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When either randomness or uncertainty modeled by probability theory is attributed to such errors, they are "errors" in the sense in which that term is used in statistics; see errors and residuals in statistics. Every time a measurement is repeated, slightly different results are obtained.
The statistical errors, on the other hand, are independent, and their sum within the random sample is almost surely not zero. One can standardize statistical errors (especially of a normal distribution) in a z-score (or "standard score"), and standardize residuals in a t-statistic, or more generally studentized residuals.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
While precision is a description of random errors (a measure of statistical variability), accuracy has two different definitions: More commonly, a description of systematic errors (a measure of statistical bias of a given measure of central tendency, such as the mean). In this definition of "accuracy", the concept is independent of "precision ...
When bootstrap aggregating is performed, two independent sets are created. One set, the bootstrap sample, is the data chosen to be "in-the-bag" by sampling with replacement.
In statistical hypothesis testing, a type I error, or a false positive, is the rejection of the null hypothesis when it is actually true. A type II error, or a false negative, is the failure to reject a null hypothesis that is actually false. [1] Type I error: an innocent person may be convicted. Type II error: a guilty person may be not convicted.
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Absolute deviation in statistics is a metric that measures the overall difference between individual data points and a central value, typically the mean or median of a dataset. It is determined by taking the absolute value of the difference between each data point and the central value and then averaging these absolute differences. [4]