Comparison of surfaces
1997
Legendre, P | Mcardle, Bh
Values of a variable observed over a delimited geographic area are called a ''surface''. The problem we investigate is how to compare measures of the same area observed at two or more Sampling times. It is important to recognise that two different null hypotheses can be tested about the surface. The first is that the corresponding values in the surfaces differ only because of measurement or sampling error. The second is that the underlying process that generated the surfaces is the same. In the first case, the surfaces should have the same shape and values, while in the second case the surfaces might have different values, but if they still have the same means, variances and autocorrelation structures, the null hypothesis cannot be rejected. To prove the null hypothesis wrong would require stronger differences in the second case than in the first. We shall only be considering the first situation, primarily because we feel it is the most commonly investigated. The null hypothesis throughout the paper is therefore that the corresponding values in the surfaces differ only because of measurement or sampling error. The techniques used to test this will depend on the sampling strategy employed in the study. The paper is organised around the three major factors affecting the solutions: (1) Have the same sampling points been measured through time? (2) Were replicate sampling units measured or observed at each sampling location at each time? (3) How were the sampling locations distributed over the study site? The techniques we propose are in standard use and are widely available. The most important are analysis of variance, log-linear modelling, and multiple regression (in the form of trend surface analysis).
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