numeray & decision making and why you should have paid more attention to your math teacher…...
TRANSCRIPT
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NUMERAY & DECISION MAKING
And why you should have paid more attention to your math teacher…
Santiago Garcia Rodriguez
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Numeracy… and the lack thereof! (Paulos, 1998)
Ability to deal and understand the fundamental notions of number and chance
Is more widespread than we imagine
Has pervasive consequences on people’s decision making processes
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Innumeracy is associated with…
Misinformed govt. policies
Susceptibility to pseudoscience
Confused personal decisions
Unawareness of the additivity of small quantities
Strong tendency to personalize
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Wait a sec… I need scientific evidence!
High numerates= better medical decision makingHamm, Bard, and Scheid (2003)
Low numerates= less trust in numerical vs. verbal info from physicians
Gurmankin, Baron, and Armstrong (2004)
High numerate people are more likely to apply the rules of Expected Value
Benjamin and Shapiro (2005)
More educated individuals (more numerate?)= more risk tolerant
Donkers, Melenerg, and van Soest (2001)
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Framing Effects and Numeracy
Less framing effects among high in quantitative skills (numeracy self-assessed)
Less risky-choice framing within-subjects (numeracy self-assessed)
High NC-High numerates suffered from less risky-choice framing effects (numeracy self-assessed)
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Peters, Västfjäll, Slovic, Mertz, Mazzocco, and Dickert (2006)
Less numeracy = stronger attribute framing
F igure 1. Num eracy and attribute fram ing. E rror bars represent standard errors of the m ean.
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Peters, Västfjäll, Slovic, Mertz, Mazzocco, and Dickert (2006)
Probabilistic vs. frequentistic modes of info presentation
F igure 2. Num eracy and percentage (10% of 100) versus frequentistic (10 outof 100) representations of risk. Error bars represent standard errors of them ean.
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Peters, Västfjäll, Slovic, Mertz, Mazzocco, and Dickert (2006)
Less numeray = less optimal choices
F igure 3. Num eracy and the je llybean task. 2 (df = 1) = 5.2; < .05.p
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Peters, Västfjäll, Slovic, Mertz, Mazzocco, and Dickert (2006)
May high numerates act less rationally?
F igure 4. Num eracy and rated attractiveness of a bet w ith and w ithout a sm all loss. Error bars represent standard errorsof the m ean.
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Peters, Västfjäll, Slovic, Mertz, Mazzocco, and Dickert (2006)
Also found high numerates to draw more precise affective meaning from numbers
Even controlling for intelligence the previous results hold true
We need more studies
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Garcia-Rodriguez, Peters, and Slovic (master’s thesis)
Take a step further Peter’s et al. (2006) initial research on framing and numeracy
Investigate the effects of numeracy on risky-choice and attribute framing problems
Find interesting results
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Risky-Choice Framing and NumeracyDesign Study 1
Between subjects design with 2 conditions– N=161, females= 47%
Cond. 1 and Cond. 2 had different frames
10 “Asian disease”-like problems
Different Expected Value– 4 equal EV– 3 option EV A>B– 3 option EV A<B
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Risky-Choice Framing and NumeracyDesign Study 1
Disease ScenarioSweden is preparing for the outbreak of an unusual disease, which is expected to kill 600 people. The following alternative programs have been proposed to limit the spreading of the disease:
If program A is adopted, 200 people will be saved. If program B is adopted, there is 1/3 probability that 600 people will be saved,
and 2/3 probability that no people will be saved.
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Risky-Choice Framing and NumeracyAnalyses Study 1
Averaged the ratings per individual for each subset of problems
Dichotomized numeracy status (low/high)
MANOVA test with the three types of problems as the DV
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Results Study 1When EV A=B
Frame main effect F(3,154)=15.04, p<.0001 Numeracy main effect F(3,154)=4.35, p=.006
Risky Choice Problems Plan A=Plan BMain Effects of Frame and Numeracy
3
3.5
4
4.5
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5.5
Positive Negative
Frame
HighNum
LowNum
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Risky Choice Problems Plan A=Plan BMain Effects of Frame and Numeracy
3
3.5
4
4.5
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5.5
Positive Negative
Frame
HighNum
LowNum
Ris
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Pla
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Saf
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Results Study 1When EV A>B
Frame main effect F(1,156)= 21.29, p<.0001
Ris
ky O
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Pla
n B
Frame Effect Risky Choice Problems A>B
3
3.5
4
4.5
5
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Positive Negative
Frame
HighNum
LowNum
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Frame Effect Risky Choice Problems A>B
3
3.5
4
4.5
5
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Positive Negative
Frame
HighNum
LowNum
Ris
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Results Study 1When EV A<B
Numeracy main effect F(1,156)=10.56, p=.005
Risky Choice Problems B>AMain Effect Numeracy
3
3.5
4
4.5
5
5.5
Positive Negative
Frame
HighNumLowNum
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Risky Choice Problems B>AMain Effect Numeracy
3
3.5
4
4.5
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Positive Negative
Frame
HighNumLowNum
Ris
ky O
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Pla
n B
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n A
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Attribute Framing and NumeracyDesign Study 2
Between/within subjects design with 2 conditions– N=161, females= 47%
Cond.1 and Cond. 2 had different frames
Frame was manipulated within subjects
Two types of problems:– Student Evaluation problems– Snack attractiveness ratings
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Attribute Framing and NumeracyDesign Study 2
Student Problems
Please, rate this student’s performance based on the course level and the % correct on the exam.
Snack Attractiveness Problems
Please, rate this snack’s attractiveness based on the calories per serving and the % of calories from sugar
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Attribute Framing and NumeracyAnalyses Study 2
Dichotomized numeracy status (low/high)
MANOVA tests separated for students’ and snacks’ tasks, and also frames
MANOVA for– Students 1,3,5– Students 2, 4– Snacks A,C,E– Snacks B,D
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Results Study 2Students’ Performance Part
Moderate performers: 1st, 3rd, and 5th students– Frame effect: F(3,155)=6.84, p<.0001
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Results Study 2Students’ Performance Part
Moderate performers: 1st, 3rd, and 5th students– Frame x Numeracy Int.: F(3,155)=3.18, p=.026
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Results Study 2Students’ Performance Part
Extreme performers: 2nd and 4th students– Frame effect: F(2,156)=12.29, p<.0001
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Results Study 2Snacks’ Attractiveness Part
Moderate sugar content: snacks A, C, & E– Frame effect: F(3,154)=23.08, p<.0001
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Results Study 2Snacks’ Attractiveness Part
Highest sugar content: snacks B & D– Unexpected Int. Frame x Num: F(2,156)=6.03, p=.003
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Results Study 2Putting everything together
Frame had an effect except in the evaluation of extreme snacks
Numeracy had an effect in the student performance task, but only with moderate performers
The evaluation of extreme snacks yielded unexpected results!!!
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Results Study 2Conclussion
There is a framing effect going on
Low and high numerates behave differently
Frame manipulation might have been weak
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Study 3Making the Frame Manipulation Evident
Within/between subjects design– Frame manipulation within subjects– Two groups receiving different frames
N=116, 59% females
Isolated Attribute-Framing problems
Participants informed about the frame manipulation
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Study 3The Task
Please rate Snack’s X attractiveness based on the information on the screen. Please circle the number that best expresses your feeling on the scale below
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Study 3Analyses
Dichotomized numeracy status (High/Low)
MANOVA with the snacks’ ratings as the DV
IV’s: Condition (1st negative/1st positive) and numeracy (high/low)
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Study 3Results
Condition main effect: F(4,109)=4.16, p=.004
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Study 3Results
Interaction Condition x Num: F(4,109)=3.88, p=.006
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Study 3Conclusions
Numeracy seems to affect attribute-framing– Low numerates suffer more from framing– Low numerates are more influenced by wording– High numerates are more influenced by numbers
Interesting:– Reverse frame effect when framing is made clear– But only for low-numerates
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Putting Everything Together
Less numeracy = More framing– Stanovich and West (1998), Peters et al. (2006), Garcia-Rodriguez et al (in
progress).
Less numeracy = More risk averse– Donkers et al. (2001), Frederick (2005), Peters et al. (2006), Garcia-
Rodriguez et al. (in progress)
Less numeracy = Less affect from numbers– Peters et al. (2006)
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Future Directions?
Numeracy and:– Risk perception– Affective decision making– Reverse framing effects– Anchoring– Time preferences
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Suggested Readings
Benjamin, Daniel and Jesse Shapiro (working paper) “Who is ‘Behavioral’? Cognitive Ability and Anomalous Preferences”
Donkers, Melenberg, and van Soest (2001), “Estimating Risk Attitudes Using Lotteries: A Large Sample Approach”. Journal of Risk and Uncertainty. 22.2 pp. 165-95
Gurmankin AD, Baron J, Armstrong K. (2004) Intended message versus message received in hypothetical physician risk communications: exploring the gap. Risk Analysis 24:1337-47.
Frederick, Shane. "Cognitive Reflection and Decision Making." Journal of Economic Perspectives 19, no. 4 (2005): 25-42.
Hamm, R.M., Bard, D.E., and Scheid, D.C. Influence of numeracy upon patients' prostate cancer screening outcome probability judgments. Poster at 2003 Judgment and Decision Making Society meetings, Vancouver, BC, November 9 - 10, 2003.
Paulos, J. A. 1988. Innumeracy: Mathematical illiteracy and its consequences. New York: Hill and Wang.
Peters, E., Västfjäll, D., Gärling, T., & Slovic, P. (2006). Affect and decision making: A “hot” topic. Journal of Behavioral Decision Making, 19(2), 79-85.
Peters, E., Västfjäll, D., Slovic, P., Mertz, C.K., Mazzocco, K., & Dickert, S. (2006). Numeracy and decision making. Psychological Science, 17(5), 408-414.
Stanovich, K. E., & West, R. F. (1998a). Individual differences in framing and conjuction effects. Thinking and Reasoning, 4, 289–317.
Stanovich, K. E., &West, R. F. (1998b). Individual differences in rational thought. Journal of Experimental Psychology: General, 127, 161–188.