shiny_sampling {ABACUS}

Shiny App to Explore Properties of Sampling Distributions

Description

An interactive Shiny app to demonstrate properties of the sampling distributions.

Usage

shiny_sampling()

Details

The interactive Shiny app demonstrates the properties of the sampling distribution. The true population parameter values of the Normal distribution are provided by the user. The user draws many samples from the population with the given sample characteristics and explore the variability of sample means. The app also includes the construction of 95% confidence interval for all samples. Altering the population and sample characteristics, the user can explore the influence of these changes on the sampling distribution.

The left panel includes the user inputs for Simulation Features, Population Parameters, Sample Characteristics and Distribution Function. To use the app at first instance, just click the Update button. To alter the input values, edit the text box or move the point on the slider and explores the changes in different tabs (see below).

To obtain identical outcomes in a separate run of the app, set a common seed value at the bottom of the left panel and click Update. All subsequent updates will produce identical results provided other inputs are identical. The seed value is ignored when the option check the box to update instantly is selected.

Value

The outcomes are presented in several tabs.

Population & Sample

contains the density plots of the population and dot plot of the sample units for the first sample randomly drawn from the population. It also includes the population parameter values are chosen by the user as well as estimates of sample mean and standard deviation based on the first sample.

Sampling Distribution

contains a panel of 8 dot plots based on the sample drawn randomly from the population with given parameters. Each plot depicts the mean and standard deviation of the random sample.

Sample Estimators

contains the histogram of the observed sample means and the empirical distribution of sample means. It also includes the rug plot of all sample means.

Confidence Interval

contains the plot showing the 95% confidence intervals (CI) of all samples. The plot shows the true population mean as a red horizontal line. It also provides the exact number of these estimated CI that include the true population mean.

Summary

includes the summary of the sampled data and outcomes from the one-sample z-test. Different sections are: (1) Sample, tabulating the full sampled data; (2) Sample Distribution, highlighting the expection of sample mean and sample standard deviation as well as standard error of mean; (3) Confidence Interval, showing the concept of 95% confidence intervals (CI) of mean.

Note

https://shiny.abdn.ac.uk/Stats/apps/

Also note that under the central limit theorem, the distribution of the sample means will follow normal distribution whatever the distribution of the variable in the population.

Author(s)

Mintu Nath

See Also

Function in base R for normal distribution including dnorm, pnorm, qnorm, rnorm, sample.

Examples

if(interactive()){
    library(ggplot2)
    library(shiny)
    library(ABACUS)
    # Run shiny app
    shiny_sampling()
}