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

2. 2 1 August 2007 Outline  Brief review of JSM 2006 paper  Modifications in current work  Methods  Results  Invitation to participate

3. 3 1 August 2007 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

4. 4 1 August 2007 Very low A.T. “Never, ever, think outside the box”

5. 5 1 August 2007 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

6. 6 1 August 2007 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?

7. 7 1 August 2007 Sample Sample:  85 undergraduates enrolled over 2 semesters  Differences among sections Technology: Minitab vs. SAS (Learning Ed.) Normal, Learning Community, Honors

8. 8 1 August 2007 Sample  Informed consent Illustration of research design Modeling ethical research practice Illustration of some methods  Credit & incentives  Course-embedded data collection

9. 9 1 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 https://data.gen.umn.edu/artist//tests/index.html

10. 10 1 August 2007 CAOS post-test Improvement

11. 11 1 August 2007 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  = 0.872

12. 12 1 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.

13. 13 1 August 2007 Distribution of AT

14. 14 1 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% 1 st year)  Math SAT

15. 15 1 August 2007 Findings: CAOS Pre-test VariableCoeffSignif Constant9.070.438 Female dummy-1.130.638 AT scale0.0480.537 First year dummy-5.5810.028 Prior course dummy5.2560.032 Math SAT score0.0630.001 F4.890.001 Adj R 2 21.3% A.T. did not have a significant main effect on Pre-test scores

16. 16 1 August 2007 Findings:CAOS Post-Test VariableCoeffSignif Constant33.3740.000 CAOS Pre-test score0.5590.000 AT scale0.1100.079 First Year dummy-3.7260.072 Prior course dummy-3.4060.099 F12.290.000 Adj R 2 37.0% AT score has an effect (p < 0.10) on Post-Test reasoning score

17. 17 1 August 2007 Findings:CAOS Post-Test VariableCoeffSignif Constant-2.5290.751 CAOS Pre-test score0.4370.000 AT scale0.1170.039 Course Cumulative Avg0.4730.000 Prior course dummy-3.9460.035 F19.460.000 Adj R 2 48.9% AT score has a significant (p < 0.05) effect on Post-Test reasoning score

18. 18 1 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

19. 19 1 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?

20. 20 1 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?

21. 21 1 August 2007 Replication?  Contact me… rcarver@stonehill.edu rcarver@brandeis.edu http://faculty.stonehill.edu/rcarver/