NUMERAY & DECISION MAKING And why you should have paid more attention to your math teacher…...

NUMERAY & DECISION MAKING

And why you should have paid more attention to your math teacher…

Santiago Garcia Rodriguez

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

Innumeracy is associated with…

Misinformed govt. policies

Susceptibility to pseudoscience

Confused personal decisions

Unawareness of the additivity of small quantities

Strong tendency to personalize

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)

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)

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.


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.


Less numeray = less optimal choices

F igure 3. Num eracy and the je llybean task. 2 (df = 1) = 5.2; < .05.p


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.


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

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

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

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.

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

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

5

5.5

Positive Negative

Frame

HighNum

LowNum

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ky O

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Saf

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Pla

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Risky Choice Problems Plan A=Plan BMain Effects of Frame and Numeracy

3

3.5

4

4.5

5

5.5

Positive Negative

Frame

HighNum

LowNum

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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

5.5

Positive Negative

Frame

HighNum

LowNum

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Frame Effect Risky Choice Problems A>B

3

3.5

4

4.5

5

5.5

Positive Negative

Frame

HighNum

LowNum

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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

5

5.5

Positive Negative

Frame

HighNumLowNum

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ky O

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Saf

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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

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

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

Results Study 2Students’ Performance Part

Moderate performers: 1st, 3rd, and 5th students– Frame effect: F(3,155)=6.84, p<.0001


Moderate performers: 1st, 3rd, and 5th students– Frame x Numeracy Int.: F(3,155)=3.18, p=.026


Extreme performers: 2nd and 4th students– Frame effect: F(2,156)=12.29, p<.0001

Results Study 2Snacks’ Attractiveness Part

Moderate sugar content: snacks A, C, & E– Frame effect: F(3,154)=23.08, p<.0001

Results Study 2Snacks’ Attractiveness Part

Highest sugar content: snacks B & D– Unexpected Int. Frame x Num: F(2,156)=6.03, p=.003

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!!!

Results Study 2Conclussion

There is a framing effect going on

Low and high numerates behave differently

Frame manipulation might have been weak

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

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

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)

Study 3Results

Condition main effect: F(4,109)=4.16, p=.004

Study 3Results

Interaction Condition x Num: F(4,109)=3.88, p=.006

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

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)

Future Directions?

Numeracy and:– Risk perception– Affective decision making– Reverse framing effects– Anchoring– Time preferences

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.

NUMERAY & DECISION MAKING And why you should have paid more attention to your math teacher…...

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