MathBench > Statistical Tests

Chi-square Tests

Detour stop #3: what's a "df"?

On the last page, I said you should look up the chi-square-crit under "number of rows minus one". Why?

When I told you that 42 out of 100 sick days were on Mondays or Fridays, you automatically knew that 58 had to be in the middle of the week, right? I was "free" to specify how many were on Monday/Friday, but then I was NOT "free" to decide how many were on non-Monday/Friday. So we say that, in this problem, there is only 1 degree of freedom.

Say you flip a coin 100 times. If we want to do a chi-square test to determine whether a coin is fair (lands equally on heads and tails), how many degrees of freedom would the test have?

 

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

I think I have the answer: There are two variables here -- number of
heads and number of tails. But only 1 is free to vary -- once I tell you
how many heads there were, you know how many tails there were,
or vice versa.

 

It is possible to do chi-square tests using more than 2 variables. For example, let's say I got data on how many sickdays fell on EACH of the five weekdays:

day observed expected
mon 22 20
tues 19 20
wed 19 20
thurs 20 20
fri 20 20

We could do a chi-square test to check whether the distribution of sick days matched our expectations for ALL FIVE weekdays

How many degrees of freedom would this test have?

 

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

I think I have the answer: Once I know how many sickdays occurred
on 4 of the 5 days, the fifth day is no longer "free" to vary.
Therefore there are only 4 degrees of freedom.

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