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 how 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.Types of data to collect 2.Avoiding pseudoreplication 3.Organization of the data matrix 4.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)

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 Points to consider in data organization cont.

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