# Re: st: Chi-square test with probabilities

 From Christoph Merkle To statalist@hsphsun2.harvard.edu Subject Re: st: Chi-square test with probabilities Date Tue, 11 Nov 2008 20:11:40 +0100

```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.

Ronan Conroy
=================================

rconroy@rcsi.ie
Royal College of Surgeons in Ireland
Epidemiology Department,
Beaux Lane House, Dublin 2, Ireland
+353 (0)1 402 2431
+353 (0)87 799 97 95
+353 (0)1 402 2764 (Fax - remember them?)
http://www.flickr.com/photos/ronanconroy/sets/72157601895416740/

P    Before printing, think about the environment

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```

Christoph Merkle

Center for Doctoral Studies in Business
GESS - University of Mannheim
Schloss, Room M 114
68161 Mannheim
Germany
Phone: +49-621-1813774
E-mail: chmerkle@rumms.uni-mannheim.de

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