Coursera Developing Data Products Reproducible Pitch Presentation

This Shiny Application calculates statistical power based on a normal distribution function using pnorm and shows this graphically in the form of a plot of two normal densities.

Power is the probability of rejecting a null hypothesis when it is false.

We consider a theoretical example where our sample mean is normally distributed and the standard deviation of the population is known.

The null hypothesis H0: mu = mu0 versus the alternative hypothesis Ha: mu > mu0 (one sided test)

The application allows varying the parameters for calculating power:

• mu0: sample mean under null;
• mua: sample mean under alternative;
• sigma: standard deviation;
• n: sample size;
• alpha: type I error rate.

library(ggplot2)
mu0 <- 30
mua <- 32
sigma <- 4
n <- 16
alpha <- 0.05
myplot <- function(sigma, mua, n, alpha){
        g = ggplot(data.frame(mu = c(mu0-3, mu0+6)), aes(x = mu))
        g = g + stat_function(fun=dnorm, geom = "line", 
                              args = list(mean = mu0, sd = sigma / sqrt(n)), 
                              size = 2, col = "red")
        g = g + stat_function(fun=dnorm, geom = "line", 
                              args = list(mean = mua, sd = sigma / sqrt(n)), 
                              size = 2, col = "blue")
        xitc = mu0 + qnorm(1 - alpha) * sigma / sqrt(n)
        g = g + geom_vline(xintercept=xitc, size = 3)
        g
    }
power <- pnorm(mu0 + qnorm(1-alpha)* sigma/sqrt(n), mean= mua, sd = sigma/sqrt(n), lower.tail = FALSE)         

This presentation is part of the project for the Developing Data Products at Coursera.

The Shiny application described here is available at: https://cogabi.shinyapps.io/StatisticalPower/

The server.R and ui.R source code can be found on github at: https://github.com/Cogabi/developingdataproducts

Thank you!