7. Finite factors

7.1 Overview - Finite factors

ANOVA is one of the most widely used statistical techniques, providing a partitioning of the meas...

7.2 Dichotomy: fixed vs random factors

Consider the classical one-way linear ANOVA model, as described in section 6.2 above. Specificall...

7.3 Not a dichotomy: a progression from fixed to random

What is meant by a 'finite' factor? Suppose, for any factor, there are a total of $A$ levels in t...

7.4 Example: environmental impact on molluscs

The study design We consider here a study examining effects of a sewage outfall for $p$ = 151 mol...

7.5 Broader implications for detecting impact

Comparison of results treating 'Locations' as random Historical wisdom for such a design would ha...

Introduction

New Statistical Methods in P8

New Tools & Utilities in P8

1.1 Expansion from P7 to P8

1.2 Definitions of statistics

1.3 Biotic data: summary stats

1.4 Split summary stats results by groups

1.5 Environmental data: summary stats

2.1 What is an empirical distribution?

2.2 Example: Empirical distributions of oyster sizes

3.1 Plots of empirical densities

3.2 Example: Dotplot of oyster sizes

3.3 Example: Violin plot of kelp holdfast volumes

4.1 Wilcoxon signed-rank test

4.2 Example: Plankton hauls

4.3 Mann-Whitney U test

4.4 Example: Snapper in marine reserves

4.5 Kruskal-Wallis test

4.6 Example: A bivalve species from Ekofisk

4.7 Kolmogorov-Smirnov test

4.8 Example: Sizes of oysters

4.9 Test of Association

4.10 Example: Ekofisk diversity

4.11 Example: Associations between species

Overview of new 'Design' options and tools

6.1 Overview - Allow heterogeneity

6.2 ANOVA in a nutshell

6.3 The Behrens-Fisher problem (BFP)

6.4 Multivariate Behrens-Fisher problem

6.5 Solution to the multivariate BFP

6.6 Example: one-way PERMANOVA allowing heterogeneity

6.7 Heterogeneity in more complex designs

6.8 Example: two-way crossed PERMANOVA allowing heterogeneity

7.1 Overview - Finite factors

7.2 Dichotomy: fixed vs random factors

7.3 Not a dichotomy: a progression from fixed to random

7.4 Example: environmental impact on molluscs

7.5 Broader implications for detecting impact

8.1 Designs lacking replication

8.2 Example: Split-plot - Woodstock vegetation

8.3 Example: Repeated measures - Victorian avifauna

9.1 Why group covariables together?

9.2 Periodic and cyclical models

9.3 Example: Annual monthly cycles - B.C. macroalgae

10.1 Ordinations for multi-factor designs

10.2 Main effects plot

10.3 Interaction plot

10.4 Example: NZ fish assemblages

11.1 What are 'residual' distances?

11.2 Example: Plankton (revisited)

12.1 Overview - Control charts

12.2 Classical univariate control chart

12.3 Classical multivariate control chart

12.4 Bivariate normal example: NZ fish

12.5 Dissimilarity-based multivariate control chart

12.6 Additional notes on implementing control charts

12.7 Example: Birds from Grand Forks

13.1 Overview

13.2 Analysing cumulative standardised data

13.3 Example: Mussel sizes in the Gulf of Alaska

13.4 Example: Gulf of Maine invertebrates - functional resemblance

14.1 Overview

14.2 Example: NE Pacific groundfish vs depth

15.1 New default colour palette

15.2 New selection options

15.3 Re-name levels of a factor (or indicator)

15.4 Add customised values/labels to graphical axes

15.5 Split data sheet by factor/indicator

15.6 Line plots for samples

15.7 Output group-level stats from dispersion (or variability) weighting

15.8 Output diagnostic plots from CAP

15.9 New diagnostics for PCA/PCO plots

7.1 Overview - Finite factors

7.2 Dichotomy: fixed vs random factors

7.3 Not a dichotomy: a progression from fixed to random

7.4 Example: environmental impact on molluscs

7.5 Broader implications for detecting impact

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