Shades of Gray: Ambiguity Tolerance & Statistical Thinking

Shades of Gray: Ambiguity Tolerance & Statistical Thinking Robert H. Carver Stonehill College/Brandeis University Session 385 JSM 2007 Salt Lake City

Outline • Brief review of JSM 2006 paper • Modifications in current work • Methods • Results • Invitation to participate

Ambiguity Tolerance • Frenkel-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

Very low A.T. “Never, ever, think outside the box”

JSM 2006 paper • Ambiguity tolerance construct • Focus 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

Research Questions • Is ambiguity tolerance (AT) a predictor of success in a student’s development of statistical thinking skills? • Does AT interact with other success factors?

Sample Sample: • 85 undergraduates enrolled over 2 semesters • Differences among sections • Technology: Minitab vs. SAS (Learning Ed.) • Normal, Learning Community, Honors

Sample • Informed consent • Illustration of research design • Modeling ethical research practice • Illustration of some methods • Credit & incentives • Course-embedded data collection

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

CAOS post-test Improvement

Questions/Methods 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

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.

Distribution of AT

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

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

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

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

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

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?

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?

Replication? • Contact me… • rcarver@stonehill.edu • rcarver@brandeis.edu • http://faculty.stonehill.edu/rcarver/

Shades of Gray: Ambiguity Tolerance & Statistical Thinking