Ambiguity Intolerance: An Impediment to Inferential Reasoning

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Ambiguity Intolerance An Impediment to
Inferential Reasoning?

• Robert H. Carver
• Stonehill College
• Session 550Thursday August 10, 2006
• rcarver_at_stonehill.edu

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Origins
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Some gross observations over years
• Intro Stats can activate profound emotional
  responses among students
• The practice of significance testing can unhinge
  some students
• Older learners may take to significance tests
  more readily than younger learners
• Some students prefer plug-insky to statistical
  reasoning

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Learners Vary
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Variation among learners
• Prior coursework
• Level of effortmotivation, capacity, etc.
• Aptitude
• Attitudinal orientation (Schau, et al.)
• Myers-Briggs (BTI)
• Other personality/emotional characteristics

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Ambiguity Tolerance
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Frenkel-Brunswik, Else (1948)
• Ambiguity Tolerance Construct
• Some are stimulated by ambiguity, some are
  threatened
• Personality trait vs. preferred process
• Stable personality attribute vs.
  context-dependent
• Relationship to rigidity, uncertainty tolerance,
  openness
• Different from meaning in Decision Theory

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Ambiguity Tolerance
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Measurement Scales
• Budner,1962
• Rydell Rydell Rosen 1966
• MacDonald, 1970
• Norton, 1975
• McLain, 1993

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Inferential Reasoning
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Per Frenkel-Brunswick
• Low ambiguity tolerance ?
• conflict anxiety in ambiguous situations ?
• rigid adherence to preconceived ideas ?
• failure to process new (contrary)
  evidence
• Inferential techniques reasoning are largely
  about incorporating new evidence in an ambiguous
  situation that includes a preconceived notion

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Questions/Methods
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Do students with low AT tend to shut down when
  presented with instruction in Inferential
  Reasoning and techniques?
• Do students with high AT tend readily to engage
  in Inferential Reasoning?
• OR
• Do students with low AT embrace inferential
  techniques as a path out of conflict anxiety?

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Questions/Methods
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Model

Previous stats coursework
Ambiguity Tolerance
Level of effort
Inferential reasoning
Analytical Aptitude
Course effect (self-selection, software, etc)
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Questions/Methods
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Sample
• 48 undergraduates enrolled in 2 sections of
  Intro. Business Statistics course
• Minitab sectionbusiness first-year students
• SAS Learning Ed. sectionpart of a sophomore
  Learning Community Calculated Risks
• Informed consent
• Modeling ethical research practice
• Illustration of some methods

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Questions/Methods
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Measures variables
• Abiguity Tolerance
• McLains 22 question instrument--paper pencil
  with 7-point Likert Scales
• Max score for extreme tolerance 74
• Min score for extreme intolerance - 58
• Reliability Cronbachs alpha 0.897

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Questions/Methods
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Typical items
• I dont tolerate ambiguous situations well.
• Im 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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Questions/Methods
Origins Learners AT Inference
Questions/Methods Findings Discussion

• AT scores

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Questions/Methods
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Other explanatory factors
• Section dummy variable
• Previous course dummy (self-report)
• Math SAT score (self-report)
• Homework grades
• Participation grade
• Attendance

Reduced to Effort Score
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Questions/Methods
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Dependent variable(s)
• Author-selected inference questions from ARTIST
  Comprehensive Assessment of Outcomes in a first
  Statistics Course (CAOS)
• Weighted average of sub-scores on course exam and
  quiz questions
• Weightings proportional to importance in course
  grade
• All items blind scored by author

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Questions/Methods
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Typical component of Inference scale
• Two parts of a final exam problem using a
  two-sample t test, applied to an observational
  study with a volunteer sample.
• Here are further results from SAS, related to
  this problem. Explain in a couple of sentences
  what these results reveal to you.
• The researchers should be reluctant to
  generalize these results to the entire population
  of middle-aged men. Explain why.

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Questions/Methods
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Typical component of Inference scale
• A recent Washington Post story began with this
  sentence A government study released yesterday
  undermines a key argument of climate change
  skeptics, concluding that there is no
  statistically significant conflict between
  measures of global warming on the earths surface
  and in the atmosphere. What is this sentence
  saying in simple English?

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Variable summaries
Origins Learners AT Inference
Questions/Methods Findings Discussion
Distribution of Variables
High Ambiguity Tolerance
Previous Course?
Dependent Inference scale
Effort Score
Math SAT
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Findings
Origins Learners AT Inference
Questions/Methods Findings Discussion
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Findings
Origins Learners AT Inference
Questions/Methods Findings Discussion
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Discussion
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Main Findings
• Ambiguity Intolerance may have a positive effect
• Significant interaction between effort and
  ambiguity tolerance
• Intensity of effort is more valuable to High AT
  students than to low AT students
• Caveats
• Untested measures
• No significant findings for CAOS scales
• Small samples

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Discussion
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Implications
• An individuals orientation toward ambiguity can
  affect his/her success with inferential
  reasoning.
• Intolerance of ambiguity may provide a motivation
  for success
• High AT students may need to apply particular
  effort to succeed.

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Discussion
Origins Learners AT Inference
Questions/Methods Findings Discussion

• Research directions
• Can these results be replicated?
• Do other personality or personal style variables
  shape success in statistical reasoning?
• How can we structure pedagogy to address
  personality variation among learners?

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Contact Info
Origins Learners AT Inference
Questions/Methods Findings Discussion

• For paper or slides
• Robert Carver
• rcarver_at_stonehill.edu