Sampling distribution

Sampling distribution

(after an idea of  David M. Lane)

For information about an unknown population, you need to draw samples.

The data you collect with random samples are the data from which to estimate measures of central tendency and spread of a population. These estimates have a degree of unreliability due to random variation in the sample data. Such unreliability will be smaller if larger samples are taken. But in practice this always means an increase in costs.

This module provides insight into the process of drawing samples and a summary of the results obtained from those samples in the sampling distribution.

You can set the sampling process in different ways and carry out the animation implemented gradually or rapidly.

The population

You can select from different populations. The distribution and key figures of the population are shown. There are seven predefined distributions. You may drag the mouse and sweep each distribution to your own liking. An "own" distribution can also be saved.

Populations may be normal, skewed left, skewed right, exponential, have two-summits or a V-shape and can be taken as populations of measured data.

In addition, there is a distribution with proportions. Think of a population with people who are in favor or against. This distinction is indicated by the colors red and green. In using random numbers often the values 0 and 1 will be chosen. See the module Random generator. At proportions involve discrete values, so the distributions look different.

If you change a population with the mouse the changes apply automatically to all key figures.

The sample

Sample size and the number of samples can be set.

A gradual animation shows how a sample is created (red dots) and then how the statistic of that sample is displayed as a blue ball in the bottom graph.

Default is set to the average. But in the sampling distribution you can select other statistics such as median, standard deviation, etc.

A fast simulation provides insight into the structure of the sampling distribution.

In a distribution of proportion you may notice that the sampling distribution is a binomial distribution.

You can compare the result in the section Distributions> Binomial distribution.

The sampling distribution

The sampling distribution shows the distribution of a statistic of all samples. You can select different statistics on center and spread. Default setting is the average and in the proportion distribution the value of green.

The theoretical sampling distribution is a limiting distribution, but it soon becomes clear when a reasonable number of simulations is performed.

It is surprising to see is that the sampling distribution of the average will become a normal distribution whatever the population distribution may be.

Center and Spread

Above on the right you can switch on the mean, median and some intervals of spread for display purposes.

The goal is to monitor these statistics during the simulation, both for population and for sample.

Regarding the sampling distribution, this option should be used with care.

Other sampling simulations

This simulation demonstrates the properties of sampling distributions.

In VUstat are more modules to draw samples from populations that you create yourself.

See the section Simulations:

- Ball pool

- Random generator

- Sampling

- Random rain

In the Data analysis module you can draw samples from a dataset.

There are two options:

- Data > A single random draw

- Data > Many random draws

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Source: http://onlinestatbook.com:80/stat_sim/sampling_dist/index.html

Rice Virtual Lab in Statistics