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

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


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
    26. TWINSPAN
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


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)

Corrections to Multivariate Analysis for Ecologists: Step-by-Step

JeriLynn E. Peck, Second Edition, 2016

Pg. 11, definition of type II error: This should read "leading us to falsely retain a false hypothesis".

Pg. 11, Bonferroni correction in right column: I wrote divided when I meant multiplied, so in two places this should read "correction involves multiplying your observed alpha" and "should thus be multiplied by 9".

Pg. 102, type II error in left column: This should read "of falsely accepting a false hypothesis".

Pg. 141, Figure 28.1

Please download this file to access the corrected figure:

2016 Step Errata.pdf

Corrections to Multivariate Analysis for Community Ecologists: Step-by-Step Using PC-ORD

JeriLynn E. Peck, First Edition, 2010

Pg. 42: The description of Whittaker's beta diversity is backwards and should instead read: "by dividing gamma diversity by mean alpha diversity (the average for the 'S' column) and subtracting 1".

Pg. 103, Figure 27.1: see for 2nd edition above.