Shades of Gray: Ambiguity Tolerance & Statistical Thinking

Robert H. CarverStonehill College/Brandeis UniversitySession 385JSM 2007 Salt Lake City

21 August 2007

Outline

Brief review of JSM 2006 paperModifications in current workMethodsResultsInvitation to participate

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Ambiguity ToleranceFrenkel-Brunswik, Else (1948)Ambiguity Tolerance Construct:

Some are stimulated by ambiguity, some are threatened

Personality trait vs. preferred process Enduring personality attribute vs. context-

dependent Relationship to rigidity, uncertainty tolerance,

openness

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Very low A.T.

“Never, ever, think outside the box”

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JSM 2006 paper

Ambiguity tolerance constructFocus on “inferential thinking”—skill of drawing

actionable conclusions based on incomplete information

Hypothesized that people with Low AT would have difficulty becoming facile with inferential thinking tasks

Mixed findings

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Research QuestionsIs ambiguity tolerance (AT) a predictor of

success in a student’s development of statistical thinking skills?

Does AT interact with other success factors?

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Sample

Sample: 85 undergraduates enrolled over 2

semestersDifferences among sections

Technology: Minitab vs. SAS (Learning Ed.)

Normal, Learning Community, Honors

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Sample

Informed consent Illustration of research design Modeling ethical research practice Illustration of some methods

Credit & incentivesCourse-embedded data collection

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Methods

Dependent variable: Score on Comprehensive Assessment of Outcomes

for a first course in Statistics (CAOS) post-test Developed by Web ARTIST Project (U.Minnesota and

Cal Poly) team Pre- and Post-test (40 items each)

URL: https://data.gen.umn.edu/artist//tests/index.html

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CAOS post-test

807060504030

90

80

70

60

50

40

30

CAOSPre

CA

OSPost

MaleFemale

Gender

Post vs. Pre-test Scores

Improvem

ent

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Questions/Methods

Independent Measures & variables: McLain’s AT scale:

22 question instrument 7-point Likert ScalesMax score for extreme tolerance = 74Min score for extreme intolerance = - 58

Reliability: Cronbach’s alpha = 0.897In this sample = 0.872

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Typical Scale Items

I don’t tolerate ambiguous situations well.

I’m drawn to situations which can be interpreted in more than one way.

I enjoy tackling problems which are complex enough to be ambiguous.

I find it hard to make a choice when the outcome is uncertain.

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Distribution of AT

644832160-16

25

20

15

10

5

0

AT

Frequency

AT Scores for Sample

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Covariates investigated

Score on CAOS Pre-test Prior Stat Education (37% had some) Section dummy variables (Honors, L.C., etc.) Course Performance variables Attendance Gender dummy (49% female; 51% male)

First-year student dummy (61% 1st year)

Math SAT

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Findings: CAOS Pre-test Variable Coeff Signif

Constant 9.07 0.438

Female dummy -1.13 0.638

AT scale 0.048 0.537

First year dummy -5.581 0.028

Prior course dummy 5.256 0.032

Math SAT score 0.063 0.001

F 4.89 0.001

Adj R2 21.3%

A.T. did not have a significant main effect on Pre-test scores

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Findings:CAOS Post-Test Variable Coeff Signif

Constant 33.374 0.000

CAOS Pre-test score 0.559 0.000

AT scale 0.110 0.079

First Year dummy -3.726 0.072

Prior course dummy -3.406 0.099

F 12.29 0.000

Adj R2 37.0%

AT score has an effect (p < 0.10) on Post-Test reasoning score

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Findings:CAOS Post-Test Variable Coeff Signif

Constant -2.529 0.751

CAOS Pre-test score 0.437 0.000

AT scale 0.117 0.039

Course Cumulative Avg 0.473 0.000

Prior course dummy -3.946 0.035

F 19.46 0.000

Adj R2 48.9%

AT score has a significant (p < 0.05) effect on Post-Test reasoning score

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Discussion

Main Findings: AT showed a positive main effect AT was not predictive of course performance

Concerns: CAOS measure several aspects of statistical

thinking AT scale may measure several factors Small sample Substantial unexplained variance

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Discussion & Questions An individual’s orientation toward ambiguity can

affect his/her success with statistical reasoning. AT construct may provide a metaphor for

statistical thinking Relationship between AT and Learning Styles? Can these results be replicated, especially in

larger samples?

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Discussion & Questions Would the results hold up with different

measures of statistical reasoning? Do other personality or personal style variables

shape success in statistical reasoning? How can we structure pedagogy to address

personality variation among learners? Does A.T. affect application of statistical

reasoning in practice?

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Replication?

Contact me… rcarver@stonehill.edu rcarver@brandeis.edu

http://faculty.stonehill.edu/rcarver/