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Topic: [ap-stat] work shown for chi-square
Replies: 1   Last Post: Dec 19, 2008 12:59 PM

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Dave Bock

Posts: 6,540
Registered: 12/6/04
Re: [ap-stat] work shown for chi-square
Posted: Dec 19, 2008 12:59 PM
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On Dec 19, 2008, at 12:11 PM, Skerbie wrote:

> What work is expected of students in a chi-square significance test?
> Can they just write the following:
> X^2 = sum((O-E)^2/E) = 13.95, df = 12, p = 0.3039, etc.,
> or do they have to show each individual component?
>
>
> Also, in checking the conditions, do they actually need to show a
> two-way table of observed values and/or a two-way table of expected
> values (particularly the latter), or can they just state "all
> expected counts are greater than 5"?



Here, as in all such situations, students must SHOW (not just state)
that they checked the conditions. That means (for example)
1) showing the histogram that supports the claim of approximate
normality;
2) showing the scatterplot that supports the claim of approximate
linearity;
3) showing the calculation that establishes np and nq are large enough;
4) showing the expected counts for chi-sq;
and so on.

I think students could get away with showing just the formula and
calculator result, but I always recommend they actually substitute
the values as an insurance policy. When pushing a wrong button leads
to the wrong calculated value, as a Reader I can't be sure the
student really knew what was going on unless I see something
convincing on the page. Every gory detail isn't necessary, but
something like this (with just a couple of terms) really helps:
X^2 = (12 - 11.37)^2/11.37 + (18 - 22.43)^2/22.43 + ....
If that much is correct, I can forgive "answers" that may be wrong
(but reasonable).

- Dave



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