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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, different sample sizes may be allocated, such as in stratified surveys or experimental designs with multiple treatment groups.
Matched or independent study designs may be used. Power, sample size, and the detectable alternative hypothesis are interrelated. The user specifies any two of these three quantities and the program derives the third. A description of each calculation, written in English, is generated and may be copied into the user's documents.
The minimum and the maximum value are the first and last order statistics (often denoted X (1) and X (n) respectively, for a sample size of n). If the sample has outliers, they necessarily include the sample maximum or sample minimum, or both, depending on whether they are extremely high or low. However, the sample maximum and minimum need not ...
Fisher's exact test (also Fisher-Irwin test) is a statistical significance test used in the analysis of contingency tables. [1] [2] [3] Although in practice it is employed when sample sizes are small, it is valid for all sample sizes.
Power analyses can be used to calculate the minimum sample size required so that one can be reasonably likely to detect an effect of a given size (in other words, producing an acceptable level of power). For example: "How many times do I need to toss a coin to conclude it is rigged by a certain amount?"
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 .
Once the sample mean is known, no further information about μ can be obtained from the sample itself. On the other hand, for an arbitrary distribution the median is not sufficient for the mean: even if the median of the sample is known, knowing the sample itself would provide further information about the population mean. For example, if the ...
If the sample size is 1,000, then the effective sample size will be 500. It means that the variance of the weighted mean based on 1,000 samples will be the same as that of a simple mean based on 500 samples obtained using a simple random sample.