# mean_vs_median: Sample mean vs sample median In smovie: Some Movies to Illustrate Concepts in Statistics

 mean_vs_median R Documentation

## 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,
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.

`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)
``````

smovie documentation built on May 29, 2024, 10:28 a.m.