Insights Blog
-- Browse All Articles --
Physics Articles
Physics Tutorials
Physics Guides
Physics FAQ
Math Articles
Math Tutorials
Math Guides
Math FAQ
Education Articles
Education Guides
Bio/Chem Articles
Technology Guides
Computer Science Tutorials
Forums
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Trending
Featured Threads
Log in
Register
What's new
Search
Search
Search titles only
By:
General Math
Calculus
Differential Equations
Topology and Analysis
Linear and Abstract Algebra
Differential Geometry
Set Theory, Logic, Probability, Statistics
MATLAB, Maple, Mathematica, LaTeX
Menu
Log in
Register
Navigation
More options
Contact us
Close Menu
JavaScript is disabled. For a better experience, please enable JavaScript in your browser before proceeding.
You are using an out of date browser. It may not display this or other websites correctly.
You should upgrade or use an
alternative browser
.
Forums
Mathematics
Set Theory, Logic, Probability, Statistics
Estimating the covariance
Reply to thread
Message
[QUOTE="gleem, post: 5489843, member: 298988"] I'm not sure I understand the use of covariance in the context of your experiment which is not of a statistical nature since you have only one measurement.. Since G =kE you only have one independent variable E which determines G and for your case G changes by an amount proportional to E, There exists a statistical quantity called the linear correlation coefficient which is one for you case. But again you have only one measurement so it is indeterminate. The covariance is not constrained to have a value of less than one. Let me explain a bit. The uncertainty in the value of a function F is related to the statistical uncertainties in the values of the variables x[SUB]i[/SUB] by the equation σ[SUB]F[/SUB][SUP]2[/SUP] = ∑[SUB]i[/SUB] σ[SUB]I[/SUB][SUP]2[/SUP](∂F/∂xi)[SUP]2[/SUP] +2⋅ Σ[SUB]ij[/SUB] σ[SUB]ij[/SUB][SUP]2[/SUP](∂F/∂x[SUB]i[/SUB])(∂F/∂x[SUB]j[/SUB]) where σ[SUB]i[/SUB][SUP]2[/SUP] is the variance of x[SUB]i[/SUB] i.e. the square of the statistical uncertainty in x[SUB]i[/SUB] where σ[SUB]ij[/SUB][SUP]2[/SUP] is the covariance of x[SUB]j[/SUB] and x[SUB]j[/SUB] where σ[SUB]ij[/SUB][SUP]2[/SUP] = < (x[SUB]i[/SUB]- < x[SUB]i[/SUB]>)⋅( x[SUB]j[/SUB]- <x[SUB]j[/SUB]>) > The brackets < quantity > refer to the average value of quantity, The covariance is important when the value of one variable affects the value of another. If they are totally independent then in the limit of large number of measurements the covariance approaches zero. Obviously the the variances and the covariance can only be determined if you have two or more values of the variables. For you case as a [U]guess[/U] since the covariance is the average of the product of the uncertainties of the variables E and G the covariance might be taken as ΔE⋅ΔG your estimated experimental uncertainties in E and G. and the error associated with this is 2∂μ/∂E⋅∂μ/∂GΔEΔG. Perhaps someone can critique this approach. If you are continuing in the experimental physical sciences I highly recommend that you find a copy of "Data Reduction and Error Analysis for the Physical Sciences" by Bevington ( original version) or the revised edition by Bevington and Robinson. [/QUOTE]
Insert quotes…
Post reply
Forums
Mathematics
Set Theory, Logic, Probability, Statistics
Estimating the covariance
Back
Top