How Much Information is Too Much?: A Comparison of Decompositional and Holistic Strategies
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Transcript of How Much Information is Too Much?: A Comparison of Decompositional and Holistic Strategies
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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
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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
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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.
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Holistic Decision MakingHolistic 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)
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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.
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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).
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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).
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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.
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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
Present Study
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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
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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.
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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
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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.
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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)
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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)
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Temporal Stability:3-Way Interaction
(Fisher’s r-to-z Transformed Correlations)
Strategy X Order X Attribute
HD, DH
Number of attributes
9 attributes6 attributes3 attributes
Est
ima
ted
Ma
rgin
al M
ea
ns
1.2
1.1
1.0
.9
.8
.7
.6
.5
DECISION
Decompositional
Holistic
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Temporal Stability:3-Way Interaction
(Fisher’s r-to-z Transformed Correlations)
Strategy X Order X Attributes
DH, HD
Number of attributes
9 attributes6 attributes3 attributes
Estim
ate
d M
arg
ina
l M
ea
ns
1.6
1.4
1.2
1.0
.8
.6
.4
DECISION
Decompositional
Holistic
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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).
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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 astatistical 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 differencebetween the three stimuli condition (M = 19.42, SD = 13.13) and theseven stimuli condition (M = 23.43, SD = 10.92; t(260) = -2.68, p =.008).
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RMS 2-Way Interaction:Strategy X Stimuli
Number of stimuli (cars)
7 stimuli5 stimuli3 stimuli
Estim
ate
d M
arg
ina
l M
ea
ns
30
20
10
0
STRATEGY
Decompositional
Holistic
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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 differencesBetween the three attribute condition (M = 20.44, SD = 12.81) and thenine attribute condition (M = 22.28, SD = 12.40; t(254) = 1.17, p =.245).
However, in the decompositional strategy there was a statisticaldifference 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).
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RMS 2-Way Interaction:Strategy X Attributes
Temporal Stability
Number of attributes
9 attributes6 attributes3 attributes
Est
ima
ted
Ma
rgin
al M
ea
ns
30
20
10
0
STRATEGY
Decompositional
Holistic
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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-statisticallysignificant 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 significantdifference between order one (hd, dh; M = 22.08, SD = 11.80) andorder two (dh, hd; M = 19.27, SD = 11.65; t(393) = 2.37, p = .018).
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RMS 2-Way Interaction: Order X Strategy Temporal Stability
STRATEGY
HolisticDecompositional
Estim
ate
d M
arg
ina
l M
ea
ns
24
22
20
18
16
14
12
10
8
6
Strategy Order
HD, DH
DH, HD
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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.
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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).
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RMS 3-Way InteractionConvergent Validity
SESSION 1
Number of attributes
9 attributes6 attributes3 attributes
Est
ima
ted
Ma
rgin
al M
ea
ns
26
25
24
23
22
21
20
19
Strategy Order
HD, DH
DH, HD
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SESSION 2
Number of attributes
9 attributes6 attributes3 attributes
Est
ima
ted
Ma
rgin
al M
ea
ns
24
23
22
21
20
19
Strategy Order
HD, DH
DH, HD
RMS 3-Way InteractionConvergent Validity
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Comparison of RMS and Correlations
Session 1 Session 2 Fisher’s r-to-z RMS
1 30 30 50 50 70 70
Rxy = 1.0 RMS = 0
2 30 30 50 40 70 50
Rxy = 1.0 RMS = 12.91
3 78.18 30 50 50 49.09 80
Rxy = .88 RMS = 33.05
4 21.92 50.71 61.63 53.97 58.12 62.44
Rxy = .42 RMS = 5.12
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Which of the two version do you prefer?
BothDecomposedHolistic (Global)
Fre
qu
en
cy300
200
100
0
Subjective Evaluations of Preferences
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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