I've written a little program to calculate quadrat count
indices (See Cressie, _Statistics for Spatial Data_,
pp 590-591, 1st ed, Wiley & Sons, 1991). Sample
output is attached.
If you know what I'm talking about here and/or
think that something like this would be useful
in GRASS, I need your assistance. The grass program,
man page, and tutorial is all ready to be distributed
except for one small problem: Morista's I. The formula
given in Cressie's book (1st ed - I couldn't afford the
2nd after buying the first 
) gives Morista's I as
\begin{displaymath} % please bear with the TeX-ease
I_\delta = \frac{\sum_{i=1}^n X_i\left(X_i-1\right)}
{n\bar{X}\left(n\bar{X}-1\right)}
\end{displaymath}% \bar{X}=mean, X_i=#sites in ith quadrat, n=#quadrats
However, this equation gave me answers that were an order
of magnitude lower that Cressie's example calculation in Table 8.3.
By altering the equation to be:
\begin{displaymath}
I_\delta = \frac{\sum_{i=1}^n X_i\left(X_i-1\right)}
{\bar{X}\left(n\bar{X}-1\right)}
\end{displaymath}
I get an answer that appears more correct (notice the n is
missing from the denominator.)
Which is correct - Cressie's equation or his calculation? (Or which
equation is correct - the printed one or the altered one?) If someone
can pull a book (Ripley?) off their shelf and check I'll make the program
available. It's too dern cold (zero farenheit) to make a special trip
to the library for this 
--Darrell
% s.qcount -q sites=pinetrees
Index Realization
-----------------------------------------------------------
Fisher el al (1922) Relative Variance 2.12795
David & Moore (1954) Index of Cluster Size 1.12795
Douglas (1975) Index of Cluster Frequency 1.38304
Lloyd (1967) "mean crowding" 2.68795
Lloyd (1967) Index of patchniess 1.72304
Morita's (1959) I (variability b/n patches) 1.72043
-----------------------------------------------------------
sites_list: pinetrees n=584 (100 quadrats of radius 6)
(also prints raw quadrat counts as a site list with an
optional flag)
I made it over to the library today and checked Ripley's
_Spatial Statistics_. He has an additional factor of
n before the summation in the numerator. Adding this,
I think that the answers are now correct (I've contacted
Noel about the potential error).
It's available now as
pasture.ecn.purdue.edu:pub/mccauley/grass/s.qcount.tar.gz
There's a tutorial along with the man page and source.
Enjoy.
BTW, anyone have a copy of Ripley's _Spatial Statistics_
that they're willing to sell me?
--Darrell
Darrell McCauley (mccauley@ecn.purdue.edu) writes on 9 Jan 94:
I've written a little program to calculate quadrat count
indices (See Cressie, _Statistics for Spatial Data_,
pp 590-591, 1st ed, Wiley & Sons, 1991). Sample
output is attached.
If you know what I'm talking about here and/or
think that something like this would be useful
in GRASS, I need your assistance. The grass program,
man page, and tutorial is all ready to be distributed
except for one small problem: Morista's I. The formula
given in Cressie's book (1st ed - I couldn't afford the
2nd after buying the first ) gives Morista's I as
\begin{displaymath} % please bear with the TeX-ease
I_\delta = \frac{\sum_{i=1}^n X_i\left(X_i-1\right)}
{n\bar{X}\left(n\bar{X}-1\right)}
\end{displaymath}% \bar{X}=mean, X_i=#sites in ith quadrat, n=#quadrats
However, this equation gave me answers that were an order
of magnitude lower that Cressie's example calculation in Table 8.3.
By altering the equation to be:
\begin{displaymath}
I_\delta = \frac{\sum_{i=1}^n X_i\left(X_i-1\right)}
{\bar{X}\left(n\bar{X}-1\right)}
\end{displaymath}
I get an answer that appears more correct (notice the n is
missing from the denominator.)
Which is correct - Cressie's equation or his calculation? (Or which
equation is correct - the printed one or the altered one?) If someone
can pull a book (Ripley?) off their shelf and check I'll make the program
available. It's too dern cold (zero farenheit) to make a special trip
to the library for this
--Darrell
% s.qcount -q sites=pinetrees
Index Realization
-----------------------------------------------------------
Fisher el al (1922) Relative Variance 2.12795
David & Moore (1954) Index of Cluster Size 1.12795
Douglas (1975) Index of Cluster Frequency 1.38304
Lloyd (1967) "mean crowding" 2.68795
Lloyd (1967) Index of patchniess 1.72304
Morita's (1959) I (variability b/n patches) 1.72043
-----------------------------------------------------------
sites_list: pinetrees n=584 (100 quadrats of radius 6)
(also prints raw quadrat counts as a site list with an
optional flag)