CHAPTER 28 Nested Designs Tables Figures and Equations
CHAPTER 28 Nested Designs Tables, Figures, and Equations From: Mc. Cune, B. & J. B. Grace. 2002. Analysis of Ecological Communities. Mj. M Software Design, Gleneden Beach, Oregon http: //www. pcord. com
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 Variation WSHED STREAM W/IN WSHED (err 1) WITHIN CELLS SS DF MS F p 0. 67 1 0. 67 0. 01 0. 933 513. 83 6 85. 64 17. 72 0. 000 77. 33 16 4. 83
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 Variation SS D MS F F p WSHED 0. 6 1 0. 6 0. 0. 7 7 7 14 15 STREAM 50 3 16 35. 0. 0 8. 8 9. 6 09 00 3 1 WSHED BY STREAM WITHIN CELLS 5. 0 3 1. 6 0. 0. 7 0 7 34 93 77. 1 4. 8 33 6 3
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 Variation WSHED STREAM W/IN WSHED (err 1) WITHIN CELLS SS DF MS F p 198. 37 124. 20 0. 000 9. 58 6 1. 60 0. 44 0. 841 58. 00 16 3. 63
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 Variation SS D MS F F p WSHED 198. 1 198. 54. 0. 0 37 37 72 00 STREAM 3. 13 3 1. 0 0. 2 4 9 0. 8 34 WSHED BY STREAM 6. 46 3 2. 1 0. 5 5 9 0. 6 28 WITHIN CELLS 58. 0 0 1 6 4. 8 3
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. WSHED STREAM PLOT RICHNESS 1 14 2 1 1 13 1 1 2 12 1 1 3 8 2 1 3 9 1 2 1 3 2 2 1 2 2 5 2 2 2 16 1 2 3 1 2 2 3 21 1 3 1 8 2 3 1 14 1 3 2 9 2 3 2 13 1 3 3 12 2 3 3 11 1 4 1 3 2 4 1 10 1 4 2 7 2 4 2 10 1 4 3 10 2 4 3 12
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 Variation SS DF MS F p WSHED 315. 37 1 315. 37 7. 71 0. 032 STREAM W/IN WSHED (err 1) 245. 58 6 40. 93 6. 42 0. 001 WITHIN CELLS 102. 00 16 6. 38
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 Variation SS D MS F F p WSHED 315. 1 315. 49. 0. 0 37 37 47 00 STREAM 0. 13 WSHED BY STREAM 245. 3 46 3 WITHIN CELLS 102. 1 00 6 0. 0 4 1 0. 9 99 81. 12. 0. 0 82 83 00 6. 3 8
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 28. 8. Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).
Example 5 Table 28. 8. Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).
Example 5 Table 28. 8. Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).
Example 5 Table 28. 8. Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).
Example 5 Table 28. 8. Nonparametric MANOVA of a Sørensen distance matrix, adapted from the example from Anderson (2001).
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