You can get your BETA copy of the PigeonWatch amalgamated data at:
https://web.csulb.edu/~rodrigue/geog330/PigeonWatch/PigeonWatchF20.ods



https://web.csulb.edu/~rodrigue/geog200/lab9.html#figure1

Eyeball that map and, even though it looks pretty haphazard, decide whether it is more clustered or more uniform.  That will be our working hypothesis.  Randomness will be our null hypothesis.  We'll decide on significance and an actual test later.


What is n (how many plants?)

What is A (area in square meters)

What is P (perimeter -- add all four sides)

What is D (density of plants -- n/A)

The tedious part: Measure and record the distance from each plant to its nearest-neighbor (remember, one plant can wind up the nearest-neighbor for more than one other plant). Actually, here are those measurements in meters already done for you (trying to make life a little easier on you) in the worksheet below. "#" stands for the individual plant identification number shown on the map, "nn" is the number of that plant's nearest neighbor, while "r" is the distance between each plant and its nearest neighbor.

      #          nn        r(m)    
     ==========================
      1           2        2.02
      2           4        1.77
      3           1        2.14
      4           2        1.77
      5           4        2.50
      6           3        2.55
      7           9        1.82
      8           9         .90
      9           8         .90
     10          11        3.81
     11          12        1.12
     12          11        1.12
     13          18        8.68
     14          15        2.02
     15          14        2.02
     16          15        2.80
     17          10        5.77
     18          19        3.02
     19          29        2.83
     20          22        3.54
     21          22        4.19
     22          21        4.19
     23          24         .79
     24          23         .79
     25          24        2.93
     26          28        1.90
     27          28        3.48
     28          29        1.90
     29          28        1.90
     30          28        6.27         


That would get old.  Here, I've done it for you:

http://www.csulb.edu/depts/geography/labs/data/nearnabedata.ods

What is the observed average nearest-neighbor distance (ro)?  Sum distances, divide by n

What is the expected average nearest-neighbor distance (re)?   the square root of D. Multiply that square root by 2. Now, divide 1 BY that answer. In Calc-speak:   =1/(2*sqrt(D)) -- where D is whichever cell you put D in.

So, now, divide the observed mean by the expected mean to get the R statistic for nearest-neighbor analysis.  You may have to adjust re for edge effects, but we'll deal with that later.

Now, let's do a seat-of-the-pants interpretation of that R statistic (we'll do a formal test later).  R is designed to range between 0 and 2.149 (the .149 bit is a bit weird!).  

If the number is close to 1, the pattern is random and any "pattern" you see is you hallucinating, because humans are pattern-seeking missiles!

If the pattern is close to 0, it's a clustered pattern (a 0 could only come from having all points on top of one another)

If the pattern is closer to 2+, it's tending toward uniformity, like an orchard.

Is it larger than 1 or smaller than 1?  How much?  

But is that important or significant?  Next time!