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<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN"><!--Converted with LaTeX2HTML 96.1-h (September 30, 1996) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds --><HTML><HEAD><TITLE>Conclusions: Testing a Hypothesis vs. Testing Against Surrogates</TITLE><META NAME="description" CONTENT="Conclusions: Testing a Hypothesis vs. Testing Against Surrogates"><META NAME="keywords" CONTENT="Surrogates"><META NAME="resource-type" CONTENT="document"><META NAME="distribution" CONTENT="global"><LINK REL=STYLESHEET HREF="Surrogates.css"></HEAD><BODY bgcolor=#ffffff LANG="EN" > <A NAME="tex2html375" HREF="node31.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="next_motif.gif"></A> <A NAME="tex2html373" HREF="Surrogates.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="up_motif.gif"></A> <A NAME="tex2html367" HREF="node29.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html376" HREF="node31.html">Acknowledgements</A><B>Up:</B> <A NAME="tex2html374" HREF="Surrogates.html">Surrogate time series</A><B> Previous:</B> <A NAME="tex2html368" HREF="node29.html">Non-stationarity</A><BR> <P><H1><A NAME="SECTION00080000000000000000">Conclusions: Testing a Hypothesis<BR> vs. Testing Against Surrogates</A></H1><P>Most of what we have to say about the interpretation of surrogate data tests,and spurious claims in the literature, can be summarised by stating that thereis no such thing in statistics as testing a result <EM>againstsurrogates</EM>. All we can do is to test a null hypothesis. This is more than adifference in words. In the former case, we assume a result to be true unlessit is rendered obsolete by finding the same with trivial data. In the lattercase, the only one that is statistically meaningful, we assume a more or lesstrivial null hypothesis to be true, unless we can reject it by findingsignificant structure in the data.<P>As everywhere in science, we are applying Occam's razor: We seek the simplest-- or least interesting -- model that is consistent with the data. Of course,as always when such categories are invoked, we can debate what is``interesting''. Is a linear model with several coefficients more or lessparsimonious than a nonlinear dynamical system written down as a one lineformula? People unfamiliar with spectral time series methods often find theiruse and interpretation at least as demanding as the computation of correlationdimensions. From such a point of view it is quite natural to take thenonlinearity of the world for granted, while linearity needs to be establishedby a test <EM>against surrogates</EM>.<P>The reluctance to take surrogate data as what they are, a means to test a nullhypothesis, is partly explainable by the choice of null hypotheses which arecurrently available for proper statistical testing. As we have tried toillustrate in this paper, recent efforts on the generalisation of randomisationschemes broaden the repertoire of null hypotheses. The hope is that we caneventually choose one that is general enough to be acceptable if we fail toreject it with the methods we have. Still, we cannot prove that there is nodynamics in the process beyond what is covered by the null hypothesis. From apractical point of view, however, there is not much of a difference betweenstructure that is not there and structure that is undetectable with ourobservational means.<P><HR><A NAME="tex2html375" HREF="node31.html"><IMG WIDTH=37 HEIGHT=24 ALIGN=BOTTOM ALT="next" SRC="next_motif.gif"></A> <A NAME="tex2html373" HREF="Surrogates.html"><IMG WIDTH=26 HEIGHT=24 ALIGN=BOTTOM ALT="up" SRC="up_motif.gif"></A> <A NAME="tex2html367" HREF="node29.html"><IMG WIDTH=63 HEIGHT=24 ALIGN=BOTTOM ALT="previous" SRC="previous_motif.gif"></A> <BR><B> Next:</B> <A NAME="tex2html376" HREF="node31.html">Acknowledgements</A><B>Up:</B> <A NAME="tex2html374" HREF="Surrogates.html">Surrogate time series</A><B> Previous:</B> <A NAME="tex2html368" HREF="node29.html">Non-stationarity</A><P><ADDRESS><I>Thomas Schreiber <BR>Mon Aug 30 17:31:48 CEST 1999</I></ADDRESS></BODY></HTML>⌨️ 快捷键说明
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