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RE: st: Chi-square test with probabilities


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Chi-square test with probabilities
Date   Tue, 11 Nov 2008 19:48:18 -0000

What makes you think this is a chi-square problem? 

If you can supply a standard error for each probability then at a
stretch each probability can be represented as z = (observed - expected)
/ se and the sum of those z-squareds might seem like a chi-square
statistic losing 1 d.f. for the constraint that probabilities add to 1
and more if anything is estimated from the data. 

So where are your standard errors coming from? 

My gut feeling, set down before Maarten Buis says something similar, is
that you would be better setting up (a) one or more measures of
discrepancy and (b) a model specifically for your problem and getting
sampling distributions by simulation. 

Nick 
n.j.cox@durham.ac.uk 

Christoph Merkle

I have to clarify this a bit:

The probabilities indeed add up to one, participants were made aware  
of to obey this rule. And if there were still some errors I corrected  
for those.
They actually had to estimate with which probability a value falls in  
a certain quartile/decile of a distribution.

My claim is not 'humans overestimate the chances of rare events  
happening' but rather 'humans violate the rules of Bayesian updating".  
Therefore ttests for the mean guessed probability compared to expected  
probability for quartiles/deciles one by one are fine for a start (and  
I calculated them already), but better would be to analyze the whole  
distribution.
That is why I proposed a chi square goodness of fit test.

I'm not an expert in repeated measure design, but I don't think it  
helps me out here.

Zitat von Ronan Conroy <rconroy@rcsi.ie>:

> On 11 Nov 2008, at 17:19, Christoph Merkle wrote:
>
>> Actually I'm only interested if the mean of these peobabilities over
>> participants is different from hyposized proportions. If I use a
>> simple ttest I can only test each of the variables one by one. But I
>> want to test the distribution over the ten
>
> If the events are mutually exclusive and collectively exhaustive, then
> the probabilities ought to add up to 1, but I fear that they won't.
>
> I think you are better testing one-by-one, using a t-test to test the
> hypothesis that the mean guessed probability is the same as the actual
> value, unless you have a hypothesis that is independent of the
> probability being guessed (such as 'humans overestimate the chances of
> rare events happening') in which case, I would treat it as a repeated
> measures design.

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