[R-sig-Geo] quick question on geary.test in spdep

[Roger Bivand]

On Mon, 24 Jan 2011, Seth J Myers wrote:

> Hi,
>
>> From R documentation, the default alternative hypothesis for moran.test 
>> in spdep is "greater" which leads me to think that the null hypothesis 
>> is then "less than or equal to zero" or no or negative autocorr.  A 
>> small p-value for this test would indicate a rejection of the null and 
>> support for positive spatial autocorrelation as measured by Moran's I. 
>> Is this correct so far?
>
> Geary's C stat as calculated by geary.test has a default alt. hypothesis 
> "greater" as well.  However, the expected value for Geary's C is 1 and 
> values below this indicates positive autocorrelation and values above 1 
> indicate negative autocorrelation.  So, it seems the null as a default 
> is "less than or equal to 1" (positive or no autocorr).  A small p-value 
> would then indicate support for negative autocorrelation.  Is this 
> correct?
>
> If I am reading the documentation correctly and asking an obvious 
> question, I am sorry.  It is confusing to me because I would expect the 
> default alternative hypotheses of the two tests to have p-values with 
> similar interpretations.

Since June 2009, geary.test() reports (EC - C) / sqrt(VC) as the standard 
deviate, replacing the previous, more usual, (C - EC) / sqrt(VC), and now 
agrees with Cliff & Ord (1973, p. 21). I've added further explanation on 
the help page. This means that the "greater" alternative for the Geary C 
test corresponds to the "greater" alternative for Moran's I test. The 
other possibility - not following Cliff & Ord - would be to do as you 
suggest, but it seems better to stay with their decision to change the 
sign for the standard deviate.

Hope this clarifies,

Roger



>
> Thanks, Seth
>
>
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>
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-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no