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Announcements 1/13/02

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Title: Announcements 1/13/02 Author: name Denison Last modified by: Windows User Created Date: 1/6/2003 3:18:30 PM Document presentation format: On-screen Show (4:3) – PowerPoint PPT presentation

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Title: Announcements 1/13/02


1
Part 1
Other Multivariate Tests
2
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?

3
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.

4
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!

5
Measuring Intelligence
WAIS-R Verbal Test Questions
6
Measuring Intelligence
WAIS-R Performance Test Questions
7
Measuring Intelligence
SAT Questions
8
Measuring Intelligence
Progressive Matrix Test What advantage does this
have some over other tests?
9
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.

10
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

11
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.
12
Measuring Intelligence
How does this diagram relate to intelligence
testing and factor analysis?
13
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

14
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.

15
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.)

16
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

17
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.

18
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).

19
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!

20
Procedures that Compare Groups
  • Analysis of variance (ANOVA)
  • Analysis of covariance (ANCOVA)
  • Multivariate analysis of variance (MANOVA)
  • Multivariate analysis of covariance (MANCOVA)

21
Part 2
Factor Analysis
22
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

23
Factor Analysis In SPSS
  • Setting It Up
  • Be sure to have your measured variables created
    in variable view.

24
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

25
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.

26
Factor Analysis In SPSS
Correlation Matrix Box
Shows the first-order correlations among all
variables in the model.
27
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.
28
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
29
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
30
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.
31
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.
32
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! ?

33
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