Contents
|
Preface |
|
i |
Why Multivariate? |
|
1 |
The 10-Step Process |
|
5 |
Step 1. Getting yourself ready |
|
8 |
1. Embracing statistics |
|
8 |
2. Articulating goals |
|
16 |
Analysis objectives |
|
17 |
Step 2. Getting your data ready |
|
19 |
3. Meeting matrices |
|
19 |
4. Starting in PC-ORD |
|
22 |
5. Inputting and screening your data |
|
27 |
Entering your data |
|
27 |
Importing your data |
|
27 |
From a spreadsheet |
|
27 |
From a database |
|
31 |
Screening your data |
|
32 |
Screening with Summary |
|
32 |
Screening with Species Lists |
|
33 |
Step 3. Structuring your data |
|
34 |
6. Sampling sufficiently |
|
34 |
Is N enough? |
|
34 |
Species Area Curves (SPA) |
|
34 |
7. Structuring your matrices |
|
36 |
Restructuring with Modify Data |
|
36 |
Step 4. Exploring and preparing your data |
|
39 |
8. What have you actually measured? |
|
39 |
Sparsity (zeros) |
|
40 |
Checking sparsity with Summary |
|
41 |
Checking sparsity with Profile |
|
41 |
Reducing sparsity with Delete Columns |
|
41 |
Non-zero values |
|
41 |
Response comparability |
|
43 |
Standardizing with General Relativization |
|
44 |
Standardizing with Relativization by Maximum |
|
45 |
9. How variable are your data? |
|
46 |
Heterogeneity |
|
46 |
Checking sparsity with SUMMARY |
|
46 |
Checking sparsity with PROFILE |
|
48 |
Reducing sparsity with Functional Diversity |
|
48 |
Outliers |
|
51 |
Checking for outliers with Summary |
|
51 |
Checking for outliers with Outlier Analysis |
|
51 |
Checking for outliers with Profile |
|
51 |
Checking for outliers with Boxplots |
|
52 |
Response distributions |
|
52 |
Checking for normality with Distributions |
|
52 |
Checking for normality with Boxplots |
|
53 |
Step 5. Selecting the tools |
|
54 |
10. Distance measures |
|
54 |
Euclidean Distance |
|
55 |
Chi-square Distance |
|
57 |
City-block Distance (e.g., Sørensen) |
|
58 |
11. Model form |
|
60 |
Hypothesizing relationships |
|
60 |
Exploring relationships with Scatterplot |
|
60 |
12. Analysis tools |
|
62 |
13. What is ordination? |
|
64 |
Step 6. Modifying your data |
|
68 |
14. Meeting parametric assumptions |
|
68 |
Transforming to a Power |
|
68 |
Transforming to the Logarithmic |
|
69 |
Transforming to Arcsinesquareroot |
|
69 |
To Multiply or add a constant |
|
69 |
15. Reweighting responses |
|
70 |
Checking influence with Dominance Curves |
|
70 |
Adjusting influence with Relativizations |
|
70 |
Step 7a: Guiding pattern (guided ordination) |
|
73 |
16. WA: Weighted averaging |
|
73 |
How to run it |
|
75 |
17. Polar (Bray-Curtis) ordination |
|
77 |
How to run it |
|
79 |
18. CCA: Canonical correspondence analysis |
|
81 |
How to run it |
|
88 |
19. RDA: Redundancy analysis |
|
91 |
How to run it |
|
95 |
20. FSO: Fuzzy set ordination |
|
97 |
How to run it |
|
100 |
21. Interpreting guided ordinations |
|
102 |
Step 7b: Seeking pattern (free ordination) |
|
104 |
22. PCA: Principal components analysis |
|
104 |
How to run it |
|
109 |
23. NMS: Nonmetric multidimensional scaling |
|
112 |
How to run it |
|
117 |
Choosing dimensionality using the stress test |
|
118 |
Verifying the final solution |
|
119 |
NMS Scores |
|
121 |
24. Interpreting free ordinations |
|
124 |
Step 7c: Looking for groups (classification) |
|
126 |
25. Cluster analysis |
|
126 |
How to run it |
|
130 |
Two-way cluster |
|
131 |
26. TWINSPAN |
|
135 |
How to run it |
|
136 |
Step 7d: Testing among groups |
|
137 |
27. MRPP: Multi-response permutation procedure |
|
137 |
28. PerMANOVA: Distance-based MANOVA |
|
141 |
How to run it |
|
144 |
29. SumF |
|
147 |
How to run it |
|
148 |
30. ISA: Indicator species analysis |
|
150 |
How to run it |
|
153 |
Blocked indicator species analysis |
|
153 |
Step 7e: Assessing associations |
|
154 |
31. Mantel test |
|
154 |
How to run it |
|
156 |
Partial Mantel test |
|
156 |
32. FCA: Fourth corner analysis |
|
157 |
How to run it |
|
160 |
Step 8: Confirming your results |
|
161 |
Step 9: Using interpretive tools |
|
163 |
33. Finding your story |
|
163 |
Interpreting ordination diagrams |
|
163 |
Simple scatterplot |
|
164 |
Overlay Main Matrix |
|
165 |
Overlay Second Matrix |
|
167 |
Joint plots |
|
168 |
Convex hulls and centroids |
|
169 |
% of variance |
|
170 |
Successional vectors |
|
170 |
Ordered Main Matrix |
|
173 |
Step 10: Presenting your story |
|
175 |
34. Communicating your message |
|
175 |
Presenting Summaries |
|
175 |
Presenting Graphics |
|
175 |
Rotating and reflecting ordinations |
|
177 |
Drawing outlines on ordered tables |
|
179 |
Appendix A: Other PC-ORD Tools |
|
180 |
Appendix B: Matrix Algebra Unplugged |
|
181 |
Appendix C: How to Report |
|
183 |
Appendix D: Further Reading |
|
186 |
Appendix E: Available Supplements |
|
187 |
Appendix F: Acronyms & Symbols |
|
188 |
Index |
|
189 |