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Scope and Method of Study: Many statistical procedures, such as repeated measures analysis, time-series, structural equation modeling, and factor analysis, require an assessment of the structure of the underlying covariance matrix. The classical parametric method of testing such a hypothesis involves the use of a likelihood ratio test (LRT). These tests have many limitations, including the need for very large sample sizes and the requirement of a random sample from a multivariate normal population. The LRT is also undefined for cases in which the sample size is not greater than the number of repeated measures. In such situations, researchers could benefit from a non-parametric testing procedure. In particular, permutation tests have no distributional assumptions and do not require random samples of any particular size. This research involves the development and analysis of a permutation/randomization test for the structure of a covariance matrix. Samples of various sizes and number of measures on each subject were simulated from multiple distributions. In each case, the type I error rates and power were examined.

We sampled seven intact nonriverine wet hardwood forests to establish target ranges for vegetation, soils and hydrology and to examine trends in plant species composition along a wetness gradient. Although quantitative vegetation analysis for this community has been published, broad drainage classes were used to represent a moisture gradient. We investigated trends along a finer-scaled wetness gradient utilizing a novel wetness index that incorporated indicators of saturated soils. Understanding small-scale patterns in plant community composition is useful in planning wetland restoration projects. Although no strong relationship was found between wetness index classes and plant community composition, these data represent the vegetative community supported by soils specific to each wetness class. Absence of this relationship is most likely a result of the dominance of A. rubrum and L. styraciflua in all wetness classes as well as a history of disturbance in each forest and other unknown stochastic variables. For the restorationist hoping to restore a historic nonriverine wet hardwood forest, once known as oak flats, we can suggest guidelines for restoring hydrology to the wetness classes in which we found oaks with high importance.