lessR (version 2.2)

sim.CLT: Pedagogical Simulation for the Central Limit Theorem

Description

Show the distribution of sample means and relevant summary statistics, such as the 95% range of variation. Provide a plot of both the specified population and the corresponding distribution of sample means.

Usage

sim.CLT(ns, n, p1=0, p2=1,
         type=c("normal", "uniform", "lognormal", "antinormal"),
         col.fill="lightsteelblue3", n.display=2, dig.dec=3, 
         subtitle=TRUE, pop=TRUE, graphics.screen=TRUE, ...)

Arguments

ns

Number of samples, that is, repetitions of the experiment.

n

Size of each sample.

p1

First parameter value for the population distribution, the mean, minimum or meanlog for the normal, uniform and lognormal populations, respectively. Must be 0, the minimum, for the anti-normal distribution.

p2

Second parameter value for the population distribution, the standard deviation, maximum or sdlog for the normal, uniform and lognormal populations, respectively. Is the maximum for the anti-normal, usually left at the default value of 1.

type

The general population distribution.

col.fill

Fill color of the graphs.

n.display

Number of samples for which to display the sample mean and data values.

dig.dec

Number of decimal digits to display on the output.

subtitle

If TRUE, then display the specific parameter values of the population or sample, depending on the graph.

pop

If TRUE, then display the graph of the population from which the data are sampled.

graphics.screen

If TRUE, then display the graphs on the screen.

...

Other parameter values for R function lm which provides the core computations.

Details

Provide a plot of both the specified population and the corresponding distribution of sample means. Include descriptive statistics including the 95% range of sampling variation in raw units and standard errors for comparison to the normal distribution. Also provide a few samples of the data and corresponding means.

Four different populations are provided: normal, uniform, lognormal for a skewed distribution, and what is called the anti-normal, the combining of two side-by-side triangular distributions so that most of the values are in the extremes and fewer values are close to the middle.

For the lognormal distribution, increase the skew by increasing the value of p2, which is the population standard deviation.

The anti-normal distribution requires the triangle package. No population mean and standard deviation are provided for the anti-normal distribution, so the 95% range of sampling variable of the sample mean in terms of standard errors is not provided.

Examples

# plot of the standardized normal 
#  and corresponding sampling distribution with 10000 samples
#  each of size 2
sim.CLT(ns=10000, n=2)

# plot of the uniform dist from 0 to 4
#  and corresponding sampling distribution with 10000 samples
#  each of size 2
sim.CLT(ns=10000, n=2, p1=0, p2=4, type="uniform", bin.width=0.01)