0th

Percentile

##### Chi-Squared Dispersion Test for Spatial Point Pattern Based on Quadrat Counts

Performs a chi-squared test of complete spatial randomness for a given point pattern, based on quadrat counts. Alternatively performs a chi-squared goodness-of-fit test of a fitted inhomogeneous Poisson model.

Keywords
spatial
##### Usage
quadrat.test(X, nx = 5, ny = nx, xbreaks = NULL, ybreaks = NULL, fit)
##### Arguments
X
A point pattern (object of class "ppp") to be subjected to the goodness-of-fit test. Alternatively a fitted point process model (object of class "ppm") to be tested.
nx,ny
Numbers of quadrats in the $x$ and $y$ directions. Incompatible with xbreaks and ybreaks.
xbreaks
Optional. Numeric vector giving the $x$ coordinates of the boundaries of the quadrats. Incompatible with nx.
ybreaks
Optional. Numeric vector giving the $y$ coordinates of the boundaries of the quadrats. Incompatible with ny.
fit
Optional. A fitted point process model (object of class "ppm"). The point pattern X will be subjected to a test of goodness-of-fit to the model fit.
##### Details

This function performs a $\chi^2$ test of goodness-of-fit to the Poisson point process (including Complete Spatial Randomness but also inhomogeneous Poisson processes), based on quadrat counts.

If X is a point pattern, it is taken as the data point pattern for the test. If X is a fitted point process model, then the data to which this model was fitted are extracted from the model object, and are treated as the data point pattern for the test. The window of observation is divided into rectangular tiles and the number of data points in each tile is counted, as described in quadratcount.

If fit is absent, then we test the null hypothesis that the data pattern is a realisation of Complete Spatial Randomness (the uniform Poisson point process) by applying the $\chi^2$ test of goodness-of-fit to the quadrat counts.

If fit is present, then it should be a point process model (object of class "ppm") and it should be a Poisson point process. Then we test the null hypothesis that the data pattern is a realisation of the (inhomogeneous) Poisson point process specified by fit. Again this is a $\chi^2$ test of goodness-of-fit to the quadrat counts.

To test the Poisson point process against a specific alternative point process model, use anova.ppm.

##### Value

• An object of class "htest". See chisq.test for explanation.

quadratcount, chisq.test

##### Examples
data(simdat)
quadrat.test(fitx)