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When only a sample of data from a population is available, the term standard deviation of the sample or sample standard deviation can refer to either the above-mentioned quantity as applied to those data, or to a modified quantity that is an unbiased estimate of the population standard deviation (the standard deviation of the entire population).
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 ...
For an approximately normal data set, the values within one standard deviation of the mean account for about 68% of the set; while within two standard deviations account for about 95%; and within three standard deviations account for about 99.7%. Shown percentages are rounded theoretical probabilities intended only to approximate the empirical ...
^ is the standard deviation of the entire design, not just that of the two groups being compared. It is possible to work with unequal sample sizes. In this case, one has to calculate the estimated standard deviation for each pairwise comparison as formalized by Clyde Kramer in 1956, so the procedure for unequal sample sizes is sometimes ...
Pooled variance - Wikipedia
The difference between the two sample means, each denoted by X i, which appears in the numerator for all the two-sample testing approaches discussed above, is ¯ ¯ = The sample standard deviations for the two samples are approximately 0.05 and 0.11, respectively. For such small samples, a test of equality between the two population variances ...
Bias in standard deviation for autocorrelated data. The figure shows the ratio of the estimated standard deviation to its known value (which can be calculated analytically for this digital filter), for several settings of α as a function of sample size n. Changing α alters the variance reduction ratio of the filter, which is known to be
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