Re: chi-square test goodness of fit

From: D. Touie (dtouie_at_tscnet.com)
Date: 01/04/05 

Date: Tue, 04 Jan 2005 07:12:03 GMT

On Mon, 03 Jan 2005 11:35:49 -0500, Bruce Weaver
<bweaver@lakeheadu.ca> wrote:

>D. Touie wrote:
>
>> On Thu, 4 Nov 2004 12:54:08 -0000, "Alexis Gatt"
>> <alexismajordomo@yahoo.co.uk> wrote:
>>
>>
>>>Hi guys,
>>>
>>>I have a very basic question regarding the goodness-of-fit statistic
>>>chi-square. The chi-square measure between the observed data and those given
>>>by the model I implemented equals 24, and there is 28 degrees of freedom.
>>>According to a chi-square table I found in a book, the equivalent
>>>probability value is between 0.5 and 0.75.
>>>
>>>And this is where I am confused. Does this mean that the model predict the
>>>data well or not? And why?
>>>
>>>Many thanks
>>>
>>>Alexis
>>
>>
>> I apologize for being so late with this response. I only now noticed
>> your original posting.
>>
>> I do not agree with Bruce Weaver's response to you.
>
>My response was:
>
>"Pearson's chi-square is based on the discrepancy between Observed and
>Expected frequencies. The more O and E differ, the larger the
>chi-square value becomes, and the smaller the p-value becomes.
>Therefore, smaller values of chi-square (and larger values of p)
>represent better fits."
>
>What do you disagree with? I was not suggesting that smaller values of
>chi-square and larger values of p *than reported by the OP* represent
>good fits. It was simply a general statement: the smaller the value of
>chi-square (and the larger the value of p), the better the fit.

You seem to believe Pearson's Chi-square is a one-sided measurement
construct. It is two-sided. A probability of .01 is the same as a
probability of .99. These two probabilities usually have a different
causality, but the exact same probability meaning.

I think part of the confusion here is the traditional misnomer
"expected" value. It could more properly be described as a
"comparative" value.

For instance, if I flip a fair coin 100 times and record the outcomes
faithfully, I do not "expect" 50 heads and 50 tails to result. That
would be an unexpectedly rare result. What I would expect is about 45
heads and 55 tails to result, or equally 45 tails and 55 heads.

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