Draft

Week 9: PCA and Report 2

1 Objectives

The aim of this component of the practical series is to introduce you to several common techniques for analysing multivariate data. At the end of them you will:

  • Be familiar with the principles underpinning principal components analysis (PCA), and non-metric multidimensional scaling (nMDS)
  • Be familiar with the principles underpinning multivariate hypothesis testing using permutational techniques such as ANOSIM and PERMANOVA
  • Be able to plan and conduct experiments that test multivariate hypotheses
  • Know how to carry out these analyses using relevant statistical software (Jamovi, PRIMER or R)
  • Be able to interpret, present, and report your findings clearly and effectively

In this specific practical you will:

2 Module 3 Submission Requirements

This assessment has two components, each with a separate submission on Canvas.

2.1 1. Group Data File

  • What to submit: A single Excel file (.xlsx) containing your group’s raw data. This file must contain two clearly labelled worksheets:
    • Worksheet 1: Species Data: Your species assemblage data.
    • Worksheet 2: Habitat Data: Your habitat data.
  • Who submits: Only one member of your group should upload the file.
  • Deadline: 8:00am on the day of your practical session in Week 11.
  • Value: This component is worth 5% of your final mark for the unit.

2.2 2. Individual Report

  • What to submit: A scientific report based on the analysis of your group’s data.
  • Who submits: This is an individual submission. Every student must submit their own report.
  • Format: The report must be formatted as a short scientific article. For detailed formatting requirements, refer to the assessment guidelines available on Canvas.
  • Deadline: The due date is listed in the “Assessments” section on Canvas.
  • Value: This component is worth 15% of your final mark for the unit.

3 Analyses covered in this practical

Principal Components Analysis (PCA) is a technique used to reduce the dimensionality of a dataset by extracting a smaller set of new variables (principal components) that capture as much of the variance in the original data as possible. These components summarise complex patterns across multiple variables, making the data easier to visualise and interpret.

4 Part 1: Principal components analysis – “perceptions of biology lecturers”

You will use PCA to reduce your set of measured variables into a coherent smaller dataset. In addition, you will be comparing your lecturer perceptions between preferred systems (marine, freshwater or terrestrial), preferred taxon (animals or plants) and gender (male or female) using conventional univariate approaches (t-tests/ANOVAs). To perform these univariate approaches, make sure that you not only create the principal components (PCs) but also save the scores (see below) for each component.

The process in JAMOVI is listed below. R instructions are given on Canvas in an R Studio file

4.1 1. Import your data

  • Open Jamovi.
  • Go to the top-left menu (☰) → click Open → Browse and select your Excel file (e.g. your lecturer dataset).
  • Once imported, check that all the columns (variables) are correctly recognised as numeric (look for a ruler icon in the column headers).

4.2 2. Run Principal Components Analysis

  • Click on the “Factor” tab in the top toolbar.
  • Select Principal Component Analysis.

4.3 3. Select your variables

  • In the Variables panel on the left, select the variables of interest and move them into the “Variables” box.

4.4 4. Descriptive statistics and suitability tests

  • Under “Assumption Checks”, tick “Bartlett’s Test of Sphericity”

4.5 5. Extraction settings

  • In the “Model” section:
    • Under Number of components, select “Eigenvalues > 1”
    • Tick Scree Plot
    • Tick Unrotated solution

4.6 6. Rotation

  • Scroll to the “Rotation” section:
    • Choose Varimax rotation.
    • Tick Display Rotated Solution.

4.7 7. Save component scores

  • Tick “Save component scores to data set” (usually found under the Scores section at the bottom).
  • This will add new variables to your dataset representing each component.

4.8 8. Missing data handling

  • At the bottom of the PCA panel, set “Missing values” to Exclude cases listwise.

4.9 9. Run the analysis

  • Click anywhere outside the setup panel, and Jamovi will display your PCA results.

5 After PCA: Review Your Output

  • Correlation Matrix: Check for variables that are not correlated with the others. These may not be suitable for PCA. You can remove them and rerun the analysis if needed.
  • Bartlett’s Test: These tell you if your data is suitable for PCA. Bartlett’s Test should be significant (p < .05).
  • Scree Plot: Helps determine how many components to retain.
  • Rotated Solution: Makes it easier to interpret your components.
  • Saved Scores: You can now use these component scores in further analyses (e.g., regression or cluster analysis).

Bartlett’s Test of Sphericity tests whether your correlation matrix is significantly different from an identity matrix—a matrix where all off-diagonal values are zero (no correlation between variables), and all diagonal values are one (each variable only correlates with itself).

If your data came from a population with no correlations between variables, the correlation matrix would be an identity matrix. In that case, Principal Components Analysis (PCA) would not be appropriate.

A significant result (p < .05) means that your correlation matrix is not an identity matrix, and PCA can be used.

That said, this test is most useful when used alongside visual inspection of your correlation matrix. If many variables aren’t correlated with others, they may not contribute much to PCA and could be removed.

5.1 Interpreting the PCA

You need to:

  • Look at the correlation matrix.
  • Examine the scree plot and determine how many PCs you can identify (eigenvalues >1, Kaiser’s Criterion).
  • Establish a meaningful name for each component based on the loadings for individual variables in the rotated solutions.

5.2 After the PCA

Examine whether gender, system biases (marine v. terrestrial) and taxon (animal v. plant) biases may affect the perceptions of biology lecturers. You will need to code the columns for each factor (i.e. males = 0, females = 1) for Jamovi to perform its standard one-way ANOVAs or t-tests.

5.3 Questions to consider:

  • Do males and females perceive lecturer qualities the same way?
  • Do botanists and zoologists perceive lecturer qualities the same way?
  • Do marine and terrestrial folk perceive lecturer qualities the same way?

6 Template

A template for your study design is provided. You can download it here.

7 References

See annotated reading list with lectures posted on unit web site.

  • Gaston, K. J., T. M. Blackburn, Lawton. J. (1993). Comparing Animals and Automobiles – a Vehicle for Understanding Body Size and Abundance Relationships in Species Assemblages. Oikos 66: 172-179.
  • Quinn G.P. and M.J. Keough. (2002). Experimental design and data analysis for biologists. Cambridge: Cambridge University Press. (appropriate chapters)
  • Quinn G.P. and M.J. Keough. (2023). Experimental design and data analysis for biologists. 2nd edn Cambridge: Cambridge University Press. (appropriate chapters)