Multivariate Statistics for the Environmental Sciences Peter J

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

1. 1 What is meant by multivariate stats? • What do stats do for us? – Descriptive Stats – Inferential Stats

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

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

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 multivariate stats contributes to environmental sciences

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

1. 4 Computing Requirements Most of the multivariate techniques require the use of a computer, except diversity indices and Bray-Curtis ordination

1. 5 Preparing the data; Points to consider 1. 2. 3. 4. Types of data to collect Avoiding pseudoreplication Organization of the data matrix Preliminary inspection of the data

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

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.

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

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

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

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

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

1. 6. 2 Life in Alaskan Streams sample data set