Shades of Gray v2
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Transcript of Shades of Gray v2
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Shades of Gray:Ambiguity Tolerance
& Statistical ThinkingRobert H. CarverStonehill College/Brandeis University
Session 385JSM 2007 Salt Lake City
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Outline
Brief review of JSM 2006 paper
Modifications in current work
Methods
Results
Invitation to participate
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Ambiguity Tolerance
Frenkel-Brunswik, Else (1948)Ambiguity Tolerance Construct:
Some are stimulatedby 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 construct
Focus on inferential thinkingskill ofdrawing actionable conclusions based onincomplete information
Hypothesized that people with Low AT wouldhave difficulty becoming facile with inferential
thinking tasksMixed findings
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Research Questions
Is ambiguity tolerance (AT) apredictor of success in a studentsdevelopment of statistical thinkingskills?
Does AT interact with other successfactors?
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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 & incentives
Course-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 andCal 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
CAOSPost
Male
Female
Gender
Post vs. Pre-test Scores
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Questions/Methods
Independent Measures & variables:
McLains AT scale:
22 question instrument 7-point Likert ScalesMax score for extreme tolerance = 74
Min score for extreme intolerance = - 58
Reliability: Cronbachs alpha = 0.897In this sample a= 0.872
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Typical Scale Items
I dont tolerate ambiguoussituations well.
Im drawn to situations which can
be interpreted in more than oneway.
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 0.028Prior course dummy 5.256 0.032
Math SAT score 0.063 0.001
F 4.89 0.001Adj R2 21.3%
A.T. did nothave 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-TestVariable 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 individuals orientation toward ambiguity
can affect his/her success with statistical
reasoning.
AT construct may provide a metaphor forstatistical thinking
Relationship between AT and Learning Styles?
Can these results be replicated, especially inlarger 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 statisticalreasoning in practice?
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Replication?
Contact me
[email protected] [email protected]
http://faculty.stonehill.edu/rcarver/
mailto:[email protected]:[email protected]://faculty.stonehill.edu/rcarver/http://faculty.stonehill.edu/rcarver/mailto:[email protected]:[email protected]
