Do quadrats have to be equal in size? I'm doing a quadrat analysis of point pattern. My study area is 2.3m by 2.3m. Can I have quadrats of 1sqm or does it have to be equal area?
If quadrats are 1sqm, then four of them would be of full size but the other five will be smaller:

The goal of the analysis is twofold:
First, to use the qudrants as a general descriptive measurement. This will also be used to calculate the intensity.
Second, to determine whether the points are as a result of random process, regular, normal or clustered using $\chi^2$. I am aware that other tests might be better but this question is about quadrants specifically.
 A: There is no law against using quadrats of different areas.  It's a free country, at least where I live.  However ....
(1) What do you mean by using quadrats to calculate (do you mean estimate?) the intensity?  By calculating the observed intensity for each quadrat you could create a rather rough estimate of the inhomogeneous intensity function of the process.  But in almost all circumstances other methods (kernel density
in particular) are superior.
(2) In order to apply a chi-squared test you need the expected cell counts to be at least 5.  You get the biggest bang for your buck if you make the quadrats all equal in area (whence the expected cell counts are all equal) and take as many quadrats as you can while keeping this expected cell count above 5.
If you apply a Monte Carlo (as opposed to a chi-squared) test, it is not so clear that you lose power by using unequal quadrats, but I suspect that you do lose power.
Anyway, as Adrian said, other tests are usually more powerful than the quadrat based chi-squared test.
Finally --- PLEASE don't muddle up the words "quadrat" and "quadrant".
They may be similar but describe very different concepts.
