Announcements 1/13/02

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Part 1
Other Multivariate Tests
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Measuring Intelligence

1. Sometimes in multi-variate testing, we dont
   know exactly what the latent variable is.
2. Id like to hear some of your definitions of
   intelligence?
3. There is very little consensus about the
   definition of intelligence. In your opinion,
   given the absence of consensus, is there any
   point in studying/measuring intelligence?

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Measuring Intelligence
Alfred Binet (1857-1911)

1. It matters very little what the tests are, so
   long as they are numerous. (Binet, 1911).
2. Critical Thinking Question What was the
   reasoning behind the above quote from Binet?
3. To his credit, Binets tests generated scores
   that correlated well with the childs school
   performance, and with the teachers evaluation of
   the child. That is, Binets test had predictive
   validity.

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Measuring Intelligence

1. The test most commonly used to assess
   intelligence in adults is the Wechsler Adult
   Intelligence Scale (Revised) WAIS-R.
2. One of the WAIS-R sub-tests is called the verbal
   test, although it measures many things,
   including general knowledge, vocabulary,
   comprehension, and arithmetic skills.
3. Another of the WAIS-R sub-tests, called the
   performance test, requires assembling parts
   into wholes, completing pictures, and rearranging
   pictures into a coherent sequence or story line.
4. Weirdly enough, there is a slight negative
   correlation between the verbal and performance
   sub-tests!

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Measuring Intelligence
WAIS-R Verbal Test Questions
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Measuring Intelligence
WAIS-R Performance Test Questions
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Measuring Intelligence
SAT Questions
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Measuring Intelligence
Progressive Matrix Test What advantage does this
have some over other tests?
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Measuring Intelligence

• Factor Analysis - a statistical method for
  studying the interrelations among various tests,
  the object of which is to discover what the tests
  have in common and whether these communalities
  can be ascribed to one or several factors that
  run through all or some of these tests.

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Factor Analysis

• Technique for determining which variables tend to
  clump together
• Which variables tend to be correlated with each
  other and not with other variables
• Clump of variables is called a factor
• Degree to which variable is correlated with a
  factor is called its factor loading

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Factor Analysis
These variables load heavily on Factor 1, but
not on factor 2
These variables load heavily on Factor 2, but
not on factor 1
Yes, loading heavily is a subjective call,
there are some stats that offer cut-off points.
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Measuring Intelligence
How does this diagram relate to intelligence
testing and factor analysis?
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Measuring Intelligence

1. When attempting to explain any phenomenon,
   scientists are often attracted to the principle
   of parsimony All other things being equal, the
   simplest explanation for a phenomenon is the best
   (i.e., the most elegant).
2. So, if performance on various mental tests rise
   and fall together, it may be parsimonious to
   attribute this pattern to a single underlying
   cause

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Measuring Intelligence

1. General Intelligence or g - according to Charles
   Spearman, a mental attribute that is called upon
   in any intellectual task a person has to perform.
2. Consistent with the notion of g, performance is
   positively correlated on tests about general
   knowledge, comprehension, arithmetic, and
   vocabulary.

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Measuring Intelligence

1. Some have speculated that g might have two
   components
2. Fluid Intelligence - The ability to respond to
   new and unusual problems, quickly and flexibly.
3. Crystallized Intelligence - The repertoire of
   previously acquired skills and information.
4. The two are strongly correlated (r.6), so it
   might be reasonable to have one descriptor, g,
   for both.
5. However, there appears to be some dissociation
   with age, crystallized intelligence increases
   while fluid intelligence decreases. (Anecdote
   Rats with stem-cell brain transplants in
   hippocampus.)

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Comparing Two Multivariate Approaches

• Lets compare and contrast two multivariate
  approachesMANOVA and Factor Analysis
• Both allow for the simultaneous evaluation of
  MULTIPLE dependent variables.
• However, in MANOVA, the researcher specifies what
  the DVs (latent variables) are in advance! (Sort
  of like a hierarchical MR.)
• The MANOVA (like all stats in the ANOVA family)
  addresses differences between means on a latent
  variable
• Between Subject Case Differences between of
  among groups
• Within Subject Case Differences between among
  IV levels

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Comparing Two Multivariate Approaches

• By contrast, in (exploratory) Factor Analysis,
  the computer looks for correlations, and the
  researcher assigns names to the emergent
  factors (latent variables) post hoc! (Sort of
  like a stepwise MR.)
• The question addressed by (exploratory) Factor
  Analysis is NOT related to group differences, but
  rather. what is the factor (latent variable)
  structure?
• Examples
• How many personality factors are there, and what
  are they?
• How many musical-genre factors are there, and
  what are they?
• How many psychological disorders are there, and
  what are they?
• Factor Analysis can show that whales or more
  similar to cows than to sharks.

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Comparing Two Multivariate Approaches

• One factor-analytic-like procedure is called
  Principle Component Analysis. This is an
  exploratory technique to reveal the primary axes
  (principle components) of a latent variable.
• All exploratory factor-analytic-like procedures
  help us with the first of our four goals of
  science DESCRIPTION!
• Another goal of science is EXPLANATION, and that
  can entail empirical tests of a hypothesis .
• Confirmatory Factor Analysis A multivariate
  technique for empirically testing hypotheses
  about the structure of, or relationships between,
  latent variables. (Like Hierarchical MR).

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How to Read Results Involving Unfamiliar
Statistical Techniques

• Dont panic!
• Look for a p level
• Look for indication of degree of association or
  size of a difference
• Reference an intermediate or advanced statistics
  text
• Take more statistics courses!

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Procedures that Compare Groups

• Analysis of variance (ANOVA)
• Analysis of covariance (ANCOVA)
• Multivariate analysis of variance (MANOVA)
• Multivariate analysis of covariance (MANCOVA)

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Part 2
Factor Analysis
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Factor Analysis In SPSS

• Factor Analysis A multivariate procedure
• More than one dependent variable is involved
• One goal of factor analysis is to reduce the
  number of measured variables into a more
  manageable set of factors.
• A factor is an abstract statistical construct
• Factors can provide parsimonious descriptions

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Factor Analysis In SPSS

• Setting It Up
• Be sure to have your measured variables created
  in variable view.

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Factor Analysis In SPSS

• What to click
• Analyze ? Dimension Reduction gt Factor
• Slide the variables of interest to the
  variables box. Ignore the Selection variable
  box
• Descriptives Button
• Click Coefficients (within the correlation matrix
  box)
• Extraction Button
• Set the Method to Principal Components
• Rotation Button
• Set the Method to Varimax
• Ignore the Scores and Options Buttons

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Factor Analysis In SPSS

• Interpreting the SPSS output
• Three of the output boxes are helpful
• Correlation Matrix Box
• Shows the simple, first order correlations of
  all variables
• Total Variance Explained Box
• Gives of variance that each significant factor
  accounts for
• The cumulative is also shown for the entire
  model
• Remember loading is the term for correlation
• A variable that strongly loads on a factor is
  strongly correlated with that factor.
• Rotated Component Box
• Shows each variables loading on (correlation
  with) each factor.

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Factor Analysis In SPSS
Correlation Matrix Box
Shows the first-order correlations among all
variables in the model.
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Factor Analysis In SPSS
Total Variance Explained Box
Components 1 and 2 are significant. Each
explains (accounts for) about 50 of the
variance. The other remaining 8 components (s 3
through 10) are computable, but n.s.
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Factor Analysis In SPSS
Rotated Component Box
A Component is a Factor

Variables 1 through 5 load strongly an Factor
1 and poorly on Factor 2

Variables 6 through 10 load strongly an
Factor 2 and poorly on Factor 1
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Factor Analysis In SPSS
Factor 1
Variables 6 through 10 load strongly on
Factor 2 and poorly on Factor 1
V2
V4
Variables 1 through 5 load strongly on Factor
1 and poorly on Factor 2
V3
V1
V5
V6
V7
Factor 2
V8
V9
V10
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Factor Analysis In SPSS
Factor 1
Variables 6 through 10 load strongly on
Factor 2 and poorly on Factor 1
V2
V4
Variables 1 through 5 load strongly on Factor
1 and poorly on Factor 2
V3
V1
V5
V6
V7
Factor 2
V8
V9
V10
The varimax rotation method identifies
orthogonal (90 deg) factors.
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Factor Analysis In SPSS
Factor 1
Variables 1 through 5 load strongly on Factor
1 and a little on Factor 2
Variables 6 through 10 load strongly on
Factor 2 and a little on Factor 1
V2
V4
V1
V3
V5
V6
V7
Factor 2
V8
V9
V10
Oblique rotation methods smaller angles (some
non-zero correlation) between factors.
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Factor Analysis In SPSS

• Conclusion
• In this example, we started with 10 measured
  variables.
• Factor Analysis parsimoniously reduced these 10
  variables to two factors, i.e., two latent
  variables.
• The two factors accounted for almost all the
  variance in the data set of interest.
• Now, its up to the researcher to provide a
  relevant name for the two factors.
• SPSS cant do such interpretation for us! ?

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