Robert H. Carver
Stonehill College/Brandeis University
Session ST-18
DSI2007 Phoenix AZ
What is Ambiguity Tolerance (AT)?
• Is it related to the development of
statistical reasoning skills?
• Some empirical findings
•
 Methods
 Results
• Implications for more effective teaching
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•
Frenkel-Brunswik (1948)
 Some are stimulated by ambiguity,
some are threatened
 Personality trait vs. preferred process
 Relationship to rigidity, uncertainty
tolerance, openness
 Enduring personality attribute vs.
context-dependent
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Low A.T.?
High AT?
“Never, ever, think outside the box”
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AMBIGUITY TOLERANCE
STATISTICAL THINKING
 When AT is low,
 Drawing actionable
people tend to cling
to preconceived
notions, reluctant to
process contrary
information
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conclusions based on
incomplete
information
 Methods for
incorporating new
information with preexisting assumptions
5
Wild & Pfannkuch (1999) 4 dimensions
of Statistical Thinking
•
 Investigative (PPDAC)
 Types of thinking (critical, imaginative,
transnumerative…)
 Interrogative (critical assessment of
observations)
 Dispositions (personal styles, qualities)
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Ignore
Allow for
•Fail to
detect?
•Overlook?
•FLEE!?
•Anticipate
•Design
safeguards
Control
•Change
system to
reduce or
manage
Adapted from Wild & Pfannkuch, 1999
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Is ambiguity tolerance (AT) a predictor of
success in a student’s development of statistical
thinking skills?
•
•
Does AT interact with other success factors?
If AT is a predictor of success, can we modify
our teaching approaches to anticipate it?
•
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Sample:
• 85 undergraduates enrolled over 2
semesters
• Differences among sections
 Technology: Minitab vs. SAS (Learning Ed.)
 Ordinary, Learning Community, Honors
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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)
Note: some questions are, themselves
ambiugous…
•
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Post vs. Pre-test Scores
100
CAOSPost
80
60
40
20
0
0
20
60
40
80
100
CAOSPre
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Independent Measures & variables:
•
McLain’s AT scale:
 22 question instrument 7-point Likert Scales


Max score for extreme tolerance = 74
Min score for extreme intolerance = - 58
 Reliability: Cronbach’s alpha = 0.897
 In this sample a = 0.872
 Did not predict performance on the pre-test
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•
•
•
•
•
•
•
•
•
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
Selected interactions with AT
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Variable
Constant
Coeff
Signif
-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
-3.946
0.035
19.46
0.000
Prior course dummy
F
Adj R2
48.9%
AT score has a significant effect on Post-Test reasoning score
Also: evidence of interaction between AT & PreTest score
Slightly Better fit with log-linear model
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•



Need to replicate
Carolyn Dobler, Gustavus Adolphus
Jennifer Kaplan, Michigan State
Stonehill, Spring 2008 (75 students)
•
Recognize and Confront this variation
among students

Differentiate from low effort/low aptitude/poor attitude
•
Re-frame the value of statistical thinking for
low-AT context
• Search for other personality variables with
similar effects?
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“It seems… that misconceptions are part of a way of
thinking about events that is deeply rooted in most
people, either as learned parts of our culture or (in
the extreme) even as brain functions arising from
natural selection in a simpler time.”
Garfield & Ahlgren, 1988
 How shall we respond to this variation in our
students?

Allow for? Control? Ignore?
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•
Contact me…
 rcarver@stonehill.edu
 rcarver@brandeis.edu
 http://faculty.stonehill.edu/rcarver/
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