CHAPTER 28 Nested Designs From: McCune, B. & J. B. Grace Analysis of Ecological Communities. MjM Software Design, Gleneden Beach, Oregon Tables, Figures, and Equations

Example 1 Correct analysis (nested): MANOVA RICHNESS by WSHED(1,2) STREAM(1,4) /DESIGN WSHED VS 1, STREAM WITHIN WSHED = 1 VS WITHIN. Table Nested sampling design analyzed with a univariate nested ANOVA. Source of VariationSSDFMSFp WSHED STREAM W/IN WSHED (err 1) WITHIN CELLS

Incorrect analysis (factorial): MANOVA RICHNESS by WSHED(1,2) STREAM(1,4) /DESIGN. Table Nested sampling design incorrectly analyzed with a factorial ANOVA. Source of VariationSSDFMSFp WSHED STREAM WSHED BY STREAM WITHIN CELLS

Example 2 In this example, the watersheds differ greatly, and there is little variation among streams within watershed. The results are again qualitatively similar between the correct and incorrect analysis (Tables 28.3 and 28.4). Correct analysis (nested): MANOVA RICHNESS by WSHED(1,2) STREAM(1,4) /DESIGN WSHED VS 1, STREAM WITHIN WSHED = 1 VS WITHIN. Table Nested sampling design analyzed with a univariate nested ANOVA. Source of VariationSSDFMSFp WSHED STREAM W/IN WSHED (err 1) WITHIN CELLS

Incorrect analysis (factorial): MANOVA RICHNESS by WSHED(1,2) STREAM(1,4) /DESIGN. Table Nested sampling design incorrectly analyzed with a factorial ANOVA. Source of VariationSSDFMSFp WSHED STREAM WSHED BY STREAM WITHIN CELLS

Example 3 In this case, streams differ greatly (Table 28.5), but the factorial analysis detects an interaction between stream and watershed (Tables 28.6 and 28.7). The results from the two analyses differ greatly. Table Data set for Example 3. WSHEDSTREAMPLOTRICHNESSWSHEDSTREAMPLOTRICHNESS

Correct analysis (nested): MANOVA RICHNESS by WSHED(1,2) STREAM(1,4) /DESIGN WSHED VS 1, STREAM WITHIN WSHED = 1 VS WITHIN. Table Nested sampling design analyzed with a univariate nested ANOVA. Source of VariationSSDFMSFp WSHED STREAM W/IN WSHED (err 1) WITHIN CELLS

Incorrect analysis (factorial): MANOVA RICHNESS by WSHED(1,2) STREAM(1,4) /DESIGN. Table Nested sampling design incorrectly analyzed with a factorial ANOVA. Source of VariationSSDFMSFp WSHED STREAM WSHED BY STREAM WITHIN CELLS

Example 4 The method for adding more levels to the design is not immediately obvious in SPSS. In this case, we added to the correct, nested design another level "VALLEY," representing three different valleys within each watershed. Streams are nested within valleys. The syntax for requesting the analysis is: MANOVA RICHNESS by WSHED(1,2) VALLEY(1,3) STREAM(1,4) /DESIGN WSHED VS 1, VALLEY WITHIN WSHED = 1 VS 2 STREAM WITHIN VALLEY WITHIN WSHED = 2 VS WITHIN. As in the other examples, variation at each level in design is compared with the variation in the next lower level.

Example 5 Table Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).

Example 5 Table Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).

Example 5 Table Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).

Example 5 Table Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).

Example 5 Table Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).