Multivariate Statistics: What is it good for

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Multivariate Statistics What is it good for?

• http//www4.ncsu.edu/jcallair/multivariate06.htm

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Intro
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Regression Class Evaluations
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Comments

• More examples in SPSS
• More practice using SPSS
• More examples of write ups
• More cowbell

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• Multivariate analysis refers to a broad class of
  statistical methods that simultaneously analyze
  multiple measurements on each individual or
  object under investigation.
• The term multivariate is often used loosely, and
  there's no formal set of multivariate statistical
  methods

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• Technically, it is multivariate whenever more
  than two variables are under study
• However, it is most common to use this term to
  refer to multiple dependent variables

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• A broader definition (which is appropriate since
  MANY of our techniques wont HAVE a DV) is
  analyses aimed at disentangling complex
  interrelationships between variables measured on
  the same individual.

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Why multivariate statistics?
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Why multivariate statistics?

• Reality
• Univariate stats only go so far when applicable
• Real data usually contains more than one DV
• Multivariate analyses are much more realistic and
  feasible

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Why multivariate?

• Minimal Increase in Complexity
• More control and less restrictive assumptions
• Using the right tool at the right time
• Remember
• Fancy stats do not make up for poor planning
• Design is more important than analysis

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When is MV analysis not useful

• Hypothesis is univariate use a univariate
  statistic
• Test individual hypotheses univariately first and
  use MV stats to explore
• The Simpler the analyses the more powerful

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First Schematic
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(No Transcript)
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Adults
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Kids
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Pets
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Males and Females
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Smart vs. Dumb
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Second Schematic
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Lost
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Heroes (?)
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Villains (?)
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Males and Females
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The third schematic

• Geriatric Depression Inventory
• Reasoning test
• CES-D
• Memory test
• Attention test
• Beck Depression Inventory
• Profile of Mood States
• Speed test

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What is the effect of a talk therapy intervention
on our set of outcomes?

• Geriatric Depression Inventory
• Reasoning test
• CES-D
• Memory test
• Attention test
• Beck Depression Inventory
• Profile of Mood States
• Speed test

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What is the effect of a talk therapy intervention
on our set of outcomes?

• Depression
• Cognition
• By reducing the number of outcome domains being
  considered, we can summarize and reduce the data
  so we can discuss it more parsimoniously
• Benefits of this summary simplicity, easier to
  get big picture
• Costs of this summary lose measure-specific
  unique variance

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First reason for using Multivariate

• Considering only a single outcome really limits
  your analyses
• A particular treatment or observed condition
  under study may exert differential effects on
  multiple related outcomes
• Considering multiple criterion measures is likely
  a better match of the theoretical model to the
  statistical model
• effects of parenting ?depression, aggression, and
  school performance)

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Second reason for using Multivariate

• When studying multiple dependent measures, these
  measures are moderately or even highly correlated
  with one another
• Incorporating this correlational structure often
  increase in statistical power.
• We thus have access to a powerful omnibus test
  about our set of IV's and DV's followed by
  univariate tests to probe this overall effect.

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Third reason for using Multivariate

• An important use of multivariate statistics is to
  control alpha inflation
• Recall that a Type I error is the probability
  that we find a difference when there isnt one
• We control this error rate by setting the ? level
  for a given test (e.g., ?.05).

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• However, this is a per comparison error rate, and
  this rate quickly becomes inflated when
  considering the Type I error rate for a set of
  tests

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1 (1 - .05)3 .15 15 chance that there is at
least one Type I error made in the set of tests
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Fourth Reason

• Executing a strong research project is often
  expensive and time consuming, and it is often
  highly efficient to consider as much information
  on the units under observation as possible

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Fifth Reason

• Including more measures helps to insure that you
  are adequately capturing the domain of interest

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Sixth Reason

• Helps you reduce the amount of data you have to
  deal with

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Seventh Reason

• Executing a strong research project is often
  expensive and time consuming, and it is often
  highly efficient to consider as much information
  on the units under observation as possible

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Overview of Multivariate Methods
Structural Equation Modeling