Randomization and Monte Carlo Methods in Biology.

Abstract

Part 1 Randomization tests and confidence intervals: the idea of a randomization test examples of a randomization test aspects of randomization testing raised by the examples confidence intervals from randomization. Part 2 Monte Carlo and other computer intensive methods: Monte Carlo tests jackknifing bootstrapping bootstrap tests of significance and confidence intervals. Part 3 Some general considerations: power determining how many randomizations are needed determining a randomization distribution exactly the computer generation of pseudo-random numbers generating random permutations. Part 4 One and two sample tests: the paired comparisons design the one sample randomization test the two sample randomization test the comparison of two samples on multiple measurements. Part 5 Analysis of variance: one factor analysis of variance Bartlett's test for constant variance examples of more complicated types of analysis of variance discussion computer program. Part 6 Regrssion analysis: simple regression testing for a non-zero beta value confidence limits for beta multiple linear regression randomizing X variable values. Part 7 Distance matrices and spatial data: testing for association between distance matrices Mantel's test determining significance by sampling randomization distribution confidence limits for a matrix regression coefficient problems involving more than two matrices. Part 8 Other analyses on spatial data: the study of spatial point patterns Mead's randomization test a test based on nearest neighbour distances testing for an association between two point patterns the Besag-Diggle test tests using distances between points. Part 9 Time series: randomization and time series randomization tests for serial correlation randomization tests for trend randomization tests for periodicity irregularly spaced series tests on times of occurence discussion of procedures for irregular series bootstrap and Monte Carlo tests. Part 10 Multivariate data: univariate and multivariate tests sample means and covariance matrices comparison on sample means vectors chi-squared analyses for count data principal component analysis and other one sample methods discriminate function analysis. Part 11 Ad hoc methods: the construction of tests in non-standard situations testing for randomness of species co-occurences on islands examining time change in niche ovelap probing multivariate data with random skewers other examples. Part 12 Conclusion: randomization methods bootstrap and Monte Carlo methods.