A "Begin" button will appear on the left when the applet is finished loading. This may take a minute or two depending on the speed of your internet connection and computer. Please be patient.

Press the "Begin" button to start the applet in another window.

After you press the "begin" button, the applet displays a window that shows the expected frequencies for each of 10 intervals based on a sample size of 100. The left side of the window shows the frequencies expected if the distribution being sampled is normal. Notice that the distribution is symmetric with higher expected frequencies for the middle intervals than for the tails. The sum of the expected frequencies is 100. On the right side are shown the expected frequencies if the distribution being sampled is uniform. The expected frequency is the same (10) for each interval.

By default, the applet samples from a normal distribution. Press the "sample" button and 100 samples will be taken and the frequencies for each of the intervals computed and displayed as the observed frequencies. Deviations from the expected frequencies are computed for the expected frequencies based on the normal and based on the uniform distribution. Since the samples are from a normal distribution, the observed frequencies should be closer to the expected frequencies based on a normal distribution than based on a uniform distribution.

For each distribution, a Chi Square
test is performed to test whether the observed frequencies differ significantly
from the expected frequencies. Computationally, this is done by computing (E-O)^{2}/E
for each interval and summing the results (E is the expected frequency and O
is the observed frequency). Most likely, the test will be not show a significant
difference for the normal distribution and will show a highly significant difference
for the uniform distribution. Of course, by chance, your results may vary.

You can choose to sample from a uniform distribution by clicking on the radio button on the left side of the window. You then expect to get a significant difference from the normal expected frequencies and not from the uniform expected frequencies.

The simulations were developed as part of a grant from NSF to David Lane of Rice University. Partial support for this work was provided by the National Science Foundation's Division of Undergraduate Education through grant DUE 9751307. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.