Permutation procedures for multi-dimensional applications in wood related research

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 o f distance functions. Earlier work on this subject has demonstrated that wh en the distance function is selected appropriately, one-dimensional MRPP re present a rational alternative to traditional comparative statistical analy sis techniques, such as the Student's t-test (t-test). In the work presente d herein, MRPP are broadened to include analyses on the effect of a treatme nt on data were containing multiple variables which may be correlated. Thes e tests are a MRPP based on Euclidean distance (MRPP-E) and a MRPP motivate d by Hotelling's T-2 test (MRPP-H) which can account for the variance-covar iance structure of the data. Four hundred eighteen data points representing the moduli of elasticity (MOE) and rupture (MOR) of eight foot-long (244 c m), nominal 2 x 4 inch(2) (51 x 102 mm(2)), No. 2 grade, Douglas-fir, dimen sion lumber from seven growing regions in the western United States were se lected for use in this study. Data were analyzed using one- and two-dimensi onal, classical, parametric techniques (i.e. t-test and Hotelling's T-2 tes t) 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, considerab le differences in inference drawn regarding the presence of statistically s ignificant differences between data sets existed as a function of the analy tical test method used. The unique structure of the data encountered in thi s study showed that MRPP-E was insufficiently sensitive to the variance-cov ariance structure of the data. Visual examination of the data suggested tha t MRPP-H is more appropriate for the present data than MRPP-E.