MathBench > Statistical Tests

Goodness of Fit Tests

Review and Words of Wisdom

The following table compares the steps necessary for the two types of goodnes-of-fit models in this module. I changed the tables a little from those given earlier, to emphasize the similarities between the two tests.



1. Decide on a null hypothesis -- a "model" that the data should fit 1. Decide on a null hypothesis -- a "model" that the data should fit
2. Decide on your p-value (usually 0.05). 2. Decide on your p-value (usually 0.05).
3. Note your "expected" and "observed" values 3. Note your "expected" and "observed" values
4. Simulate lots of data 4. Calculate the chi-square [add up (o-e)2 / e ]
5. Determine whether the agreement of the simulated data with the observed data falls within the threshhold -- if so, we say the model fits the data well. 5. Look up the chi-square-crit based on your p-value and degrees of freedom (df=rows-1). Determine whether chi-square-calc < chi-square crit-- if so, we say the model fits the data well.


The hardest steps are 1 (deciding on your null model) and 3 (figuring out what you "expected" to see based on the null model).

Usually your null model is that "chance alone" is responsible for any patterns in the observed data. (However, either approach can also handle much more complicated null models, which just makes things more fun... But we didn't discuss non-random null models in this module).

This step (#1) also encompasses setting up your chi-square table or your simulations. For the chi-square table, you need to think in terms of how outcomes you have to test. Each of these becomes a row. Now you also know the degrees of freedom for your test, which is the number of rows minus 1.

Step #3, finding the expected values, often means doing some probability calculations, using the Laws of AND and OR.

Once you know the expected values, filling out the rest of the chi-square table is just a matter of arithmetic.

Now simulating the data, that's another story...

Now go back to the main menu and try your hand at the quiz!




If you want a printer-friendly version of this module, you can find it here in a Microsoft Word document. This printer-friendly version should be used only to review, as it does not contain any of the interactive material, and only a skeletal version of problems solved in the module.