Multivariate Statistics for the Environmental Sciences

1. Multivariate Statistics for the Environmental Sciences Peter J. A. Shaw Chapter 1 Introduction

2. 1.1 What is meant by multivariate stats? • What do stats do for us? • Descriptive Stats • Inferential Stats

3. Univariate • Multivariate “Multivariate statistics tell you what you already know, but couldn’t quite put your finger on” Michael Usher

5. 1.1.1 Why use multivariate stats? • Save time by reducing analytical work • Reduces the danger of misinterpreting random noise • Can be used to explore and describe data sets with many variables • Allows for the generation of a hypothesis • Suggests patterns to be found with relatively little work

6. 1.2 Scope of the Book • Explain application of multivariate techniques • Will not focus on data collection • 5 approaches that will be discussed: diversity indices, multiple regression, ordination, cluster analysis and canonical correspondence analysis • Chapter structure: • Introduce the technique • Apply the technique to small, model datasets to explain procedures • Show how multivariate stats contributes to environmental sciences

7. 1.3 When to use multivariate stats • Don’t use when there is just one specific dependent variable responding to one defined factor • Refer to page 7 of Shaw for a list of common environmental research situations in which multivariate stats should/can be used

8. 1.4 Computing Requirements Most of the multivariate techniques require the use of a computer, except diversity indices and Bray-Curtis ordination

9. 1.5 Preparing the data; Points to consider • Types of data to collect • Avoiding pseudoreplication • Organization of the data matrix • Preliminary inspection of the data

10. 1.5.1 Types of data to collect • Four different types of data, in order of increasing information content • Nominal data • Ordinal data • Continuous data • Interval data • Ratio data

11. 1.5.2 Avoiding pseudoreplication • Defined by Hurlbert (1984) as: “the use of inferential statistics to test for treatment effects with data from experiments where either treatments are not replicated (though samples may be) or replicates are not statistically independent.” • Essentially, it is organizing the data in such a way that it appears more independent observations have been made than are actually the case.

14. 1.5.3 Organization of the data matrix • Remember, computers are stupid, therefore you must pick up the slack! Properly format your data • Store data in a matrix (rectangular array of data) • Metadata

17. Points to consider in data organization Column organization • Classification variables • Metadata Missing values • Exclude the variable(s) • Exclude the observation(s)

18. Points to consider in data organization cont. Format errors • Format data so it is compatible with the requirements of the software packages used for analysis Recoding data • Only do inside the statistical package once the data matrix has been assembled • Collinear

19. 1.5.4 Preliminary inspection of the data • GIGO: Garbage In Garbage Out • If the matrix data is odd or incorrectly entered, it will likely affect the analysis

21. Inspect data for outliers before analysis • Normal distribution • Multivariate normal distribution

22. 1.6.2 Life in Alaskan Streams sample data set