A Statistical Test for Ripley’s K Function Rejection of Poisson Null Hypothesis

Ripley’s K function is the classical tool to characterize the spatial structure of point patterns. It is widely used in vegetation studies. Testing its values against a null hypothesis usually relies on Monte-Carlo simulations since little is known about its distribution. We introduce a statistical test against complete spatial randomness (CSR). The test returns the P value to reject the null hypothesis of independence between point locations. It is more rigorous and faster than classical Monte-Carlo simulations. We show how to apply it to a tropical forest plot. The necessary R code is provided.

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A simple method for implementing Monte Carlo tests

Computational Statistics ◽

10.1007/s00180-019-00927-6 ◽

2019 ◽

Vol 35 (3) ◽

pp. 1373-1392 ◽

Cited By ~ 1

Author(s):

Dong Ding ◽

Axel Gandy ◽

Georg Hahn

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Statistical Test ◽

Uniform Bound ◽

Data Set ◽

Simple Method ◽

Practical Applications ◽

Tuning Parameters ◽

Sequence Method ◽

Uniformly Bounded

Abstract We consider a statistical test whose p value can only be approximated using Monte Carlo simulations. We are interested in deciding whether the p value for an observed data set lies above or below a given threshold such as 5%. We want to ensure that the resampling risk, the probability of the (Monte Carlo) decision being different from the true decision, is uniformly bounded. This article introduces a simple open-ended method with this property, the confidence sequence method (CSM). We compare our approach to another algorithm, SIMCTEST, which also guarantees an (asymptotic) uniform bound on the resampling risk, as well as to other Monte Carlo procedures without a uniform bound. CSM is free of tuning parameters and conservative. It has the same theoretical guarantee as SIMCTEST and, in many settings, similar stopping boundaries. As it is much simpler than other methods, CSM is a useful method for practical applications.

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A Test of Randomness for Finite Spatial Distributions

Perceptual and Motor Skills ◽

10.1177/003151259407800305 ◽

1994 ◽

Vol 78 (3) ◽

pp. 707-714 ◽

Cited By ~ 7

Author(s):

Frank O'brien

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Null Hypothesis ◽

Nearest Neighbor ◽

Dimensional Space ◽

Spatial Distributions ◽

Two Dimensional ◽

Model Extension ◽

Spatially Distributed ◽

Test Of Randomness

A statistical method is presented for determining randomness of points spatially distributed in two-dimensional space. The procedure is based on a distance-to-particle (nearest neighbor) model derived from an elementary Poisson process. In a previous derivation of the method, an extension to the model was proposed and used without adequate empirical justification. Herein the test is derived in detail and its performance evaluated with Monte Carlo simulations. Results indicate that the model extension provides adequate representations when the null hypothesis is true.

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Spatial stochastic modeling of resin yield from pine stands

Canadian Journal of Forest Research ◽

10.1139/x01-047 ◽

2001 ◽

Vol 31 (7) ◽

pp. 1140-1147 ◽

Cited By ~ 13

Author(s):

Nikos Nanos ◽

Wubalem Tadesse ◽

Gregorio Montero ◽

Luis Gil ◽

Ricardo Alia

Keyword(s):

Spatial Structure ◽

Stochastic Modeling ◽

Economic Modeling ◽

Complete Spatial Randomness ◽

The Mean ◽

Pine Stands ◽

K Function ◽

Modeling Strategy ◽

Future Work ◽

Scale Data

The spatial structure of resin-yield in maritime pine stands in central Spain was studied on two different scales and with data from two tapping periods (1998 and 1999). For the fine scale, Moran's I and the K function were used to study within-stand spatial variation. We found that in one plot, trees separated by distances of less than 5 m had similar production. The K function results showed that the distribution of trees did not depart significantly from complete spatial randomness. For a much larger scale, data was available from 37 and 59 ten-tree plots for years 1998 and 1999, respectively. Partial (monthly) yields were also measured. The experimental variograms for the mean plot production showed that a large percentage of the total variance was spatially structured. Furthermore, the experimental variograms for the partial yields revealed changes in the spatial structure of this phenomenon within the same year. Spatial stochastic modeling was shown to be an effective and economic modeling strategy. Temporal variation should be included in future work, with the use of geostatistical space-time models.

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Monte Carlo simulations of the spatial structure of end-linked bimodal polymer networks: part II

Computational and Theoretical Polymer Science ◽

10.1016/s1089-3156(01)00008-3 ◽

2001 ◽

Vol 11 (6) ◽

pp. 459-466 ◽

Cited By ~ 8

Author(s):

W Michalke ◽

S Kreitmeier ◽

M Lang ◽

A Buchner ◽

D Göritz

Keyword(s):

Monte Carlo ◽

Spatial Structure ◽

Monte Carlo Simulations ◽

Polymer Networks

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Characterizing the Relative Spatial Structure of Point Patterns

International Journal of Ecology ◽

10.1155/2012/619281 ◽

2012 ◽

Vol 2012 ◽

pp. 1-11 ◽

Cited By ~ 5

Author(s):

Eric Marcon ◽

Florence Puech ◽

Stéphane Traissac

Keyword(s):

Spatial Structure ◽

Interspecific Competition ◽

Null Hypothesis ◽

Tropical Tree ◽

Point Pattern ◽

Data Set ◽

New Approach ◽

Point Patterns ◽

Tree Data

We generalize Ripley’sKfunction to get a new function,M, to characterize the spatial structure of a point pattern relatively to another one. We show that this new approach is pertinent in ecology when space is not homogenous and the size of objects matters. We present how to use the function and test the data against the null hypothesis of independence between points. In a tropical tree data set we detect intraspecific aggregation and interspecific competition.

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The Statistics of Agreement on a Single Item or Object by Multiple Raters

Perceptual and Motor Skills ◽

10.2466/pms.1993.77.2.377 ◽

1993 ◽

Vol 77 (2) ◽

pp. 377-378 ◽

Cited By ~ 5

Author(s):

John Paul Szalai

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Statistical Significance ◽

Statistical Test ◽

Interrater Agreement ◽

Single Item

Kappa on a single item Ksi is proposed as a measure of the interrater agreement when a single item or object is rated by multiple raters. A statistical test and Monte Carlo simulations are provided for testing the statistical significance of Ksi beyond chance agreement.

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Low-voltage EDS of magnesium ferrite Dendrites in a FEG-SEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100164854 ◽

1996 ◽

Vol 54 ◽

pp. 478-479

Author(s):

Matthew T. Johnson ◽

Ian M. Anderson ◽

Jim Bentley ◽

C. Barry Carter

Keyword(s):

Monte Carlo ◽

Quantitative Analysis ◽

Monte Carlo Simulations ◽

Cross Section ◽

Spatial Resolution ◽

Low Voltage ◽

Magnesium Ferrite ◽

X Ray ◽

Interaction Volume ◽

Ferrite Spinel

Energy-dispersive X-ray spectrometry (EDS) performed at low (≤ 5 kV) accelerating voltages in the SEM has the potential for providing quantitative microanalytical information with a spatial resolution of ∼100 nm. In the present work, EDS analyses were performed on magnesium ferrite spinel [(MgxFe1−x)Fe2O4] dendrites embedded in a MgO matrix, as shown in Fig. 1. spatial resolution of X-ray microanalysis at conventional accelerating voltages is insufficient for the quantitative analysis of these dendrites, which have widths of the order of a few hundred nanometers, without deconvolution of contributions from the MgO matrix. However, Monte Carlo simulations indicate that the interaction volume for MgFe2O4 is ∼150 nm at 3 kV accelerating voltage and therefore sufficient to analyze the dendrites without matrix contributions.Single-crystal {001}-oriented MgO was reacted with hematite (Fe2O3) powder for 6 h at 1450°C in air and furnace cooled. The specimen was then cleaved to expose a clean cross-section suitable for microanalysis.

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