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# Conclusions: Testing a Hypothesis
vs. Testing Against Surrogates

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 there is no such thing in statistics as testing a result against surrogates. All we can do is to test a null hypothesis. This is more than a difference in words. In the former case, we assume a result to be true unless it is rendered obsolete by finding the same with trivial data. In the latter case, the only one that is statistically meaningful, we assume a more or less trivial null hypothesis to be true, unless we can reject it by finding significant structure in the data.

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 less parsimonious than a nonlinear dynamical system written down as a one line formula? People unfamiliar with spectral time series methods often find their use and interpretation at least as demanding as the computation of correlation dimensions. From such a point of view it is quite natural to take the nonlinearity of the world for granted, while linearity needs to be established by a test against surrogates.

The reluctance to take surrogate data as what they are, a means to test a null hypothesis, is partly explainable by the choice of null hypotheses which are currently available for proper statistical testing. As we have tried to illustrate in this paper, recent efforts on the generalisation of randomisation schemes broaden the repertoire of null hypotheses. The hope is that we can eventually choose one that is general enough to be acceptable if we fail to reject it with the methods we have. Still, we cannot prove that there is no dynamics in the process beyond what is covered by the null hypothesis. From a practical point of view, however, there is not much of a difference between structure that is not there and structure that is undetectable with our observational means.

Next: Acknowledgements Up: Surrogate time series Previous: Non-stationarity