Multivariate Statistics for the Environmental Sciences

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Multivariate Statistics for the Environmental
Sciences

• Peter J. A. Shaw
• Chapter 1
• Introduction

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1.1 What is meant by multivariate stats?

• What do stats do for us?
• Descriptive Stats
• Inferential Stats

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• Univariate
• Multivariate
• Multivariate statistics tell you what you
  already know, but couldnt quite put your finger
  on
• Michael Usher

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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

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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

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1.3 When to use multivariate stats

• Dont 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

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1.4 Computing Requirements

• Most of the multivariate techniques require the
  use of a computer, except diversity indices and
  Bray-Curtis ordination

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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

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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

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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.

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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

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Points to consider in data organization

• Column organization
• Classification variables
• Metadata
• Missing values
• Exclude the variable(s)
• Exclude the observation(s)

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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

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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

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

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1.6.2 Life in Alaskan Streams sample data set
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