampling may consist of extreme or very ...
The theory of statistics provides a basis for the whole range of techniques, in both study design and data analysis, that are used within applications of statistics. [1] [2] The theory covers approaches to statistical-decision problems and to statistical inference, and the actions and deductions that satisfy the basic principles stated for these different approaches.
Examples of empirically inspired statistical laws that have a firm theoretical basis include: Statistical regularity; Law of large numbers; Law of truly large numbers; Central limit theorem; Regression toward the mean; Examples of "laws" with a weaker foundation include: Safety in numbers; Benford's law
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 ...
Theoretical basis When evaluating a ... Bootstrapping is a non-parametric resampling procedure that can build an empirical approximation of the sampling distribution ...
the proper sampling technique is used; the algorithm used is valid for what is being modeled; it simulates the phenomenon in question. Pseudo-random number sampling algorithms are used to transform uniformly distributed pseudo-random numbers into numbers that are distributed according to a given probability distribution.
Sample sizes may be evaluated by the quality of the resulting estimates, as follows. It is usually determined on the basis of the cost, time or convenience of data collection and the need for sufficient statistical power. For example, if a proportion is being estimated, one may wish to have the 95% confidence interval be less than 0.06 units wide.