vegetation properties should exist. Because a soil series 

 or series-phase classification was not available for most of 

 the study area, and because the samples had not been 

 chemically analyzed, physical soil characteristics were 

 used to analyze soil-habitat type relationships. 



Data were reduced by removing redundant variables. 

 An "inverse" ordination analysis, sometimes called Q- 

 technique (Williams and Lambert 1961), sorts sample- 

 pairs into similarity groups rather than species-pairs. 

 The four "inverse" ordinations of soil characteristics re- 

 sulted in a high concurrence of rankings of variables 

 (table 2). The assignment of statistical significance to 

 these rankings is meaningless, as the assumptions of 

 linear relationships and independence of terms cannot be 

 met. But almost identical rankings of variables at the 

 extremes of all four ordination techniques identified the 

 same primary group of variables. Structural ped size, ped 

 shape, and coarse fragment content contain variation that 

 appears to be related to internal structure of the data. 

 These relationships were supported by correlation coeffi- 

 cients greater than 0.70 between structural and coarse 

 fragment groups within horizons. 



Factor analysis, an eigenvector analysis similar to prin- 

 cipal component analysis, describes covariance relation- 

 ships between two or more variables. If structural ped 

 size and shape, or any other group of variables, are sig- 

 nificant covariates, then a single variable is sufficient for 

 analysis. But if a set of variables are not related, then all 

 variables should be retained. Significant covariate rela- 

 tionships were found for seven groups in the first six fac- 

 tors of a varimax rotated factor analysis (SAS 1982b). In 

 Factor 1, the silt and clay content of horizons 2 and 3 



Table 2 — Comparison of first axis ordination selection of coarse- 

 textured parent material soil characteristics by polar 

 ordination (PO), centered principal components analysis 

 (PCA), two-way species indicator analysis (TWINSPAN), 

 and detrended correspondence analysis (DCA). Data set 

 consisted of 22 variables and n = 55. Variable suffix 

 indicates associated horizon number 



Axis 



PO 



PCA 



TWINSPAN 



DCA 



1 



Size2 



Size2 



Shape2 



Size2 



2 



Shape2 



Shape2 



Size2 



Shape2 



3 



Shape3 



Size3 



Shape3 



Shape3 



4 



Size3 



Shape3 



Size3 



Size3 



5 



Depth3 



Depth3 



Chroma3 



Depth3 



6 



Clay2 



Clay2 



Chroma2 



pH3 



7 



pH3 



Depth2 



Value3 



Depth2 



8 



Silt2 



Silt2 



Depth3 



Clay2 



9 



Depth2 



pH3 



pH2 



Clay3 



10 



pH2 



Silt3 



Clay2 



pH2 



11 



Silt3 



Clay3 



Value2 



Silt3 



12 



Clay3 



pH2 



Depth2 



Silt2 



13 



Value3 



Value2 



pH3 



Value2 



14 



Value2 



Value3 



Clay3 



Value3 



15 



%Stone2 



Chroma3 



Silt3 



Chroma3 



16 



Chroma3 



%Cobble3 



Silt2 



%Cobble3 



17 



Chroma2 



%Gravel3 



%Stone3 



Chroma2 



18 



%Cobble3 



Chroma2 



%Stone2 



%Gravel3 



19 



%Stone3 



%Cobble2 



%Cobble2 



%Stone2 



20 



%Cobble2 



%Stone2 



%Cobble3 



%Cobble2 



21 



%Gravel3 



%Stone3 



%Gravel3 



%Stone3 



22 



%Gravel2 



%Gravel2 



%Gravel2 



%Gravel2 



were highly related to each other. In Factor 2, structural 

 size and ped shape in horizon 2 and percentage of gravel 

 and cobble content, also in horizon 2, were related, but the 

 two pairs of variables are inversely related to each other. 

 This supports the positioning at the extremes of spatial 

 structure developed by ordination (table 2). The only 

 variables not exhibiting good covariate relationships were 

 chroma and pH of the second horizon and chroma, per- 

 centage gravel, percentage cobble, and pH of the third 

 horizon. 



Stepwise discriminant analysis (Dixon 1981) computes 

 classification functions for subsets of quantitative vari- 

 ables by means of F values from an analysis of covariance. 

 Table 3 lists the stratification combinations and selected 

 variables for which F values were significant at the 0.90 

 level or greater. Through this analysis, 14 variables were 

 identified as containing useful information for discrimi- 

 nating between various stratifications of the data. These 

 variables were: 



Chroma2 Clay2 Size3 Shape3 %Cobble3 



Size2 %Cobble2 Depth3 Silt3 pH3 

 Shape2 pH2 Value3 %Gravel3 



Canonical discriminant analysis of the coarse-textured 

 parent material samples stratified into six habitat types 

 resulted in the first three canonical components having 

 F values significant at the 90 percent probability level or 

 greater. All 22 variables had positive or negative correla- 

 tion values greater than 0.5 within the first three canoni- 

 cal components. This is not surprising because factor 

 analysis showed all variables, but five, were members of 

 highly related covariate groups. By selecting the two 

 largest positive and negative values within each of the 

 three canonical components, six pairs of soil variables 

 were identified as being good discriminators for habitat 

 types. 



Positive canonical coefficient pairs: 



Value3 - Chroma2 %Gravel2 - %Gravel3 

 pH3 - Shape3 



Negative canonical coefficient pairs: 

 Depth3 - %Cobble3 Clay2 - Silt2 

 Shape2 - Size2 



Calculations similar to those of stepwise discriminant 

 analysis were produced by canonical discriminant analy- 

 sis for each of the 11 other data stratifications. Due to re- 

 dundancy of results, these analyses are not presented. 

 Based on the results of principal component analysis, 

 factor analysis, and stepwise and canonical discriminant 

 analysis, the following four variables were chosen for use 

 in developing discriminant functions: Size2, Size3, 

 %Cobble2, and %Cobble3. 



Discriminant functions are the most valuable when 

 analyzing homogeneous groups in which clusters of 

 samples overlap (Sneath and Sokal 1973). This appears 

 to be the situation among habitat types and soils. Statis- 

 tical significance can only be ascribed to discriminant 

 functions if the variables are multivariate normal, the 

 variance-covariance matrices are similar, prior probabili- 

 ties are identifiable, and the relationships between vari- 

 ables are linear (Greig-Smith 1983; Pielou 1977; Williams 



7 



