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.
(obs - exp)
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 )|
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.
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