1. CHAPTER 28 Nested Designs From: McCune, B. & J. B. Grace. 2002. Analysis of Ecological Communities. MjM Software Design, Gleneden Beach, Oregon http://www.pcord.comhttp://www.pcord.com Tables, Figures, and Equations

2. 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 28.1. Nested sampling design analyzed with a univariate nested ANOVA. Source of VariationSSDFMSFp WSHED0.671 0.010.933 STREAM W/IN WSHED (err 1)513.83685.6417.720.000 WITHIN CELLS77.33164.83

3. Incorrect analysis (factorial): MANOVA RICHNESS by WSHED(1,2) STREAM(1,4) /DESIGN. Table 28.2. Nested sampling design incorrectly analyzed with a factorial ANOVA. Source of VariationSSDFMSFp WSHED0.671 0.140.715 STREAM508.833169.6135.090.000 WSHED BY STREAM5.0031.670.340.793 WITHIN CELLS77.33164.83

4. 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 28.3. Nested sampling design analyzed with a univariate nested ANOVA. Source of VariationSSDFMSFp WSHED198.371 124.200.000 STREAM W/IN WSHED (err 1)9.5861.600.440.841 WITHIN CELLS58.00163.63

5. Incorrect analysis (factorial): MANOVA RICHNESS by WSHED(1,2) STREAM(1,4) /DESIGN. Table 28.4. Nested sampling design incorrectly analyzed with a factorial ANOVA. Source of VariationSSDFMSFp WSHED198.371 54.720.000 STREAM3.1331.040.290.834 WSHED BY STREAM6.4632.150.590.628 WITHIN CELLS58.00164.83

6. 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 28.5. Data set for Example 3. WSHEDSTREAMPLOTRICHNESSWSHEDSTREAMPLOTRICHNESS 11114 21 113 11 212 21 2 11 3 8 21 3 9 12 1 3 22 122 12 2 5 22 216 12 3 1 22 321 13 1 8 23 114 13 2 9 23 213 13 312 23 311 14 1 3 24 110 14 2 7 24 2 14 3 24 312

7. Correct analysis (nested): MANOVA RICHNESS by WSHED(1,2) STREAM(1,4) /DESIGN WSHED VS 1, STREAM WITHIN WSHED = 1 VS WITHIN. Table 28.6. Nested sampling design analyzed with a univariate nested ANOVA. Source of VariationSSDFMSFp WSHED315.371 7.710.032 STREAM W/IN WSHED (err 1)245.58640.936.420.001 WITHIN CELLS102.00166.38

8. Incorrect analysis (factorial): MANOVA RICHNESS by WSHED(1,2) STREAM(1,4) /DESIGN. Table 28.7. Nested sampling design incorrectly analyzed with a factorial ANOVA. Source of VariationSSDFMSFp WSHED315.371 49.470.000 STREAM0.1330.040.010.999 WSHED BY STREAM245.46381.8212.830.000 WITHIN CELLS102.00166.38

9. 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.

10. Example 5 Table 28.8. Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).

11. Example 5 Table 28.8. Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).

12. Example 5 Table 28.8. Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).

13. Example 5 Table 28.8. Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).

14. Example 5 Table 28.8. Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).