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This property, undesirable in many applications, has led researchers to use alternatives such as the

**mean****absolute****error**, or those based on the median. See also. Bias–variance tradeoff; Hodges' estimator; James–Stein estimator;**Mean**percentage**error**;**Mean**square quantization**error**;**Mean**square weighted deviation;**Mean**squared displacement**Formula**. The RMSD of an estimator ^ with respect to an estimated parameter is defined as the square root of the**mean**square**error**: (^) = (^) = ((^)). For an unbiased estimator, the RMSD is the square root of the variance, known as the standard deviation.In statistics, the

**absolute**deviation of an element of a data set is the**absolute**difference between that element and a given point. Typically the deviation is reckoned from the central value, being construed as some type of average, most often the median or sometimes the**mean**of the data set:**Mean**-value forms of the remainder — Let f : R → R be k + 1 times differentiable on the open interval with f (k) continuous on the closed interval between a and x. Then R k ( x ) = f ( k + 1 ) ( ξ L ) ( k + 1 ) !In this context, there are several choices for a measure of variability: the range, the interquartile range, the

**mean****absolute**deviation, and the**median****absolute**deviation. For practical purposes, different measures of location and dispersion are often compared on the basis of how well the corresponding population values can be estimated from a ...Otherwise, the

**formula**would be () = /, which yields = (). For example, if we are interested in estimating the proportion of the US population who supports a particular presidential candidate, and we want the width of 95% confidence interval to be at most 2 percentage points (0.02), then we would need a sample size of (1.96) 2 / (0.02 2 ) = 9604.In statistics, an

**effect size**is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the**effect size**value.1) By performing the same analysis on the random variable -X, one can get the same bound in the other direction. Pr (X ≤ a) ≤ inf t ≥ 0 e t a ∏ i E [e − t X i] {\displaystyle \Pr(X\leq a)\leq \inf _{t\geq 0}e^{ta}\prod _{i}\operatorname {E} \left[e^{-tX_{i}}\right]} Specific Chernoff bounds are attained by calculating the moment-generating function E [e − t ⋅ X i ...