Many of your projects will involve involve small numbers. When using small numbers the use of the normal curve to find confidence intervals and determine whether to reject or accept an hypothesis is not necessarily a good idea. Hence I am providing you with some computational tools to help you accurately report and deal with small numbers.
Perhaps the most important is to be able to accurately compute the confidence you have about a percentage you wish to quote. This program will allow to explore the reportable confidence for your given number samples as you vary the choice of confidence interval. It will also provide you with a picture which may help you and any reader of your work to understand where this computation came from and why they should put faith in it. It is based on using our good friend the binomial distributions.
The next most important tool will likely be your ability to test an hypothesis (new and improved!). Many common tests (like the chi-squared test) will not work well if when testing a single hypothesis and are rather inaccurate when using small amount of data. Here we give a way to explore the chance that a given measurement is due to chance alone, given the acceptance a null hypothesis. It also provides a picture so that you may easily remind your readers why they should put faith in your methodology. Once again this test is based on using our good friend the binomial distributions.
Here is a program allowing you to compete hypothesis against each other.
Excel does not produce nice histograms with out some effort. This maple program does a pretty good job ,and will help you confirm some of the numbers which arise when looking at a single set of data.
Excel does a better job at producing scatter plots . This maple program however will fuzz out the data and will be particularly useful if you data contains lots of repeated information. Once again it may also will help you confirm some of you numerical suspicions.
Here is a program to help you understand steaks and run large numbers of streak experiments to compare empirical data.
Here is program allowing you to simulate your own probability distribution. This will help you compare what you believe is going on with some actual data produced given this belief.
Here is a program allowing you to use the slightly more involved chi-square test (corrected 11/28/01). This program does involve an approximation and for small amounts of data may not be accurate. If you use this test and any of the "classes" involved have less than five members or there are only two classes you must warn your reader that this test is known to be inaccurate when applied in such a setting. Otherwise it is a test you are free to simply use it.
Here is a program that probably will not help you deal with non-linear correlations, but if you see me together we can probably get it to do so!