Table of Contents

• Prequiz...
• 1: Do those shoes fit?
• 2: Dilbert's 3 day work week
• 3: The day is saved . or not
• 4: The Brute Force method
• 5: Computer = brute force
• 6: What's your threshold for pain?
• 7: Sick-day sistribution
• 8: A brief recap of the Brute Force Method
• 9: The Brute Force method again
• 10: Using arithmetic instead of Brute Force
• 11: One small correction
• 12: How big is big?
• 13: Degrees of Freedom
• 14: The magic lookup table
• 15: The answer, finally
• 16: Summary of chi-square
• 17: Another example for chi-square
• 18: So, which method do you like better?
• 19: Applications
• 20: Example 1: Testing for a dihybrid ratio
• 21: Example 2: Habitat selection (ecology)
• 22: Review and Words of Wisdom

The problem with Brute Force...

is that you either have to have a lot of patience or a degree in programming. Luckily, there is an easier way to test goodness of fit, at least for simple questions.

[Note from the management: If you've already read the Chi-square module (and you remember it), you can skim through this section quickly. ]

What we want to do is test how far apart the "observed" and "expected" answers are, right? So a logical first step is to subtract one from the other -- that tells us how different they are.

	observed	expected	difference (obs - exp)
Mon/Fri	42
Midweek	58

Then we want to know how important this difference is. Is it big compared to what we expected, or small? To compare the size of two numbers, you need to find a ratio -- in other words, use division. You need to find out how big the difference is compared to the number you expected to get. So, divide the difference (between the observed and expected) by the expected value:

	observed	expected	difference (obs - exp)	relative deviation: (difference compared to expected )
Mon/Fri	42	40	+2
Midweek	58	60	-2

The last column in the table above show the magnitude of deviations. If we ignore the negative signs and add them up, we have a way of measuring the TOTAL deviation for all the data, in this case . Big deviations would mean that we probably have the wrong explanation, whereas small deviations would probably mean we're on the center track. Since we're tying to show that sickdays are RANDOM, big deviations are bad for our case, while small deviations are good for our case.