On tests of spatial pattern based on simulation envelopes

Adrian Baddeley, Peter J. Diggle, Andrew Hardegen, Thomas Lawrence, Robin K. Milne, Gopalan Nair

Research output: Contribution to journalArticlepeer-review

106 Scopus citations


In the analysis of spatial point patterns, an important role is played by statistical tests based on simulation envelopes, such as the envelope of simulations of Ripley's K function. Recent ecological literature has correctly pointed out a common error in the interpretation of simulation envelopes. However, this has led to a widespread belief that the tests themselves are invalid. On the contrary, envelope-based statistical tests are correct statistical procedures, under appropriate conditions. In this paper, we explain the principles of Monte Carlo tests and their correct interpretation, canvas the benefits of graphical procedures, measure the statistical performance of several popular tests, and make practical recommendations. There are several caveats including the under-recognized problem that Monte Carlo tests of goodness of fit are probably conservative if the model parameters have to be estimated from data. Finally, we discuss whether graphs of simulation envelopes can be used to infer the scale of spatial interaction.

Original languageEnglish (US)
Pages (from-to)477-489
Number of pages13
JournalEcological Monographs
Issue number3
StatePublished - 2014
Externally publishedYes


  • Confidence bands
  • Conservative test
  • Deviation test
  • Global test
  • K function
  • Monte Carlo test
  • Null model
  • Pair correlation function
  • Pointwise test
  • Scale of interaction
  • Spatial point pattern
  • Variance stabilization

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics


Dive into the research topics of 'On tests of spatial pattern based on simulation envelopes'. Together they form a unique fingerprint.

Cite this