shades of gray: ambiguity tolerance & statistical thinking robert h. carver stonehill...
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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
31 August 2007
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
41 August 2007
Very low A.T.
“Never, ever, think outside the box”
51 August 2007
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
61 August 2007
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?
71 August 2007
Sample
Sample: 85 undergraduates enrolled over 2
semestersDifferences among sections
Technology: Minitab vs. SAS (Learning Ed.)
Normal, Learning Community, Honors
81 August 2007
Sample
Informed consent Illustration of research design Modeling ethical research practice Illustration of some methods
Credit & incentivesCourse-embedded data collection
91 August 2007
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
101 August 2007
CAOS post-test
807060504030
90
80
70
60
50
40
30
CAOSPre
CA
OSPost
MaleFemale
Gender
Post vs. Pre-test Scores
Improvem
ent
111 August 2007
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
121 August 2007
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.
131 August 2007
Distribution of AT
644832160-16
25
20
15
10
5
0
AT
Frequency
AT Scores for Sample
141 August 2007
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
151 August 2007
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
161 August 2007
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
171 August 2007
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
181 August 2007
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
191 August 2007
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?
201 August 2007
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?
211 August 2007
Replication?
Contact me… rcarver@stonehill.edu rcarver@brandeis.edu
http://faculty.stonehill.edu/rcarver/
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