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Confidence intervals from permutations

To: s-news@lists.biostat.wustl.edu
Subject: Confidence intervals from permutations
From: David Douglas <bgydjtd@leeds.ac.uk>
Date: Mon, 9 Apr 2007 13:05:10 +0100
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Dear S+ users,

I'm using S+SpatialStats in S+ 7.0 to calculate spatial autocorrelations (using
three neighbour matrices combined) using the function "spatial.cor".
Part of the procedure computes randomisations to test the significance of the
sample correlations. The output includes the summary quantiles of the
permutation correlations (min, max, IQ range etc). I want to calculate 95%
confidence intervals for the correlations so I need the 2.5% and 97.5%
quantiles. How do I obtain these?

Many thanks,
David.

spatcorwb1<-spatial.cor(wb1$total.insect.nos,
neighbor=spat.snhbr.wb1,statistic="moran",sampling="nonfree",npermutes=10000)

spatcorwb1

        Spatial Correlation Estimate

Statistic = "moran" Sampling = "nonfree"

Correlation =  0.485  0.4186 0.3003
Variance    =  0.005698 0.005671 0.01756
Std. Error  =  0.07548 0.07531 0.1325

Normal statistic =  6.481 5.614 2.298
Normal p-value (2-sided) =  9.116e-11 1.982e-8  0.02157

Null Hypothesis:  No spatial autocorrelation

Quantiles of the permutation-correlations :
             x1.1      x1.2      x1.3
   Min. -0.240794 -0.271843 -0.472903
1st Qu. -0.056602 -0.055549 -0.094665
 Median -0.005584 -0.005741 -0.010004
   Mean -0.004362 -0.004003 -0.004504
3rd Qu.  0.046117  0.046052  0.079771
   Max.  0.302984  0.294322  0.510544

permutation p-value = 0.0000 0.0000 0.0173



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