12PowerFTest - POWER OF THE F-TEST Suppose C is a q p...

Info icon This preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
POWER OF THE F-TEST Suppose C is a q × p matrix such that C β is testable. We have established that F = ( C ˆ β - d ) 0 [ C ( X 0 X ) - C 0 ] - 1 ( C ˆ β - d ) / q ˆ σ 2 F q , n - r ( δ 2 ) where δ 2 = ( C β - d ) 0 [ C ( X 0 X ) - C 0 ] - 1 ( C β - d ) σ 2 . Copyright c 2012 (Iowa State University) Statistics 511 1 / 10
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Let F q , n - r , 1 - α denote the 1 - α quantile of the central F distribution with q and n - r d.f. The power of the significance level α test of H 0 : C β = d is given by P ( F F q , n - r , 1 - α ) . The power is an increasing function of the noncentrality parameter δ 2 . Copyright c 2012 (Iowa State University) Statistics 511 2 / 10
Image of page 2
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
x=seq(0,15,by=.01) y1=df(x,3,26) y2=df(x,3,26,ncp=10) plot(c(x,x),c(y1,y2),pch=" ", xlab="x",ylab="Density", main="A Comparison of Central and Non-Central F Densities") lines(x,y1,col="blue",lwd=2) lines(x,y2,lty=2,col="red",lwd=2) legend(6,.6, c(expression(paste(F[list(3,26)]," density")), expression(paste(F[list(3,26)](10)," density"))), lty=1:2, col=c("blue","red"), lwd=2)
Image of page 4
qf(.95,3,26) 2.975154 1-pf(qf(.95,3,26),3,26,10) 0.6895487
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 6
plot(c(x,x),c(y1,y2),pch=" ", xlab="x",ylab="Density", main="A Comparison of Central and Non-Central F Densities")
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern