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Summary
| Description |
English: Illustration of the idea of statistical power for a two sided test. Made in R. |
| Date | |
| Source | Own work |
| Author | Fangz |
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)
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:01, 18 July 2024 | | 734 × 774 (13 KB) | Fangz | Uploaded own work with UploadWizard |
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