File:PowerOfTest.png

Source code:

par(mfrow = c(2,1), mar = c(2,2,2,2))
t = seq(-4,9, len=200)
plot(t,dnorm(t), type="l", col=0, axes= F, xlab = "", ylab="")
crt=  qnorm(0.975)
polygon(c(crt,crt, t[t>crt]), c(0,dnorm(crt), dnorm(t)[t>crt]), col = 4, lty=0)
polygon(-c(crt,crt, t[t>crt]), c(0, dnorm(crt) ,dnorm(t)[t>crt]), col = 4, lty=0)
abline(h=0)
lines(t,dnorm(t), type="l")
text(-4.5,0.4, "Distribution of statistic under\nNull hypothesis", adj=c(0,0), xpd=NA)
text(3.5, 0.23, "Critical value - value of statistic such \nthat probability of rejection under Null\n(blue area) equals desired\nsignificance level (e.g. 0.05)", adj=c(0,0))
tt= -1
arrows(-2, 0.37, tt, dnorm(tt), length = 0.1)
arrows( 6, 0.2, crt, 0.1, length = 0.1)
plot(t,dnorm(t-crt - qnorm(0.9)), type="l", col=0, axes= F, xlab = "", ylab="")
crt=  qnorm(0.975)
 polygon(c(crt, crt, t[t>crt]), c(0,dnorm( -qnorm(0.9)), dnorm(t-crt - qnorm(0.9))[t>crt]), col = 2, lty=0)
lines(t,dnorm(t-crt - qnorm(0.9)), type="l")
abline(h=0)
abline(v = qnorm(0.975), xpd=NA, lty=2)
text(-4.5,0.4, "Distribution of statistic under\nAlternative hypothesis", adj=c(0,0), xpd=NA)
text(5, 0.3, "Power of test - Probability\nstatistic exceeds critical\nlevel under alternative\n(red area)", adj=c(0,0), xpd=NA)
arrows( 6.5, 0.27, 4, 0.1, length = 0.1)
tt= 0.9
arrows(-2, 0.37, tt, dnorm(tt-crt-qnorm(0.9)), length = 0.1)

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution 4.0 International license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

https://creativecommons.org/licenses/by/4.0CC BY 4.0 Creative Commons Attribution 4.0 truetrue

This media file is uncategorized. Please help improve this media file by adding it to one or more categories, so it may be associated with related media files (how?), and so that it can be more easily found. Please notify the uploader with {{subst:Please link images|File:PowerOfTest.png}} ~~~~