.- help for clt Central limit theorem demonstration .-The programs clt is designed to illustrate the Central Limit Theorem.

clt allows you to take a given number of samples of size n from a given distribution and show the distribution of sample means.

After you invoke clt, a dialogue box is shown allowing you to make the following choices regarding how the data is sampled.

Distribution Type Normal - A normal distribution. Log normal - Log of a normal distribution. Exp normal - Exponential of a normal distribution. Exponential - Exponential of a uniform distribution Bimodal - Two normal populations with means 3 units apart that are added together Binomial - A 0/1 variable. If you choose this, you can use the If Binomial, P= pulldown to choose the probability of a 1 occurring. Uniform - A uniform distribution.

If Binomial, P= If you draw from a binomial distribution, you can use the p() option to specify the probability of success. The default is .5 .

N per sample Allows you to choose the sample size, default is 1.

# of Samples Allows you to choose how many samples are drawn, default is 1000.

You can also make the following choices regarding how the graph of the sampling distribution is displayed.

Show Normal Overlay Includes a normal overlay on the histogram.

Draw Lines as +-1SD and +-2SD Draws lines at xbar - 2sd xbar - 1sd xbar xbar + 1sd xbar + 2sd

Show means as Z scores Shows the X axis as Z scores, helping you to see skewness in the data.

Show sums instead of means Shows the values on the X axis as the sum of the scores in the sample (rather than the mean). This is useful when the distribution is binomial.

Show distribution being built This shows the sampling distribution being built, rather than just showing the final product. You can control the samples per step and the delay between steps.

After you have made your selections, you can click the show button and the results are calculated and displayed. If you choose a large number of samples (say over 3000), then there may be a delay while the samples are drawn.

When you want to exit the program, click on the done button.

Author ------

Statistical Consulting Group Institute for Digital Research and Education, UCLA idrestat@ucla.edu