library(ggplot2) library("tidyverse") # Load tidyverse packages library("dplyr") library("reshape2") # Load reshape2 package alfavarden <- c(0.10, 0.05, 0.01) if(x == 0) {alfavarden <- alfavarden * 2 } # All sann i andra svansen. alfa <- alfavarden[1] conf <- 1 - alfa/2 v1 <- 2*(n-x + 1) v2 <- 2*x v3 <- 2*(x + 1) v4 <- 2*(n-x) if(x > 1) {F1 <- qf(conf, v1, v2)} F2 <- qf(conf, v3, v4) estp010 <- x/n if (x > 1) { lower010 <- x/(x+(n-x+1)*F1) } else {lower010 = 0 } upper010 <- (x+1)/(x+1+(n-x)/F2) # The upper endpoint of the interval. alfa <- alfavarden[2] conf <- 1 - alfa/2 if(x > 1) {F1 <- qf(conf, v1, v2)} F2 <- qf(conf, v3, v4) estp005 <- x/n if (x > 1) { lower005 <- x/(x+(n-x+1)*F1) } else {lower005 = 0 } upper005 <- (x+1)/(x+1+(n-x)/F2) # The upper endpoint of the interval. alfa <- alfavarden[3] conf <- 1 - alfa/2 if(x > 1) {F1 <- qf(conf, v1, v2)} F2 <- qf(conf, v3, v4) estp001 <- x/n if (x > 1) { lower001 <- x/(x+(n-x+1)*F1) } else {lower001 = 0 } upper001 <- (x+1)/(x+1+(n-x)/F2) # The upper endpoint of the interval. # --------------------------------------- del1 <- "Konfidensintervall för p " del2 <- "(x = " del3 <- ", n = " del4 <- ")" titel <- paste(c(del1, del2, x, del3, n, del4), collapse="") if(x == n) upper010 = 1 # Om x = n kan inte F-värde hämtas. if(x == n) upper005 = 1 # Därav denna justering. if(x == n) upper001 = 1 lower <- c(lower010, lower005, lower001) estp <- c(x/n, x/n, x/n) upper <- c(upper010, upper005, upper001) Y <- c(3, 2, 1) intervall <- data.frame(lower, estp, upper, Y) View(intervall) intervall <- melt(intervall, id.vars = "Y") confDiagram <- ggplot(intervall, aes(x = value, y = Y)) + geom_point(size=3) # Ritar grafen. confDiagram <- confDiagram + theme(axis.text.y = element_blank()) confDiagram <- confDiagram + ylim(0, 4) confDiagram <- confDiagram + geom_hline(yintercept=1) + geom_hline(yintercept=2) + geom_hline(yintercept=3) confDiagram <- confDiagram + geom_segment(aes(x = lower[1], y = 3, xend = upper[1], yend = 3), color = "red", linewidth = 2) confDiagram <- confDiagram + geom_segment(aes(x = lower[2], y = 2, xend = upper[2], yend = 2), color = "red", linewidth = 2) confDiagram <- confDiagram + geom_segment(aes(x = lower[3], y = 1, xend = upper[3], yend = 1), color = "red", linewidth = 2) confDiagram <- confDiagram + geom_segment(aes(x = estp[1], y = 0.9, xend = estp[1], yend = 1.1), color = "blue", linewidth = 1) confDiagram <- confDiagram + geom_segment(aes(x = estp[1], y = 1.9, xend = estp[1], yend = 2.1), color = "blue", linewidth = 1) confDiagram <- confDiagram + geom_segment(aes(x = estp[1], y = 2.9, xend = estp[1], yend = 3.1), color = "blue", linewidth = 1) confDiagram <- confDiagram + labs(y = "", x = " Konfidensintervall") confDiagram <- confDiagram + annotate("text", x=lower[3], y=1.2, label="alfa = 0.01", hjust = 0) confDiagram <- confDiagram + annotate("text", x=lower[3], y=2.2, label="alfa = 0.05", hjust = 0) confDiagram <- confDiagram + annotate("text", x=lower[3], y=3.2, label="alfa = 0.10", hjust = 0) confDiagram <- confDiagram + annotate("text", x = -Inf, y = Inf, hjust = -0.2, label=titel, vjust = 3.5, size = 5, colour = "blue" ) confDiagram

Info, referenser, m.m...

Show/hide program code for R

Show/hide comments

49. Confidence intervals for p

p is a parameter in [0, 1] and is often called 'fault rate' or similar

With the number of faults (x) in a sample (n)
a confidence interval for p can be calculated

'x' is simulated with the two slides and the 'Repeate...'-button