Table of Contents

• 1: Do those shoes fit?
• 2: Dilbert's 3 day work week
• 3: The day is saved ... or not
• 4: What you observe vs expect
• 5: The Chi-squared Equation
• 6: Give it a try
• Detour
• 7: What's a p-value?
• 8: What's a Lookup Table?
• 9: What's a "df"?
• Completing the Chi-squared Test
• 10: Interpreting a chi-squared
• 11: The answer, finally
• 12: Summary
• 13: What about 90% M/F sick days?
• 14: What about 50% M/F sick days?
• Chi-squared in Biology
• 15: Testing for a dihybrid ratio
• 16: Review and Words of Wisdom

Review and Words of Wisdom

Chi-squared steps

1. Decide on a null hypothesis -- a "model" that the data should fit

2. Decide on your α value (usually 0.05).

3. Note your "expected" and "observed" values

4. Calculate the chi-squared statistic [add up (o-e)2 / e ]

5. Look up the chi-squared critical value based on your α value and degrees of freedom (df=rows-1). Determine whether chi-squared statistic < chi-squared critical value. If so, we say the model fits the data well.

 

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

Usually your null model is that "chance alone" is responsible for any patterns in the observed data. For example, the 9:3:3:1 ratio for a dihybrid cross is what happens by chance alone, given that you are mating two dihybrids.

This step (#1) also encompasses setting up your chi-squared table or your simulations. For the chi-squared table, you need to think in terms of how many 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-squared table is just a matter of arithmetic.

Summary

In this module you have:

• An overview of the statistical test, the chi-squared test
• Calculated the test statistic associated with the chi-squared
• Made some conclusions about a set of data using the chi-squared test.

 

 

 

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.