Perform a studentised permutation test for a difference between groups of point patterns.

```
studpermu.test(X, formula, summaryfunction = Kest,
..., rinterval = NULL, nperm = 999,
use.Tbar = FALSE, minpoints = 20, rsteps = 128,
r = NULL, arguments.in.data = FALSE)
```

Object of class `"studpermutest"`

.

- X
Data. Either a

`hyperframe`

or a list of lists of point patterns.- formula
Formula describing the grouping, when

`X`

is a hyperframe. The left side of the formula identifies which column of`X`

contains the point patterns. The right side identifies the grouping factor. If the formula is missing, the grouping variable is taken to be the first column of`X`

that contains a factor, and the point patterns are taken from the first column that contains point patterns.- summaryfunction
Summary function applicable to point patterns.

- ...
Additional arguments passed to

`summaryfunction`

.- rinterval
Interval of distance values \(r\) over which the summary function should be evaluated and over which the test statistic will be integrated. If

`NULL`

, the default range of the summary statistic is used (taking the intersection of these ranges over all patterns).- nperm
Number of random permutations for the test.

- use.Tbar
Logical value indicating choice of test statistic. If

`TRUE`

, use the alternative test statistic, which is appropriate for summary functions with roughly constant variance, such as \(K(r)/r\) or \(L(r)\).- minpoints
Minimum permissible number of points in a point pattern for inclusion in the test calculation.

- rsteps
Number of discretisation steps in the

`rinterval`

.- r
Optional vector of distance values as the argument for

`summaryfunction`

. Should not usually be given. There is a sensible default.- arguments.in.data
Logical. If

`TRUE`

, individual extra arguments to`summaryfunction`

will be taken from`X`

(which must be a hyperframe). This assumes that the first argument of`summaryfunction`

is the point pattern dataset.

Ute Hahn.

Modified for `spatstat`

by
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

This function performs the studentized permutation test of Hahn (2012) for a difference between groups of point patterns.

The first argument `X`

should be either

- a list of lists of point patterns.
Each element of

`X`

will be interpreted as a group of point patterns, assumed to be replicates of the same point process.- a hyperframe:
One column of the hyperframe should contain point patterns, and another column should contain a factor indicating the grouping. The argument

`formula`

should be a formula in the R language specifying the grouping: it should be of the form`P ~ G`

where`P`

is the name of the column of point patterns, and`G`

is the name of the factor.

A group needs to contain at least two point patterns with at least
`minpoints`

points in each pattern.

The function returns an object of class `"htest"`

and `"studpermutest"`

that can be printed and plotted.
The printout shows the test result and \(p\)-value.
The plot shows the summary functions for the
groups (and the group means if requested).

Hahn, U. (2012)
A studentized permutation test for the comparison of
spatial point patterns.
*Journal of the American Statistical Association*
**107** (498), 754--764.

`plot.studpermutest`

```
np <- if(interactive()) 99 else 19
testpyramidal <- studpermu.test(pyramidal, Neurons ~ group, nperm=np)
testpyramidal
```

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