Discussion Beth Chance Cal Poly San Luis Obispo
Discussion Beth Chance Cal Poly – San Luis Obispo bchance@calpoly. edu 1
What have we seen/heard today? n Great justifications for using simulations/ randomization-based methods to help students understand concepts of statistical inference q q More closely tied to the logic of inference Little prior knowledge required Same method throughout course More efficient discussion (and lesser role) of theoretical methods 2
What have we seen/heard today? n Great examples of using simulations/ randomization-based methods to help students understand concepts of statistical inference q Technology tools allow direct student exploration, ownership, support n n q Unified tools offering contextual animations, flexibility, interactivity, speed, comparison to theoretical methods But still start with tactile simulations (population) Simultaneously develop technology/curriculum 3
What have we seen/heard today? n Some cautions q q May not be for all students May not be for all instructors Need to satisfy demand for traditional methods/CLT May introduce misconceptions? n n q Parameter vs. statistic vs. “it” What is the parameter in re-randomization? Student intuition of randomness, process, modeling, abstraction n Repeated randomizations vs. repeated studies 4
Exam Question Suppose I conduct a study to see whether students perform better on tests printed on green paper or on tests printed on blue paper. n In conducting this study, I randomly assign students to use either blue paper or green paper. Explain the purpose of this use of randomness in my study. 5
Exam Question n After recording student test scores, I use an applet to randomly mix up the scores and reassign them back to two groups and record the simulated difference in sample means each time, repeating this a large number of times. Explain the purpose of this use of randomness. (What does it tell me? ) 6
A few more concerns/questions n Students get it! Could we get data like this by random chance alone? q q n Can they go beyond the coin tossing model? How technically correct does the understanding need to be? Technical details… 7
Example: Height vs. Foot length 8
A few more concerns/questions n How technically correct does the understanding need to be? q q SD from random shuffling vs. repeated random samples One crank or two? n n q “Intrinsically connected to concepts” “to emphasize the connection between data production and inference” (Cobb, 2007) Naïve bootstrap, 2 SD confidence intervals 9
A few more concerns/questions n Students get to explore! Distributions of medians, other statistics… q q q n Danny Kaplan: Latitude for creativity and judgment vs. leaving them at sea What’s enough? What’s too much? Do students care? Students get to replicate genuine research studies! Mythbusters: Is Yawning Contagious? q “Interference” of context? 10
Can we do this? n n n Yes, with consistency and reinforcement throughout the course in the activities and exposition accompanying the course, and in the course assessments Yes, with effective technology tools designed by teachers, well integrated into the course, with scaffolding for students Yes, with openness and encouragement of different approaches 11
Should we do this? n I think so… q But really, really need collaborative assessment efforts to identify when, where, how, and how well students are learning key concepts in the course n n q e. g. , How the two approaches interact Student perception vs. performance vs. retention And what are those key concepts? n n n Too much emphasis on inference? What is missing? What topics can go? 12
Should we do this? n Yes! q Still too many people who are not able to consider chance variability in making decisions n n n Mythbusters yawning study Tom Moore: Sample size needed for margin of error 3% Inference for mean vs. individual observations (prediction intervals) Need to believe in high quality studies Less focused on one method and more on considering appropriateness of methods Consideration of entire statistical investigative process 13
Thank you! 14
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