An approximate distribution of estimates of variance components.

By F. E. Satterthwaite. 1946

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Citations in the corpus

Kernel‐based tests for joint independence (2016, background): “…essential idea behind the gamma approximation (see also Kankainen (1995) and Gretton et al. (2005)) is that a distribution of the form Σ∞i=1λiZ 2 i can be approximated fairly well by a gamma distribution with matched first and second moments (see Satterthwaite (1946) for basic empirical evidence).”
Fitting Linear Mixed-Effects Models Using lme4 (2014, methodology): “Thus approximate methods for computing the approximate degrees of freedom for t distributions, or the denominator degrees of freedom for F statistics (Satterthwaite 1946; Kenward and Roger 1997), are at best ad hoc solutions.”
Approximate Kernel-Based Conditional Independence Tests for Fast Non-Parametric Causal Discovery (2017, methodology): “We may for example derive the ﬁrst three cumulants: We then recover the moments from the cumulants as follows: Now the Satterthwaite-Welch method (Welch, 1938, Satterthwaite, 1946, Fairﬁeld-Smith, 1936) represents perhaps the simplest and earliest moment matching method.”
The Fruits of Legitimacy: Why Some New Ventures Gain More from Innovation Than Others. (2008, methodology): “types of actions associated with legitimacy differentially 9Specifically, if we denote the estimates for the go-alone model as 1 and those for the alliance model as 2, then βnew = βn1 – βn2, σnew = √σ(2)n1 + σ(2)n2, and DFnew = (σ(2)n1 + σ(2)n2)(2)/(σ(4)n1/DFn1 + σ(4)n2/DFn2), where the first equati”
Quadratic distances on probabilities: A unified foundation (2008, unknown): “We will use a Satterthwaite approximation [Satterthwaite (1946)] to the χ∗(λ) distribution to interpret DOF.”
Trait emotional intelligence: behavioural validation in two studies of emotion recognition and reactivity to mood induction (2003, methodology): “Nevertheless, a simple main effects analysis, with the degrees of freedom adjusted as per Satterthwaite (1946), showed that there were significant group differences on happiness (F(1, 89)¼ 4.27, p 0.05) and surprise (F(1, 89)¼ 2.97, p 0.05, one tailed), both of which were recognized faster by…”
Communication Efficiency and Congestion of Signal Traffic in Large-Scale Brain Networks (2014, methodology): “Comparisons between node-specific metrics were made using Welch’s t-test for samples with unequal variances [49], and evaluated with respect to degrees of freedom determined using the Satterthwaite approximation [50].”
A Powerful Portmanteau Test of Lack of Fit for Time Series (2002, methodology): “This procedure requires only one-dimensional numerical integration, but for simplicity, we prefer to use the approximation proposed by Satterthwaite (1941, 1946) and Box (1954).”
The Wild Bootstrap For Few (treated) Clusters (2018, unknown): “The Bell-McCaffrey degrees-of-freedom parameter, dfBM, for testing a hypothesis about βj is based on results in Satterthwaite (1946) and is computed as follows: 1.”
Sampling Weights in Latent Variable Modeling (2005, methodology): “…it is not possible to generalize the MLM estimator to the large class of models in which the MLR estimator is available, it is easy to develop Satterthwaite (1946) variance correction for the MLR estimator, which would substantially improve its performance, just as the variance correction of…”
A Practitioner’s Guide to Cluster-Robust Inference (2015, methodology): “Satterthwaite (1946) proposed an approximation that was extended to regression with clustered errors in Bell and McCaffrey (2002) and developed further in Imbens and Kolesar (2012). The T(N – k) distribution is the ratio of N[0,1] to independent [ 2(N − K )] / (N − k) .”
HiCS: High Contrast Subspaces for Density-Based Outlier Ranking (2012, background): “However, a detailed examination of the subspaces selected by Enclus shows that it mainly found all two and some of the three-dimensional subspaces.”
Linking growth strategies to long‐term population dynamics in a guild of desert annuals (2007, methodology): “D) obtained by Satterthwaite’s approximation (Satterthwaite 1946)”
Hunting reduces recruitment of primate-dispersed trees in Amazonian Peru (2008, methodology): “Significance tests of fixed factors use Satterthwaite’s method, allowing non-integer degrees of freedom (Satterthwaite, 1946).”
Using the Student's "t"-Test with Extremely Small Sample Sizes. (2013, unknown): “The degrees of freedom for the Welch test was determined with the Welch-Satterthwaite equation (Satterthwaite, 1946).”