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									How Much Information is Too
 Much?: A Comparison of
Decompositional and Holistic
       Strategies


   Norma P Fernandez & Osvaldo F Morera
    University of Texas at El Paso
      Making Complex
        Decisions
A multiattribute decision must have at least two
choices from which to choose, defined on at least two
attributes.

Meehl (1954) has shown that statistical decision
making typically outperforms clinical expert judgment
in the diagnosis of patients of MMPI-profiles

Meehl (1954) has influenced how behavioral decision
theorists think about complex decision making
        Decompoisitional
        Decision Making
Decompositional Strategy: These strategies break down
complex decisions into smaller parts. These smaller parts
are then aggregated to derive an overall course of action.
One common decompositional technique is

SMARTS (Edwards & Barron, 1994)
                           U(x) = ki u(xij)

The aggregation of attribute weights and utility judgments are often
made in a linear fashion such that the overall utility of a stimulus can be
calculated, where ki represents the attribute weight and u(xij) represents
the single-attribute utility judgment.
Holistic Decision Making
 Holistic Strategy


       An individual makes one general judgment,
while simultaneously keeping in mind all the relevant
information during the judgment process, to find the
best stimulus.

This strategy is analogous to clinical decision making in Meehl
(1954)
    Assessing Decompositional
      and Holistic Decisions
                    Temporal stability

•   In order to measure temporal stability, a participant
    is given the same stimuli at two different sessions.

•   The scores of the stimuli from the first session are
    correlated with the scores of stimuli from the
    seconds session.

•   While people’s preferences may change over time,
    it is assumed that the decision strategy with the
    highest test-retest correlation is the better strategy.
Assessing Decompositional
  and Holistic Decisions
                Convergent validity

We compare two strategies that have something in
common.

Convergent validity “is useful to assess the
association between decompositional and holistic
judgments, and identify factors and circumstances
that affect the levels of this association” (Morera &
Budescu, 2001).
   Decompositional and
   Holistic Comparisons
As decisions become more complex, holistic
temporal stability deteriorates more rapidly
than decomposed temporal stability (von
Winterfeldt & Edwards, 1986).

Convergent validity is similarly affected by
increases in decision complexity (von
Winterfeldt & Edwards, 1986).
        Present Study
The primary purpose of this project is to
investigate the simultaneous effects of
attribute complexity and number of stimuli on
the temporal consistency and convergent
validity of decomposed and holistic
judgments.
              Present Study

                        3 attributes   6 attributes   9 attributes

                        S1      S2     S1      S2     S1       S2

3 Stimuli (Cars)   O1   D-H    H-D     D-H     H-D    D-H     H-D
                   O2   H-D    D-H     H-D     D-H    H-D     D-H
5 Stimuli (Cars)   O1   D-H    H-D     D-H     H-D    D-H     H-D
                   O2   H-D    D-H     H-D     D-H    H-D     D-H
7 Stimuli (Cars)   O1   D-H    H-D     D-H     H-D    D-H     H-D
                   O2   H-D    D-H     H-D     D-H    H-D     D-H
            Sample
430 participants (33 did not complete
session two)
Mean age 20.57 years old (SD = 4.22).
77.8% identified as Hispanics
58.6% first language was English
52.3% women
   Outcome Measures


Temporal stability outcomes: the correlation between
holistic (hh) and decomposed (dd) judgments across
days, as well as a measure of distance (smaller
distance is indicative of increased stability).

Convergent Validity outcome: the correlation between
strategies (hd, dh) across days, as well as a measure
of distance.
More on the Outcome
     Meausures
Fisher r-to-z transformation of the
correlations
         z' = .5[ln(1+r) - ln(1-r)]
Root mean square error (RMS)
   Measures distance between two decisions
    Temporal Stability
     (Fisher’s r-to-z Transformed
             Correlations)
2(order) X 2(gender) X 2(strategy) X 3
(attributes) X 3 (stimuli) mixed ANOVA

Main effect for complexity in attributes (F(2,
376) = 4.77, p = .009, partial 2= .025).

The three attribute condition (M = 1.05) had
higher temporal stability than the six (M = .88)
and nine (M = .69) attributes condition.
      Temporal Stability
 (Fisher’s r-to-z Transformed
         Correlations)
Main effect for complexity in stimuli
(F(2, 376) = 3.17, p = .043, partial 2=
.017).
The three stimuli condition (M = 1.03)
had higher temporal stability than the
five (M = .83) and seven (M = .76)
stimuli conditions.
  Temporal Stability
  (Fisher’s r-to-z Transformed
          Correlations)
Main effect for strategy (F(1, 376) = 4.50, p =
.035 partial 2 = .012).
However unexpectedly, the holistic strategies
(M = .98) were more stable over time than
decomposition strategies (M = .76).

Strategy X order X attribute interaction (F(2,
376) = 3.06, p = .048, partial 2= .016)
   Temporal Stability:
   3-Way Interaction
(Fisher’s r-to-z Transformed Correlations)

              Strategy X Order X Attribute
                            HD, DH
     1.2


     1.1

     1.0


      .9


      .8

      .7
                                                 DECISION

      .6                                                  Decompos itional

      .5                                                  Holis tic
    3 attributes            6 attributes   9 attributes


           Number of attributes
       Temporal Stability:
        3-Way Interaction
(Fisher’s r-to-z Transformed Correlations)

         Strategy X Order X Attributes
                        DH, HD
 1.6


 1.4


 1.2


 1.0


  .8                                         DECISION

  .6                                                  Decompos itional

  .4                                                  Holis tic
3 attributes            6 attributes   9 attributes


       Number of attributes
      Temporal Stability
               (RMS Main Effects)
2(order) X 2(gender) X 2(strategy) X 3 (attributes) X 3 (stimuli)
mixed ANOVA

Main effect for complexity in stimuli (F(2, 376) = 4.83, p = .008,
partial 2= .025). The three (M = 14.20) stimuli condition was
statistically significant from the seven (M = 16.42) stimuli
condition. Furthermore, the five (M = 14.02) stimuli condition
was statistically different from the seven stimuli condition.

Main effect for strategy (F(1, 376) = 130.24, p = .000 partial 2 =
.257). Decompositional strategies (M = 8.96) seemed to have
smaller RMS distance values, indicating increased temporal
stability than the holistic strategies (M = 20.80).
         Temporal Stability
  (RMS Strategy X Stimuli Interaction)
Strategy X stimuli interaction (F(2, 376) = 3.06, p = .048, partial 2=
.016).

A t-test indicated that in the decompositional strategy there was not a
statistical difference between the three stimuli condition (M = 9.17, SD
= 6.73) and the seven stimuli condition (M = 9.39, SD = 7.31; t(260) =
.252, p = .801).

However, in the holistic strategy there was a statistical difference
between the three stimuli condition (M = 19.42, SD = 13.13) and the
seven stimuli condition (M = 23.43, SD = 10.92; t(260) = -2.68, p =
.008).
RMS 2-Way Interaction:
  Strategy X Stimuli
  30




  20




  10

                                            STRATEGY

                                                    Decompos itional

   0                                                Holis tic
  3 s timuli              5 s timuli   7 s timuli


       Number of stimuli (cars)
         Temporal Stability
(RMS Strategy X Attribute Interaction)

There was also a Strategy X attribute interaction: F(2, 376) = 8.15, p =
.000, partial 2= .042.

A t-test indicated in the holistic strategy no statistical differences
Between the three attribute condition (M = 20.44, SD = 12.81) and the
nine attribute condition (M = 22.28, SD = 12.40; t(254) = 1.17, p =
.245).

However, in the decompositional strategy there was a statistical
difference between the three attribute condition (M = 11.18, SD 8.27)
and the nine attribute condition (M = 6.69, SD = 3.72; t(254) = 5.38, p
= 000).
RMS 2-Way Interaction:
 Strategy X Attributes
  Temporal Stability
 30




 20




 10

                                             STRATEGY

                                                      Decompos itional

   0                                                  Holis tic
3 attributes            6 attributes   9 attributes


       Number of attributes
         Temporal Stability
    (RMS Strategy X Order Interaction)


There was a strategy X order interaction (F(1, 376) = 10.58, p = .001,
partial 2= .027).

A t-test indicated in the decompositional strategy a non-statistically
significant difference between order one (hd, dh; M = 8.40, SC = 6.13)
and order two (dh, hd; M = 9.67, SD = 7.16; t(260) = -1.89, p = .060).

However, in the holistic strategy there was a statistically significant
difference between order one (hd, dh; M = 22.08, SD = 11.80) and
order two (dh, hd; M = 19.27, SD = 11.65; t(393) = 2.37, p = .018).
     RMS 2-Way Interaction:
        Order X Strategy
       Temporal Stability
   24

   22


   20


   18

   16


   14

   12


   10
                          Strategy Order

     8                            HD, DH

     6                            DH, HD
Decompos itional      Holis tic


         STRATEGY
  Convergent Validity
       (Fisher r-to-z Transformed
               Correlations)
2 (order) X 2 (gender) X 2 (session) X 3
(attributes) X 3 (stimuli) mixed ANOVA


Main effect for complexity for the stimuli
conditions (F(2, 376) = 7.29, p = .001, partial
2= .037). The three stimuli condition (M =
.71) had higher convergent validity than the
five (M = .38) and seven (M = .34) stimuli
condition.
   Convergent Validity
                      (RMS)
2 (order) X 2 (gender) X 2 (session) X 3 (attributes) X
3 (stimuli) mixed ANOVA
Main effect for complexity for the attribute conditions
(F(2, 376) = 10.06, p = .000, partial 2= .051). The
three attribute condition (M = 23.74) was different
than the six attribute condition (M = 20.51) and the
nine attribute condition (M = 21.01), indicating that
increase in complexity leads to less distance.
Session X attribute X order (F(2, 376) = 3.48, p =
.032, partial 2= .018).
RMS 3-Way Interaction
 Convergent Validity
        SESSION 1
   26


   25


   24


   23


   22


   21                                          Strategy Order

   20                                                   HD, DH

   19                                                   DH, HD
  3 attributes            6 attributes   9 attributes


        Number of attributes
RMS 3-Way Interaction
 Convergent Validity
        SESSION 2
   24



   23



   22



   21


                                               Strategy Order
   20
                                                        HD, DH

   19                                                   DH, HD
  3 attributes            6 attributes   9 attributes


        Number of attributes
              Comparison of RMS and
                  Correlations
    Session 1   Session 2   Fisher’s r-to-z      RMS

1
         30         30        Rxy = 1.0        RMS = 0
         50         50
         70         70
2
         30         30        Rxy = 1.0       RMS = 12.91
         50         40
         70         50
3
        78.18       30        Rxy = .88       RMS = 33.05
         50         50
        49.09       80
4       21.92      50.71
        61.63      53.97      Rxy = .42       RMS = 5.12
        58.12      62.44
Subjective Evaluations
    of Preferences
            300




            200




            100
Frequency




             0
                         Holis tic (Global)   Decompos ed      Both


                  Which of the two v ersion do y ou pref er?
     Future Directions
Order effects may suggest that a replication
of this study should be performed where only
one strategy is performed per occasion
(Morera & Budescu, 1998).

Discrepant findings with RMS and
correlations is worthy of future investigation

								
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