Repeated Sampling App

The user can adjust:

• Number of repeated samples (2, 4, or 9)

• The size of each sample (n = 2 to n = 10)

• The characteristics of the population from which data are sampled (this is a beta distribution; the parameters are labeled "moves right" and "moves left")

Some notes on what makes this app different from most "sampling distribution" apps:

• The three plots on the bottom show values of a statistic under repeated sampling, but these are not sampling distributions or even approximations to sampling distributions, because the number of repeated samples is finite and very small.  

• Sampling distributions are intangible and can be challenging to understand.  Most apps demonstrate sampling distributions using histograms; to understand these the user must understand the fundamental connection between distributions of data and distributions of statistics.  The goal of this app is to make that connection; this is why the number of repeated samples is small and the statistics are plotted as lines or dots.

• There are three different statistics being plotted: means, maximums, and standard deviations.  Most explanations and demonstrations of sampling distributions use only the sample mean.  It is easier to grasp the concept of "repeated sampling" is it it demonstrated for different statistics that have different behaviors: 

  • The means tend to end up near the center of the population distribution; these are plotted as solid vertical lines.

  • The maximums tend to end up near the right end of the population distribution; these are plotted as dashed vertical lines.

  • The standard deviations reflect the spread of the population distribution; these are plotted as horizontal lines

• Each value of each statistic is plotted on its respective data plot, and on its "repeated sampling" plot.  This helps the user connect the values in the plots of statistics to the samples of data from which they were calculated.