Permutation procedures for multi-dimensional applications in wood related research

Summary Two nonparametric statistical techniques are presented which allow the user to evaluate the effect of a treatment on an n-dimensional set of variables associated with forest products. The multi-response permutation procedures (MRPP) are a broad category of permutation techniques based on a variety of distance functions. Earlier work on this subject has demonstrated that when the distance function is selected appropriately, one-dimensional MRPP represent a rational alternative to traditional comparative statistical analysis techniques, such as the Student's t-test (t-test). In the work presented herein, MRPP are broadened to include analyses on the effect of a treatment on data were containing multiple variables which may be correlated. These tests are a MRPP based on Euclidean distance (MRPP-E) and a MRPP motivated by Hotelling's T² test (MRPP-H) which can account for the variance-covariance structure of the data. Four hundred eighteen data points representing the moduli of elasticity (MOE) and rupture (MOR) of eight foot-long (244 cm), nominal 2 × 4 inch² (51 × 102 mm²), No. 2 grade, Douglas-fir, dimension lumber from seven growing regions in the western United States were selected for use in this study. Data were analyzed using one- and two-dimensional, classical, parametric techniques (i.e. t-test and Hotelling's T² test) and the more intuitive and nonparametric MRPP in similar dimensions. The results indicated that the MOE demonstrated some degree of sensitivity to the growth region, while the MOR proved to be insensitive. Also, considerable differences in inference drawn regarding the presence of statistically significant differences between data sets existed as a function of the analytical test method used. The unique structure of the data encountered in this study showed that MRPP-E was insufficiently sensitive to the variance-covariance structure of the data. Visual examination of the data suggested that MRPP-H is more appropriate for the present data than MRPP-E. Received 7 October 1998