MathBench > Statistical Tests

Goodness of Fit Tests

Computer = brute force

If you have clicked the button a few times, you've seen that the results vary quite a bit. Here are the first ten results that I got:

Trial #: 1 2 3 4 5 6 7 8 9 10
Mondays/Fridays 43 33 37 47 40 37 39 41 41 51

What have we accomplished so far? First, we made a hypothesis about what causes sickdays -- namely, they happen on randomly chosen days. The competing hypothesis, held by the pointy-haired boss, is that sickdays occur disproportionately on Mondays and Fridays.

First step: pick a hypothesis
dilbert says: nobody chosses when to get sick -- it just happens, it's random.
boss says: That's not true! I bet I can prove they are planing fishing trips on Fridays!

Secondly, we calculated how many sickdays "should" fall on Mondays or Fridays according to our hypothesis -- that is, 40%, or 40 out of 100. This is the expected value of sickdays. But since we're dealing with a random process, we also expect some scatter around that expected value. The key question is, how much scatter?

Second step: calculate the expected result
dilbert says: If people het sick randomly, we would expect 40 ou of 100 sickdays to be on Monday or Friday!
boss says: huh?

Next we used a simulation of randomly chosen weekdays to investigate how much scatter to expect around the 40 out of 100 prediction.

Third step: simulate the scatter
dilbert says: Let's see if the value we observed was unusual...
boss says: Look I've got my fingers in my ears, I'm not listening, la la la-la!

In the 10 trials, listed above, how common was it to get 42 or more Monday/Friday sickdays?


(To make this problem interactive, turn on javascript!)

I think I have the answer: 3 out of 10 trials had at least 42 Mon/Fri sickdays,
or 30%, which seems pretty common.

Time for a donut break!