Purpose: The purpose of this program is to facilitate the comparison between a standard normal distribution and the sampling distribution of the mean for the sample size specified by the user.

Download: You can download this program from within Stata by typingsearch sdmdemo(see How can I use the search command to search for programs and get additional help? for more information about usingsearch).

Use of program: To use this program, typesdmdemoin the Stata command window. A dialogue window will open that allows the user to add or subtract one from the sample size (N) by clicking on the appropriate button. Thesdmdemocommand also opens a Stata graph window showing a graph of a normal distribution in yellow and the sampling distribution in red. In this graph, the sampling distribution is overlaid on the normal distribution because by default N = 1. The user can increase or decrease the sample size by clicking on the "N + 1" or "N – 1" buttons. Clicking on the "show movie" button in the dialogue window will show a "movie" in which the mean of the sampling distribution is increased from one to 25. A pull-down menu allows the user to control the speed of the frames of the movie. This can be done by clicking on the down-arrow to the right of "delay = ". The higher the number, the slower the movie. To exit the program, click on the "done" button.

Examples: The following shows the output from issuing thesdmdemocommand.

The following example shows the results of increasing the sample size to three. Notice that increasing the sample size results in a steeper curve.

The following example shows the results of increasing the sample size to fifteen. Notice how the distribution is becoming "tighter" around the mean.