Welch–Satterthwaite equation
In statistics and uncertainty analysis, the Welch–Satterthwaite equation is used to calculate an approximation to the effective degrees of freedom of a linear combination of independent sample variances.
For n sample variances si2 (i = 1, ..., n), each respectively having νi degrees of freedom, often one computes the linear combination
\chi' = \sum_{i=1}^n k_i s_i^2.
In general, the distribution of χ' cannot be expressed analytically. However, its distribution can be approximated by another chi-squared distribution, whose effective degrees of freedom are given by the Welch–Satterthwaite equation
\nu_{\chi'} \approx \frac{\displaystyle\left(\sum_{i=1}^n k_i s_i^2\right)^2}<br />
                          {\displaystyle\sum_{i=1}^n \frac{(k_i s_i^2)^2}<br />
                                               {\nu_i}<br />
                          }
There is no assumption that the underlying population variances σi2 are equal.
The result can be used to perform approximate statistical inference tests. The simplest application of this equation is in performing Welch's t test.

This is an excerpt from the article Welch–Satterthwaite equation from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
The article Welch–Satterthwaite equation at en.wikipedia.org was accessed 1,450 times in the last 30 days. (as of: 06/09/2013)
Images on Welch–Satterthwaite equation
Preview image:
Original:
Search results from Google and Bing
1
>30
1
Welch–Satterthwaite equation - Wikipedia, the free encyclopedia
In statistics and uncertainty analysis, the Welch–Satterthwaite equation is used to calculate an approximation to the effective degrees of freedom of a linear ...
en.wikipedia.org/wiki/Welch%E2%80%93Satterthwaite_equation
2
>30
2
Welch's t test - Wikipedia, the free encyclopedia
associated with this variance estimate is approximated using the Welch-Satterthwaite equation: \nu \quad = \quad {{\left( \; {s_1. Here \nu_i = N_i-1 , the degrees ...
en.wikipedia.org/wiki/Welch's_t_test
3
>30
3
Welch–Satterthwaite equation: proof or derivation? - Talk Stats
Hi, I'm studying now the Welch's t-test in which we use the Welch–Satterthwaite equation to calculate the degrees of freedom of the ...
www.talkstats.com/showthread.php/12753-Welch%E2%80%93Satterthwaite-equation-proof-or-derivation
4
>30
4
2.5.7.1. Degrees of freedom
... components of uncertainty with small degrees of freedom. In this case, the degrees of freedom is approximated by the Welch-Satterthwaite formula ( Brownlee).
www.itl.nist.gov/div898/handbook/mpc/section5/mpc571.htm
5
>30
5
Stick To Your GUMs Applying Welch-Satterthwaite to Correlated Errors
Summary. Where's my GUM? Assigning DOF to a combined uncertainty. The GUM recommends the Welch-Satterthwaite formula. Welch-Satterthwaite formula ...
www.ncsli.org/c/f/p11/165.335.pdf
6
>30
6
Comparing Two Means Example: 10 men in this class have a mean ...
The Welch-Satterthwaite Formula: df = (s. 2. 1 n1. + s. 2. 2 n2. ) 2. 1 n1−1. (s. 2. 1 n1. ) 2. +. 1 n2−1. (s. 2. 2 n2. ) 2 where s1,s2are the individual standard ...
www.unc.edu/~rls/s151-09/class26.pdf
7
>30
7
Study of the effective freedom degree in Welch-Satterthwaite formula
The purpose of this research is utilizing ISO-GUM and making the result of blood chemical analysis (BCA) into the reference value that can be assurance, ...
ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4108137
8
>30
8
A generalization of the Welch–Satterthwaite formula for ... - IOPscience
Sep 12, 2007 ... The Welch–Satterthwaite (W–S) formula described in the Guide to the Expression of Uncertainty in Measurement enables an effective number ...
iopscience.iop.org/0026-1394/44/5/010/
9
>30
9
A Welch-Satterthwaite Relation for Correlated Errors - Integrated ...
The Welch-Satterthwaite relation provides a useful tool for estimating the ...... [3] Willink, R., “A generalization of the Welch–Satterthwaite formula for use with ...
www.isgmax.com/Articles_Papers/Welch-Satterthwaite%20for%20Correlated%20Errors.pdf
10
>30
10
Welch-Satterthwaite Equation - Google Books
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In statistics and uncertainty analysis, ...
books.google.com/books/about/Welch_Satterthwaite_Equation.html?id=osU4YgEACAAJ
Search results for "Welch–Satterthwaite equation"
Google: approx. 15.800
Welch–Satterthwaite equation in science
Satterthwaite (disambiguation) - Wikipedia, the free encyclopedia
John Satterthwaite (born 1925) was a Church of England bishop whose ... at the Kellogg School of Management at Northwestern University in Evanston, Illinois. ... The Welch–Satterthwaite equation is an equation in statistics relating to the ...
[PDF]CERTIFICATE OF ANALYSIS - LGC Standards
separately for each analyte according to the Welch-Satterthwaite equation for effective .... Innovation, Universities and Skills as part of the National Measurement ...
[PDF]Fan-averaging for ultrasound tongue contour evaluation
Tanja Kocjancic - Queen Margaret University, Edinburgh. UK. Once contours have been fitted ... applying the Welch-Satterthwaite equation. The highlights of this ...
Darwin Central • View topic - Welch's t test
... I think I need to do Welch's t test. I calculated the degrees of freedom with the Welch-Satterthwaite equation. I've got the math right, but I want ...
[R] Tail area of sum of Chi-square variables
Mar 29, 2007 ... You might also check out Welch and Satterthwaite's (separate) papers ... which led to a thing called the welch-satterthwaite equation by one (more ... 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) ...
R-Forge: metRology: SCM Repository
R-Forge Home. Project, People. Log In | New Account ...
RNArobo/source/welchtest.cpp at master · rampasek ... - GitHub
Description : Welch Two Sample t-test ... Institution : Comenius University in Bratislava. *. */ ..... //calculate estimate using the Welch-Satterthwaite equation ...
Bioequivalence and Bioavailability Forum • Welch/Satterthwaite in ...
Sep 21, 2011 ... So Welch/Satterthwaite's equation for calculation of DF's come into play for the unequal ..... University of Science and Technology of China ...
[R] Tail area of sum of Chi-square variables - Grokbase
Mar 29, 2007 ... You might also check out Welch and Satterthwaite's (separate) papers on ... which led to a thing called the welch-satterthwaite equation by one (more or less .... tlumley at u.washington.edu University of Washington, Seattle ...
Relative Quantity and Error Propagation with qPCR? - ResearchGate
Mar 20, 2013 ... Jack Gallup · Iowa State University. Here is the link to a ... The number of degrees of freedom, v, is obtained by the Satterthwaite equation: ...
Books on the term Welch–Satterthwaite equation
Measurement and Data Analysis for Engineering and Science, Second ...
Measurement and Data Analysis for Engineering and Science, Second ...
Patrick F. Dunn, 2011
Note that the covariances in Equation 7.19 should not be ignored simply for convenience when performing an ... for ux. and veff < ∑ Ji=ivi- This equation, known as the Welch-Satterthwaite formula, was presented originally by Welch [9].
Challenges at the Interface of Data Analysis, Computer Science, ...
Challenges at the Interface of Data Analysis, Computer Science, ...
Wolfgang Gaul, Andreas. Geyer-Schulz, Lars. Schmidt-Thieme, 2012
The t-statistic as provided by Equation 1 is known to perform reasonably well if the two empirical bootstrap distributions are ... The number of the degrees of freedom for the t-statistic is determined by means of the Welch-Satterthwaite equation ...
Validation in Chemical Measurement
Validation in Chemical Measurement
Paul De Bièvre, Helmut Günzler, 2005
As in the other cases, the degrees of freedom were calculated by the Welch-Satterthwaite equation. Sample signal interpolation from a calibration curve The mathematical model used to describe our calibration curve was validated by the ...
An Introduction to Uncertainty in Measurement Using the Gum: ...
An Introduction to Uncertainty in Measurement Using the Gum: ...
L. Kirkup, R. Bob Frenkel, 2006
from. the. Welch–Satterthwaite. formula. The effective number of degrees of freedom associated with the uncertainty of a measurand can never exceed the ... This is a consequence of the Welch–Satterthwaite formula discussed in section 10.3.
Differences in Venture Capital Financing of U.S., UK, German and ...
Differences in Venture Capital Financing of U.S., UK, German and ...
Michael Jurgen Garbade, 2011
... sample variance formula : sample variance 1 21S : sample variance 2 22S t: t- statistic D.F.: degree of freedom n SnS XXt 2 22 1 21 21 + −= ( )2 n 1iiXSS¦=−=X ¦ = = n 1i i X n 1 X ( ) 1-n X S n 1 i 2 i 2 ¦ = − = X Welch-Satterthwaite equation344 ...
Development of Google searches


Blog posts on the term
Welch–Satterthwaite equation
Expanded Uncertainty Determination - MaplePrimes
www.mapleprimes.com/questions/145649-Expanded-Uncertainty-Determination?ref=Feed:MaplePrimes:New%20Questions%20&%20Posts
Statistic on aiR: Two sample Student's t-test #2
Comparison of the averages of two independent groups, extracted from two populations at variance unknown; sample variances are not homogeneous. We want to compare the heights in inches of two groups of individuals.
statistic-on-air.blogspot.com/2009/07/two-sample-students-t-test-2.html
Process Engineering | Put uncertainty analysis to work | Chemical Processing
Determine how much confidence to place in your data.
www.chemicalprocessing.com/articles/2007/157/
Degrees of Freedom with Linear Regression - Pressure Sensor Uncertainty
Degrees of Freedom with Linear Regression - Pressure Sensor Uncertainty Measurement Uncertainty (MU)
elsmar.com/Forums/showthread.php?t=52524
Prospects and Pitfalls of Statistical Testing
jasss.soc.surrey.ac.uk/13/4/1.html
Experiment 2 (4/10 – 4/20) completed | GatorNuke's Lab
Forex numerical experiments
gatornuke.wordpress.com/2011/04/20/183/
An introduction to uncertainty in measurement using the GUM (guide to the expression of uncertainty in measurement) (Book, 2006) [WorldCat.org]
Get this from a library! An introduction to uncertainty in measurement using the GUM (guide to the expression of uncertainty in measurement). [Les Kirkup; R B Frenkel] -- This book presents the need for clarity, consistancy, and accuracy when making measurements; some of the GUM guidelines are presented in this book. A background in first-year calculus and some basic ...
www.worldcat.org/title/introduction-to-uncertainty-in-measurement-using-the-gum-guide-to-the-expression-of-uncertainty-in-measurement/oclc/62532875
Log In
dgMarket is the largest international portal for tenders and procurement opportunities from governments and international organizations.
www.dgmarket.com/tenders/np-notice.do~3997476
The irregular mail - Do you hear me, I'm talking to you
meakame.livejournal.com/157862.html
123