--- title: "Normal Calculator" author: "Russell Almond" date: "9/10/2019" output: html_document runtime: shiny resource_files: - Chi2calculator.Rmd - Studenttcalculator.Rmd --- ```{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE) ``` ## Normal Probabilities. In this tool, you input a z score, and get a corresponding normal probability. ```{r probabilities, echo=FALSE} inputPanel( selectInput("tails", label = "Which tails", choices = c("Upper tail: Pr(z < Z)"="upper", "Lower tail: Pr(Z < z)"="lower", "Both tails: Pr(Z <-z or z< Z)"="both", "Middle: Pr(-z < Z < z)"="middle"), selected = "both"), numericInput("z", label = "Normal quantile (z):", value=2) ) renderPlot({ q <- input$z p <- switch(input$tails, upper=1-pnorm(q), lower=pnorm(q), both=2*pnorm(-abs(q)), middle=1-2*pnorm(-abs(q))) xl <- round(max(3,ceiling(abs(q)+.5)),1) curve(dnorm(x),main=paste("Probability of shaded region = ",round(p,3)), sub=paste("z = ",round(q,3)), xlim = c(-xl,xl),yaxt="n",cex=3,cex.lab=2,cex.main=2,ylab="",xlab="z") switch(input$tails, upper={ cord.xu <- c(q,seq(q,xl,0.01),xl) cord.yu <- c(0,dnorm(seq(q,xl,0.01)),0) polygon(cord.xu,cord.yu,col='skyblue') axis(1,q,paste(round(q,3)),cex.axis=2) }, lower={ cord.xl <- c(-xl,seq(-xl,q,0.01),q) cord.yl <- c(0,dnorm(seq(-xl,q,0.01)),0) polygon(cord.xl,cord.yl,col='skyblue') axis(1,q,paste(round(q,3)),cex.axis=2) }, both={ q <- abs(q) cord.xu <- c(q,seq(q,xl,0.01),xl) cord.yu <- c(0,dnorm(seq(q,xl,0.01)),0) polygon(cord.xu,cord.yu,col='skyblue') cord.xl <- c(-xl,seq(-xl,-q,0.01),-q) cord.yl <- c(0,dnorm(seq(-xl,-q,0.01)),0) polygon(cord.xl,cord.yl,col='skyblue') axis(1,q,paste(round(q,3)),cex.axis=2) axis(1,-q,paste(-round(q,3)),cex.axis=2) }, middle={ q <- abs(q) cord.xmid <- c(-q,seq(-q,q,0.01),q) cord.ymid <- c(0,dnorm(seq(-q,q,0.01)),0) polygon(cord.xmid,cord.ymid,col='skyblue') axis(1,q,paste(round(q,3)),cex.axis=2) axis(1,-q,paste(-round(q,3)),cex.axis=2) }) }) ``` ## Normal Quantiles. In this tool, you input a probability, and get a corresponding *z* score. ```{r quantiles, echo=FALSE} inputPanel( selectInput("tails1", label = "Which tails", choices = c("Upper tail: Pr(z < Z)"="upper", "Lower tail: Pr(Z < z)"="lower", "Both tails: Pr(Z <-z or z< Z)"="both", "Middle: Pr(-z < Z < z)"="middle"), selected = "both"), numericInput("p", label = "Probability of shaded region:", value=0.05, min=0, max=1) ) renderPlot({ pp <- input$p q <- switch(input$tails1, upper=qnorm(1-pp), lower=qnorm(pp), both=qnorm(1-pp/2), middle=qnorm(.5+pp/2)) xl <- round(max(3,ceiling(abs(q)+.5)),1) curve(dnorm(x),main=paste("Probability of shaded region = ",round(pp,3)), sub=paste("z = ",round(q,3)), xlim = c(-xl,xl),yaxt="n",cex=3,cex.lab=2,cex.main=2,ylab="",xlab="z") switch(input$tails1, upper={ cord.xu <- c(q,seq(q,xl,0.01),xl) cord.yu <- c(0,dnorm(seq(q,xl,0.01)),0) polygon(cord.xu,cord.yu,col='skyblue') axis(1,q,paste(round(q,3)),cex.axis=2) }, lower={ cord.xl <- c(-xl,seq(-xl,q,0.01),q) cord.yl <- c(0,dnorm(seq(-xl,q,0.01)),0) polygon(cord.xl,cord.yl,col='skyblue') axis(1,q,paste(round(q,3)),cex.axis=2) }, both={ q <- abs(q) cord.xu <- c(q,seq(q,xl,0.01),xl) cord.yu <- c(0,dnorm(seq(q,xl,0.01)),0) polygon(cord.xu,cord.yu,col='skyblue') cord.xl <- c(-xl,seq(-xl,-q,0.01),-q) cord.yl <- c(0,dnorm(seq(-xl,-q,0.01)),0) polygon(cord.xl,cord.yl,col='skyblue') axis(1,q,paste(round(q,3)),cex.axis=2) axis(1,-q,paste(-round(q,3)),cex.axis=2) }, middle={ q <- abs(q) cord.xmid <- c(-q,seq(-q,q,0.01),q) cord.ymid <- c(0,dnorm(seq(-q,q,0.01)),0) polygon(cord.xmid,cord.ymid,col='skyblue') axis(1,q,paste(round(q,3)),cex.axis=2) axis(1,-q,paste(-round(q,3)),cex.axis=2) }) })