mean_vs_median {smovie}

Sample mean vs sample median

Description

A movie to compare the sampling distributions of the sample mean and sample median based on a random sample of size n from either a standard normal distribution or a standard Student's t distribution. An interesting comparison is between the normal and Student t with 2 degrees of freedom cases (see Examples).

Usage

mean_vs_median(
  n = 10,
  t_df = NULL,
  panel_plot = TRUE,
  hscale = NA,
  vscale = hscale,
  n_add = 1,
  delta_n = 1,
  arrow = TRUE,
  leg_cex = 1.75,
  ...
)

Arguments

n

An integer scalar. The size of the samples drawn from a standard normal distribution.

t_df

A positive scalar. The degrees of freedom df of a Student t distribution, as in TDist. If t_df is not supplied then data are simulated from a standard normal distribution.

panel_plot

A logical parameter that determines whether the plot is placed inside the panel (TRUE) or in the standard graphics window (FALSE). If the plot is to be placed inside the panel then the tkrplot library is required.

hscale, vscale

Numeric scalars. Scaling parameters for the size of the plot when panel_plot = TRUE. The default values are 1.4 on Unix platforms and 2 on Windows platforms.

n_add

An integer scalar. The number of simulated datasets to add to each new frame of the movie.

delta_n

A numeric scalar. The amount by which n is increased (or decreased) after one click of the + (or -) button in the parameter window.

arrow

A logical scalar. Should an arrow be included to show the simulated sample maximum from the top plot being placed into the bottom plot?

leg_cex

The argument cex to legend. Allows the size of the legend to be controlled manually.

...

Additional arguments to the rpanel functions rp.button and rp.doublebutton, not including panel, variable, title, step, action, initval, range.

Details

The movie is based on simulating repeatedly samples of size n from either a standard normal N(0,1) distribution or a standard Student t distribution. The latter is selected by supplying the degrees of freedom of this distribution, using t_df. The movie contains three plots. The top plot contains a histogram of the most recently simulated dataset, with the relevant probability density function (p.d.f.) superimposed. A rug is added to a histogram provided that it contains no more than 1000 points.

Each time a sample is simulated the sample mean and sample median are calculated. These values are indicated on the top plot using an arrow (if arrow = TRUE) or a vertical (rug) line on the horizontal axis (arrow = FALSE), coloured red for the sample mean and blue for the sample median. If arrow = TRUE then the arrows show the positionings of most recent mean and median in the two plots below. If arrow = FALSE then the rug lines are replicated in these plots.

The plot in the middle contains a histogram of the sample means of all the simulated samples. The plot on the bottom contains a histogram of the sample medians of all the simulated samples. A rug is added to these histograms provided that they contains no more than 1000 points.

Once it starts, three aspects of this movie are controlled by the user.

• There are buttons to increase (+) or decrease (-) the sample size, that is, the number of values over which a maximum is calculated.

• Each time the button labelled "simulate another n_add samples of size n" is clicked n_add new samples are simulated and their sample mean are added to the bottom histogram.

• For the N(0,1) case only, there is a checkbox to add to the bottom plot the p.d.f.s of the distribution of the sample mean and the (approximate, large n) distribution of the sample median.

Value

Nothing is returned, only the animation is produced.

See Also

movies: a user-friendly menu panel.

smovie: general information about smovie.

Examples

# Sampling from a standard normal distribution
mean_vs_median()

# Sampling from a standard t(2) distribution
mean_vs_median(t_df = 2)