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DISTANCE-SAMPLING  July 2008

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Subject:

Re: Z-test for density

From:

Nurul Winarni <[log in to unmask]>

Reply-To:

Nurul Winarni <[log in to unmask]>

Date:

Thu, 31 Jul 2008 02:11:34 -0700

Content-Type:

text/plain

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text/plain (155 lines)

Hi,
I'm referring to the last email on z-test.   I'm trying to do
the same, by comparing the density estimates of several birds (multiple
species) at two different levels of disturbance.  I used CDS with
post-stratification based on disturbance level and density was
estimated for each species.  In the distance book (Buckland et al 2001)
at page 353, there is  the z test calculation.  The example was from
fin whale survey and the z test tested the differences of mean size of
two different pods (cluster size).  Would that be a problem if I use
the same calculation to compare the density estimates at two
disturbance levels?  

Thanks.

Best,
Nurul
 Nurul Winarni
Email1. [log in to unmask]
Email2. [log in to unmask]
http://noonathome.wordpress.com/
http://wildlifewisdom.wordpress.com




----- Original Message ----
From: Jeff Laake <[log in to unmask]>
To: [log in to unmask]
Sent: Monday, June 23, 2008 11:06:58 PM
Subject: Re: [DIST-SAMP] Z-test for density

Sergio

You are confusing two different types of tests.  The one you describe is 
testing whether a sample mean is different from a population mean or 
whether it is different from a hypothesized value (eg. 0).  The other is 
testing whether two sample means differ from each other and this is the 
more common. The first is a one sample test and the second is a 2-sample 
test.  There are many different types of 2 sample tests.  They can be 
paired or non-paired samples and non-paired tests can assume a common 
variance or different variances.  The test we have been discussing is 
non-paired with different variances.  Also, note that the formula you 
gave for the one sample test was incorrect because the denominator 
should have been the standard error of the mean and what you wrote was 
the sample variance/ sqrt (n). It should have been sqrt(sample 
variance/n) which is the standard error of the mean.  On this point, the 
standard errors for density (from DISTANCE) are equivalent to the 
standard error of the mean and they are not standard deviations, so you 
do NOT divide the std error by the sqrt of n.  This often confuses 
folks.  For parameters (eg density) we use standard errors and not 
standard deviations.  A standard deviation describes the spread in the 
data and a standard error is the uncertainty about a parameter (eg 
mean).  The confusion comes from the fact that the standard error for a 
sample mean is the standard deviation divided by the sqrt of n.  That 
does not apply to all parameters and there is typically no relationship 
between the standard deviation (of the data) and the standard error of a 
parameter, except for a mean.

With regards to the contents of Snedecor and Cochran, my reference to it 
was a wry joke at myself because it is so old.  Any basic stats text 
should give the formula for the hypothesis test we described.  Len 
Thomas replied to me individually that my book (used) can be bought for 
$4.80 at
http://www.abebooks.com/.  Note that I'm not recommending either this 
site or book. 

On a related subject, for what you want to do you are probably less 
interested in hypothesis testing than you are in estimating differences 
in densities between various guild.  In the ecology and other fields 
there is a move away from hypothesis testing towards model selection.  
David Anderson or others may want to add more here.  Unfortunately, the 
current DISTANCE software does not provide a lot of options (at present) 
to represent the abundance data by models.  We have models for detection 
probability but the estimates of density are  based on sampling concepts 
and are not model based for most of the analysis techniques in 
DISTANCE.  I believe in one of the past list server messages Steve 
Buckland mentioned a paper that he and others have put together on 
analysis of experimental distance sampling data, so he may have more to 
contribute here.

regards --jeff


SERGIO . wrote:
> Dear All,
>  
> The equation:                               D^_1 - D^_2                            Z = -----------------------------------                                sqrt[{se(D^_1)}**2 + {se(D^_2)}**2]
>  
> that Claire Meid referes to in his email, it is not the classical z-test equation to compare a sample mean with the population mean. How can i cited this formula to compare density between guilds and/or habitats and how can i consider this a validated equation (aproximation of z-test?) for my bird census analysis?
>  
> The original formula at statistics books and statistics tests is this one:
>  
>                                           x - Uo
>                            Z =  ------------------
>                                      var / sqrt [N]
>  
> where x is a sample mean, Uo the population mean, var is the variance of the population and N is the sample size.
>  
> In the density case the N could be always the same so its not consider and i can use densities from 2 samples to be compared, but the acceptance range could be always the same for z-test with this modifications?  - 1,96<Z<1.96 for two tailed test (for alfa = 0.05).  
> Thanks to all,
>  
> Best Regards,
>  
> Sergio Nolazco Plasier
> Bach. Biology
> Lima-Peru
>
>
>  
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