[Blindmath] (no subject)

Tue Sep 15 00:18:18 UTC 2009

Hi,
  First, thank you sincerely for the information. A slight clarification, 
and maybe this will make my reasoning for using this analysis a little 
better,or potentially a lot worse. I am open to any arguments either way as 
I am always eager to learn.

  What I am actually attempting to do is to see if  removing one parameter 
from a 4-parameter model will yield a null result when compared to the 
4-parameter model. Variance testing (e.g., ANOVA results) with the data 
suggest that holding one particular parameter constant does not change the 
results. Thus, I am planning to use the statistic to essentially demonstrate 
that allowing the additional parameter to vary yields no changes in  the 
data.
Many thanks,
Chris

Christine M. Szostak
Graduate Student
Language Perception Laboratory
Department of Psychology, Cognitive Area
The Ohio State University
Columbus, Ohio
szostak.1 at osu.edu
----- Original Message ----- 
From: "Jonathan Godfrey" <a.j.godfrey at massey.ac.nz>
To: "Blind Math list for those interested in mathematics" 
<blindmath at nfbnet.org>
Sent: Monday, September 14, 2009 4:56 PM
Subject: Re: [Blindmath] (no subject)

> Hi Christine et al,
>
> I have several comments and concerns and then the details below.
>
> First your question about accessibility to information is well directed in 
> terms of sending it to this list. My problem is that the reason for asking 
> the question is in my opinion misguided on statistical grounds.
>
> A quote often attributed to George Box goes something like "All models are 
> wrong, but some are useful." It's usually misquoted (including here) and 
> was actually first published in a NASA report before it appeared in a Box 
> article.
>
> A chi-square test can tell you if a model is useful - well more exactly it 
> will tell you if it is not useful. This is a direct consequence of the way 
> we do hypothesis tests.
>
> Having decided that two or more models are useful though, the chi-square 
> test becomes irrelevant for deciding which model is the one to use. You 
> must have other reasons for even considering various models and their 
> usefulness to your situation. To go back to the Box quote, you might find 
> out that two models are actually valid and useful. You then need to ask if 
> they yield differing results in terms of what you want to do with them. If 
> they don't differ then it probably doesn't matter which one you use. If 
> they do differ then you have a problem with choosing the one to apply on 
> the grounds of the assumptions made behind each model (and there are 
> always assumptions).
> Ultimately we do not want our opinion to depend on the assumptions we 
> make.
>
> Now to remind you of the basics of chi-square testing.
>
> 1. Under any model, you should know how many observed values fall into 
> well defined classes. In situations where you are counting things then 
> this is easy. If the response is continuous then you must be careful 
> determining the cutoffs between the classes.
> 2. You must now consider how many observations you would expect to fall 
> into each of the classes defined in step 1.
> 3. If any of the classes have expected values less than 5, you will need 
> to merge classes. This normally occurs at the extremes. Merge until all 
> expected values are >=5. Of course you will need to merge the observed 
> counts as well to match.
> 4. The chi-square value is the sum of (O-E)^2/E where O is observed (step 
> 1) and E is expected (step 2).
> 5. This should follow a chi-square distribution with n-p-1 degrees of 
> freedom. n is the number of classes after merging, p is the number of 
> parameters you estimated under each of your models.
> 6. Either
> 6a. Using some software (EXCEL will do) find the p-value for the 
> chi-square test statistic found in step 4, compare this to the 
> pre-determined level of significance you are happy with - normally 0.05 is 
> applied. If your p-value is less than 0.05 then your model is not useful.
> or
> 6b. determine the critical value for the chi-square distribution with the 
> right degrees  of freedom found in step 5. If your test statistic is >= 
> critical value then your model is not useful.
>
> Jonathan
>
>
>
>
>
>
> At 04:29 a.m. 11/09/2009, you wrote:
>>Hi All,
>>   Do any of you happen to know where I might be able to obtain 
>> speech-software friendly information on running a Chi Square Analysis 
>> (e.g., the actual statistics involved). It has been a long time since I 
>> have done such an analysis and I need to do so to compare which of a few 
>> mathematical models provides a best-fit to some behavioral data I have 
>> collected in Cognitive Psychology.
>>Many thanks,
>>Christine
>>Christine M. Szostak
>>Graduate Student
>>Language Perception Laboratory
>>Department of Psychology, Cognitive Area
>>The Ohio State University
>>Columbus, Ohio
>>szostak.1 at osu.edu
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> _____
> Dr A. Jonathan R. Godfrey
> Lecturer in Statistics
> Institute of Fundamental Sciences
> Massey University
> Palmerston North
>
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