[PDF] Analysis of Variance

WEIGHTED STANDARD DEVIATION - NIST

WEIGHTED STANDARD DEVIATION PURPOSE Compute the weighted standard deviation of a variable DESCRIPTION The formula for the standard deviation is: (EQ 2-21) while the formula for the weighted standard deviation is: (EQ 2-22) where wi is the weight for the ith observation, N’ is the number of non-zero weights, andxw is the weighted mean of the

WEIGHTED VARIANCE - NIST

LET VAR = WEIGHTED VARIANCE Y1 WEIGHT LET VAR = WEIGHTED VARIANCE Y1 WEIGHT SUBSET TAG > 2 DEFAULT None SYNONYMS None RELATED COMMANDS VARIANCE = Compute the variance of a variable WEIGHTED MEAN = Compute the weighted mean of a variable WEIGHTED STANDARD DEVI = Compute the weighted standard deviation of a variable APPLICATIONS Data Analysis

Incremental calculation of weighted mean and variance

Weighted Standard Error and its Impact on Significance

the weighted mean It is s2 given above that is used in WinCross, in conjunction with the effective sample size b, as the basis for the standard errors used in significance testing involving the weighted mean 2 SPSS approach SPSS uses a “weighted” variance as its estimate of 2 This weighted variance is given by 2 2 1 1 2 11 1 1 1 n ii w

Simple Statistical Functions - open-stdorg

weighted sample standard deviation [39] is defined as the square root of the weighted sample variance 4 Proposal This document proposes the inclusion of the statistics mean (arithmetic, geometric and harmonic), quantile (and me-dian), mode, skewness, kurtosis, variance and standard deviation in the C++ library as both freestanding functions

Analysis of Variance

and the sample standard deviation in group j is s j = v u u u t X i:j(i)=j ( Y i j)2 n j 1 ANOVA ANOVA Table Variance 10 / 59 Grand Mean The grand mean Y is the mean of all observations Note that the grand mean Y = Xk j=1 n j n Y j is the weighted average of the sample means, weighted by sample size ANOVA ANOVA Table Variance 11 / 59 Modeling

Extending Linear Regression: Weighted Least Squares

2 1 Weighted Least Squares as a Solution to Heteroskedas-ticity Suppose we visit the Oracle of Regression (Figure 4), who tells us that the noise has a standard deviation that goes as 1 + x2=2 We can then use this to improve our regression, by solving the weighted least squares problem rather than ordinary least squares (Figure 5)