spatstat.explore (version 3.5-2)

hopskel: Hopkins-Skellam Test

Description

Perform the Hopkins-Skellam test of Complete Spatial Randomness, or simply calculate the test statistic.

Usage

hopskel(X)
hopskel.test(X, ...,
             alternative=c("two.sided", "less", "greater",
                           "clustered", "regular"),
             method=c("asymptotic", "MonteCarlo"),
             nsim=999)

Value

The value of hopskel is a single number.

The value of hopskel.test is an object of class "htest"

representing the outcome of the test. It can be printed.

Details

Hopkins and Skellam (1954) proposed a test of Complete Spatial Randomness based on comparing nearest-neighbour distances with point-event distances.

If the point pattern X contains n points, we first compute the nearest-neighbour distances \(P_1, \ldots, P_n\) so that \(P_i\) is the distance from the \(i\)th data point to the nearest other data point. Then we generate another completely random pattern U with the same number n of points, and compute for each point of U the distance to the nearest point of X, giving distances \(I_1, \ldots, I_n\). The test statistic is $$ A = \frac{\sum_i P_i^2}{\sum_i I_i^2} $$ The null distribution of \(A\) is roughly an \(F\) distribution with shape parameters \((2n,2n)\). (This is equivalent to using the test statistic \(H=A/(1+A)\) and referring \(H\) to the Beta distribution with parameters \((n,n)\)).

The function hopskel calculates the Hopkins-Skellam test statistic \(A\), and returns its numeric value. This can be used as a simple summary of spatial pattern: the value \(H=1\) is consistent with Complete Spatial Randomness, while values \(H < 1\) are consistent with spatial clustering, and values \(H > 1\) are consistent with spatial regularity.

The function hopskel.test performs the test. If method="asymptotic" (the default), the test statistic \(H\) is referred to the \(F\) distribution. If method="MonteCarlo", a Monte Carlo test is performed using nsim simulated point patterns.

References

Hopkins, B. and Skellam, J.G. (1954) A new method of determining the type of distribution of plant individuals. Annals of Botany 18, 213--227.

See Also

clarkevans, clarkevans.test, nndist, nncross

Examples

  hopskel(redwood)
  hopskel.test(redwood, alternative="clustered")