Quadrat count test

Counts the points in an nx by ny grid of equal tiles of the rectangle win and tests complete spatial randomness by Pearson's chi-square, X2 = sum (n_k - e)^2 / e with e the mean count, on `nx ny

• 1degrees of freedom: the upper tail against clustering and the two-sided p-value (twice the smaller tail,quadrat.test()'s default), which also flags regular patterns. A point on an inner tile boundary goes to the tile above or to its right, one on the outer edge to the tile inside. These are the values of spatstat.explore::quadrat.test()`. The counts feed morsta().

Usage

qdrtst(x, y = NULL, win, nx, ny = nx)

Arguments

x, y

The points in planar coordinates (project longitude and latitude with eqproj() first): x and y numeric vectors of equal length, or x a matrix or data frame with columns named x and y. At least two points; no missing values.

win

The study rectangle c(xmin, xmax, ymin, ymax), holding every point.

nx, ny

The tiles across and up: whole numbers from 1, at least 2 tiles.

Value

A list of class qdrtst: counts, a matrix with one row per row of tiles from the top and one column per column from the left; stat, a named vector: x2, df, p (upper tail), ptwo and lambda (the points per unit area).

References

Greig-Smith, P. (1952). The use of random and contiguous quadrats in the study of the structure of plant communities. Annals of Botany, 16(2), 293-316. doi:10.1093/oxfordjournals.aob.a083317

Examples

set.seed(1)
p <- cbind(x = runif(100, 0, 2), y = runif(100))
q <- qdrtst(p, win = c(0, 2, 0, 1), nx = 4, ny = 2)
q
#> qdrtst: X2 5.6 on 7 df, p 0.587 (two-sided 0.826)
#>      [,1] [,2] [,3] [,4]
#> [1,]   13   16   10   15
#> [2,]    7   16   11   12
morsta(q$counts)
#>       imor       mclu       muni       imst        chi          p 
#>  0.9858586  1.0910380  0.9463623 -0.1318235  5.6000000  0.5871510