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As explained above, while s 2 is an unbiased estimator for the population variance, s is still a biased estimator for the population standard deviation, though markedly less biased than the uncorrected sample standard deviation. This estimator is commonly used and generally known simply as the "sample standard deviation".
A statistical hypothesis test typically involves a calculation of a test statistic. Then a decision is made, either by comparing the test statistic to a critical value or equivalently by evaluating a p -value computed from the test statistic. Roughly 100 specialized statistical tests have been defined. [ 1 ][ 2 ]
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. [1] Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.
In general, with a normally-distributed sample mean, Ẋ, and with a known value for the standard deviation, σ, a 100(1-α)% confidence interval for the true μ is formed by taking Ẋ ± e, with e = z 1-α/2 (σ/n 1/2), where z 1-α/2 is the 100(1-α/2)% cumulative value of the standard normal curve, and n is the number of data values in that ...
Unbiased estimation of standard deviation. In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the ...
Variability hypothesis. Two distribution curves with identical means but different variabilities. The curve with the greater variability (green) yields higher values in both the lowest and highest ends of the range. The variability hypothesis, also known as the greater male variability hypothesis, is the hypothesis that males generally display ...
Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample. 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 ...
In statistics, the bias of an estimator (or bias function) is the difference between this estimator 's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator. Bias is a distinct concept from consistency ...