quadrat count indices: program now ready

[Darrell McCauley]

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 at 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)
>
>