 View SourceThe problem is not unique to testing significance of spatial correlation.
Any traditional hypothesis test is nonsensical as you describe because we
ALWAYS know that the null hypothesis is wrong. The question of interest is
how wrong it is and whether the detected effect is of practical consequence.
However, a hypothesis test does not test practical relevance of an effect
but statistical power to detect it, which depends on sample size, inherent
variability and also on effect size. Given a large enough sample size, one
will always reject the null hypothesis. Why then do people still hold on to
hypothesis tests? Because it gives them a false sense of objectivity. No one
wants to admit that the judgement of whether an effect is of practical
consequence is a to a certain degree inherently subjective decision (as is
the level of alpha etc).
Cheers
Volker
 Original Message 
From: "Edzer J. Pebesma" <e.pebesma@...>
To: <trevor.middel@...>
Cc: <aigeostats@...>
Sent: Thursday, November 20, 2003 5:11
Subject: Re: AIGEOSTATS: Detecting spatial autocorrelation in highly non
normal data
 Trevor,

 I always wonder what the value of testing significance of spatial
 correlation is, and never advise to do it. See, if data are spatial, it
 is extremely unlikely that they are spatially uncorrelated. Rejecting
 the test is usually only a matter of collecting sufficient evidence,
 and not at all an interesting finding, because the data were spatial.

 Probably a more real problem is: to what extent does the spatial
 correlation present (which may be very weak!) mess up an analysis
 that assumes independence of observations. If you choose for
 an analysis method that addresses spatial correlation, you're always
 on safe ground.

 If your data were collected using some form of random sampling,
 analysis based on independent observations is perfectly valid for
 estimating areal mean values. This does not imply that data are
 spatially uncorrelated, but just that they may be treated independent
 because of the sampling scheme.
 
 Edzer

 trevor.middel@... wrote:

 >Hi Folks,
 >
 >I'm hoping someone can help steer me in the right direction.
 >
 >I have several sets of data acquired from acoustic surveys conducted on a
 >small lake trout lake. The data consist of sampling units aligned in
 >transects. Each sampling unit is 50 m in length. A mean lake trout
density
 >is associated with each sampling unit.
 >
 >I'm interested in examining whether any significant spatial
autocorrelation
 >in the exists in the observed distribution of lake trout. The data are
 >highly nonnormal with 7590% of the observations being zero. Log and Ln
 >transformations do not normalize the data.
 >
 >I've been doing some reading and it seems that most methods of
quantifying
 >spatial autocorrelation require some kind of normality in the data. Any
 >suggestions on how I might proceed with these data?
 >
 >Thanks in advance for all suggestions.
 >
 >Apologies for the simplicity of the question, but I'm just beginning my
 >foray into spatial statistics.
 >
 >Trevor Middel
 >
 >
 >* To post a message to the list, send it to aigeostats@...
 >* As a general service to the users, please remember to post a summary of
any useful responses to your questions.
 >* To unsubscribe, send an email to majordomo@... with no subject and
"unsubscribe aigeostats" followed by "end" on the next line in the message
body. DO NOT SEND Subscribe/Unsubscribe requests to the list
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 >
 >


 
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* Support to the list is provided at http://www.aigeostats.org  View Source
> Trevor,
A cautionary note. The use of randomsampling estimators, i.e. those whose
>
> I always wonder what the value of testing significance of spatial
> correlation is, and never advise to do it. See, if data are spatial, it
> is extremely unlikely that they are spatially uncorrelated. Rejecting
> the test is usually only a matter of collecting sufficient evidence,
> and not at all an interesting finding, because the data were spatial.
>
> Probably a more real problem is: to what extent does the spatial
> correlation present (which may be very weak!) mess up an analysis
> that assumes independence of observations. If you choose for
> an analysis method that addresses spatial correlation, you're always
> on safe ground.
>
> If your data were collected using some form of random sampling,
> analysis based on independent observations is perfectly valid for
> estimating areal mean values. This does not imply that data are
> spatially uncorrelated, but just that they may be treated independent
> because of the sampling scheme.
> 
> Edzer
expectations are computed over the space of potential samples by using the
probabilities assigned by the artificial sampling design, is highly
questionable. Thus it is not at all clear that estimating areal mean
values using the sampling scheme is valid, not only in the case of
spatially correlated phenomena, but generally. See Valliant et al., 2000,
Finite Population Sampling and Inference, A prediction Approach, Wiley;
the discussion on the paper of Hansen et al. 1983 An evaluation of
modeldependent and probabilitysampling inferences in sample surveys.
Journal of the American Statistical Association 78:776793. I think
Godambe's paradox (Godambe 1982 Ancillarity principle and a statistical
paradox. J. Amer. Stats. Assoc. 77:931933) proves that inference based on
artificial independence introduced by the sampling scheme is basically
flawed. Maybe this is too statistical for the mail list but i guess it is
better to be aware of the problem.
RubĂ©n

* To post a message to the list, send it to aigeostats@...
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* Support to the list is provided at http://www.aigeostats.org  View SourceHello,
I agree that in most situations testing for spatial correlation
is not very informative since the null hypothesis of spatial
independence is unrealistici and its rejection is trivial.
This is why at Biomedware we are working on tests
of hypothesis where the null hypothesis is a particular spatial pattern.
Stochastic simulation allows one to generate many realizations of this
spatial pattern that are then used to derive the distribution of the
test statistics. More information can be found in the following
publication: http://wwwpersonal.engin.umich.edu/~goovaert/liebisch.pdf
Cheers,
Pierre Goovaerts
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
Dr. Pierre Goovaerts
President of PGeostat, LLC
Chief Scientist with Biomedware Inc.
710 Ridgemont Lane
Ann Arbor, Michigan, 481031535, U.S.A.
Email: goovaert@...
Phone: (734) 6689900
Fax: (734) 6687788
http://alumni.engin.umich.edu/~goovaert/
<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>
On Thu, 20 Nov 2003, Volker Bahn wrote:
> The problem is not unique to testing significance of spatial correlation.
> Any traditional hypothesis test is nonsensical as you describe because we
> ALWAYS know that the null hypothesis is wrong. The question of interest is
> how wrong it is and whether the detected effect is of practical consequence.
> However, a hypothesis test does not test practical relevance of an effect
> but statistical power to detect it, which depends on sample size, inherent
> variability and also on effect size. Given a large enough sample size, one
> will always reject the null hypothesis. Why then do people still hold on to
> hypothesis tests? Because it gives them a false sense of objectivity. No one
> wants to admit that the judgement of whether an effect is of practical
> consequence is a to a certain degree inherently subjective decision (as is
> the level of alpha etc).
>
> Cheers
>
> Volker
>
>
>  Original Message 
> From: "Edzer J. Pebesma" <e.pebesma@...>
> To: <trevor.middel@...>
> Cc: <aigeostats@...>
> Sent: Thursday, November 20, 2003 5:11
> Subject: Re: AIGEOSTATS: Detecting spatial autocorrelation in highly non
> normal data
>
>
>  Trevor,
> 
>  I always wonder what the value of testing significance of spatial
>  correlation is, and never advise to do it. See, if data are spatial, it
>  is extremely unlikely that they are spatially uncorrelated. Rejecting
>  the test is usually only a matter of collecting sufficient evidence,
>  and not at all an interesting finding, because the data were spatial.
> 
>  Probably a more real problem is: to what extent does the spatial
>  correlation present (which may be very weak!) mess up an analysis
>  that assumes independence of observations. If you choose for
>  an analysis method that addresses spatial correlation, you're always
>  on safe ground.
> 
>  If your data were collected using some form of random sampling,
>  analysis based on independent observations is perfectly valid for
>  estimating areal mean values. This does not imply that data are
>  spatially uncorrelated, but just that they may be treated independent
>  because of the sampling scheme.
>  
>  Edzer
> 
>  trevor.middel@... wrote:
> 
>  >Hi Folks,
>  >
>  >I'm hoping someone can help steer me in the right direction.
>  >
>  >I have several sets of data acquired from acoustic surveys conducted on a
>  >small lake trout lake. The data consist of sampling units aligned in
>  >transects. Each sampling unit is 50 m in length. A mean lake trout
> density
>  >is associated with each sampling unit.
>  >
>  >I'm interested in examining whether any significant spatial
> autocorrelation
>  >in the exists in the observed distribution of lake trout. The data are
>  >highly nonnormal with 7590% of the observations being zero. Log and Ln
>  >transformations do not normalize the data.
>  >
>  >I've been doing some reading and it seems that most methods of
> quantifying
>  >spatial autocorrelation require some kind of normality in the data. Any
>  >suggestions on how I might proceed with these data?
>  >
>  >Thanks in advance for all suggestions.
>  >
>  >Apologies for the simplicity of the question, but I'm just beginning my
>  >foray into spatial statistics.
>  >
>  >Trevor Middel
>  >
>  >
>  >* To post a message to the list, send it to aigeostats@...
>  >* As a general service to the users, please remember to post a summary of
> any useful responses to your questions.
>  >* To unsubscribe, send an email to majordomo@... with no subject and
> "unsubscribe aigeostats" followed by "end" on the next line in the message
> body. DO NOT SEND Subscribe/Unsubscribe requests to the list
>  >* Support to the list is provided at http://www.aigeostats.org
>  >
>  >
> 
> 
>  
>  * To post a message to the list, send it to aigeostats@...
>  * As a general service to the users, please remember to post a summary of
> any useful responses to your questions.
>  * To unsubscribe, send an email to majordomo@... with no subject and
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> body. DO NOT SEND Subscribe/Unsubscribe requests to the list
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>
>
> 
> * To post a message to the list, send it to aigeostats@...
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>

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