Peck, J.E. 2016. Multivariate Analysis for Ecologists: Step-by-Step. Second Edition. MjM Software Design, Gleneden Beach, OR. 192 pages, spiral bound to lay flat.


a) a required supplement to the PC‑ORD workshops;
b) a stand-alone guide for self-taught beginning multivariate analysis.

This companion book is available from the new distributor at


The book introduces techniques and procedures in the order in which you would use them if you were to follow this 10-step analysis process:

  1. get yourself ready--brush up on basic statistical concepts
  2. get your data ready--enter and screen the data for errors
  3. get your data structured--structure the matrices for your question of interest
  4. explore and prepare your data--get to know the properties of your data
  5. select the tools--select tools appropriate to your data and question
  6. modify the data--adjust the data as needed to use those tools
  7. apply the selected tools--run your chosen analysis tools
  8. confirm the patterns--run some other tools and see what you find
  9. interpret your results--use graphing tools to infer relationships
  10. present your 'story'--customize figures to convey your story


Step 1. Getting yourself ready
1. Embracing statistics
2. Articulating goals

Step 2. Getting your data ready
3. Meeting matrices
4. Starting in PC-ORD
5. Inputting and screening your data

Step 3. Structuring your data
6. Sampling sufficiently
7. Structuring your matrices

Step 4. Exploring and preparing your data
8. What have you actually measured?
9. How variable are your data?

Step 5. Selecting the tools
10. Distance measures
11. Model form
12. Analysis tools
13. What is ordination?

Step 6. Modifying your data
14. Meeting parametric assumptions
15. Reweighting responses

Step 7a: Guiding pattern (guided ordination)
16. WA: Weighted averaging
17. Polar (Bray-Curtis) ordination
18. CCA: Canonical correspondence analysis
19. RDA: Redundancy analysis
20. FSO: Fuzzy set ordination
21. Interpreting guided ordinations

Step 7b: Seeking pattern (free ordination)
22. PCA: Principal components analysis
23. NMS: Nonmetric multidimensional scaling

Step 7c: Looking for groups (classification)
25. Cluster analysis

Step 7d: Testing among groups
27. MRPP: Multi-response permutation procedure
28. PerMANOVA: Distance-based MANOVA
29. SumF
30. ISA: Indicator species analysis

Step 7e: Assessing associations
31. Mantel test
32. FCA: Fourth corner analysis

Step 8: Confirming your results

Step 9: Using interpretive tools
33. Finding your story

Step 10: Presenting your story
34. Communicating your message

Appendix A: Other PC-ORD Tools
Appendix B: Matrix Algebra Unplugged
Appendix C: How to Report
Appendix D: Further Reading
Appendix E: Available Supplements
Appendix F: Acronyms & Symbols

What you'll learn

For each tool, there are sections on:

  • what you can do with it
  • when you might use it
  • what it does
  • what it means
  • what you need
  • what you get
  • what else you need to know
  • how to run it (in PC-ORD v. 7)
  • how to interpret it


Supplement A: Check-list Template
Supplement B: Example Analysis Pathways
Supplement C: Examples from the Literature
Supplements D & E are available by request (see Appendix E in Second Edition)
Supplement F: Distance measures calculation spreadsheet

Supplement G: Book figures are available by request (for instruction only)