A1256654956XvjMU

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CHAPTER 28 Nested Designs
Tables, Figures, and Equations
From McCune, B. J. B. Grace. 2002. Analysis
of Ecological Communities. MjM Software Design,
Gleneden Beach, Oregon http//www.pcord.com
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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 SS DF MS F p
WSHED 0.67 1 0.67 0.01 0.933
STREAM W/IN WSHED (err 1) 513.83 6 85.64 17.72 0.000
WITHIN CELLS 77.33 16 4.83
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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 DF MS F p
WSHED 0.67 1 0.67 0.14 0.715
STREAM 508.83 3 169.61 35.09 0.000
WSHED BY STREAM 5.00 3 1.67 0.34 0.793
WITHIN CELLS 77.33 16 4.83
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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 SS DF MS F p
WSHED 198.37 1 198.37 124.20 0.000
STREAM W/IN WSHED (err 1) 9.58 6 1.60 0.44 0.841
WITHIN CELLS 58.00 16 3.63
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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 DF MS F p
WSHED 198.37 1 198.37 54.72 0.000
STREAM 3.13 3 1.04 0.29 0.834
WSHED BY STREAM 6.46 3 2.15 0.59 0.628
WITHIN CELLS 58.00 16 4.83
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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 WSHED STREAM PLOT RICHNESS
1 1 1 14 2 1 1 13
1 1 2 12 2 1 2 12
1 1 3 8 2 1 3 9
1 2 1 3 2 2 1 22
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
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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
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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 DF MS F p
WSHED 315.37 1 315.37 49.47 0.000
STREAM 0.13 3 0.04 0.01 0.999
WSHED BY STREAM 245.46 3 81.82 12.83 0.000
WITHIN CELLS 102.00 16 6.38
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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.
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Example 5
Table 28.8. Nonparametric MANOVA of a Sørensen
distance matrix, adapted from the example from
Anderson (2001).
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Example 5
Table 28.8. Nonparametric MANOVA of a Sørensen
distance matrix, adapted from the example from
Anderson (2001).
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Example 5
Table 28.8. Nonparametric MANOVA of a Sørensen
distance matrix, adapted from the example from
Anderson (2001).
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Example 5
Table 28.8. Nonparametric MANOVA of a Sørensen
distance matrix, adapted from the example from
Anderson (2001).
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Example 5
Table 28.8. Nonparametric MANOVA of a Sørensen
distance matrix, adapted from the example from
Anderson (2001).