Randomization workshop May 22, 2014eCOTS workshop Presenters: Nathan Tintle and Beth ChanceHour #2
Overview of next hour • Hour #2 (after short 5 minute break) • First 10-15 minutes: The ISI curriculum: What, how and why* • Next 15-20 minutes: Activity: Is yawning contagious?* • Final 10-15 minutes: Cautions, implementation, assessment* • Final 10-15 minutes: Next steps, class testing, ongoing discussion* • *Ask questions both during and immediately following each presentation
The ISI curriculum Introduction to statistical investigations Authors: Tintle, Chance, Cobb, Rossman, Roy, Swanson, and Vanderstoep Preliminary edition available via Wiley fall 2014
Goals • Introduce the particular curriculum that we have developed over the last 4+ years • Goals • Distinctive features • Technology • Key things to keep in mind
Vision An alternative Stat 101 (Algebra-based intro stats) course which uses randomization and simulation to motivate inference GAISE from ground up Not alienating client departments
Six distinctive features to achieve the goals 1. Spiral approach to the 6-steps of statistical investigation
Six Step Process Students have been able to consider the entire statistical process: Can dolphins communicate? Performance of Buzz/Doris Assessing statistical significance Draw appropriate conclusions
6 distinctive features to achieve the goals • 1. Spiral approach to the 6-steps of statistical investigation • Start in Preliminaries • Revisit repeatedly throughout the book, starting with simpler data (e.g., single binary variable), and moving through a variety of more complex data situations • Deeper and deeper look at the 6-steps as the course moves on • Emphasizes a big picture, research-oriented view of statistical reasoning
6 distinctive features to achieve the goals • 2. Randomization-based introduction to statistical inference • Use simulation and randomization to first introduce statistical inference • Transition to traditional (asymptotic methods) as a prediction to the simulation/randomization results • Simple and direct connections between method of data production, method used to analyze the data, and the appropriate scope of conclusions
6 distinctive features to achieve the goals • 3. Focus on the logic and scope of inference (the “pillars” of statistical inference • Logic: • Significance (How strong is the evidence?) • Confidence (How large is the tendency for difference and how confident can we be in our inferences?) • Scope: • Generalizability (To which population can the conclusion be reasonably generalized?) • Causation (Is a cause-effect conclusion possible?) • Once we have the tools, we ask these four questions of nearly every data set we look at; as part of the entire 6-step statistical investigation process we walk through nearly every time
6 distinctive features to achieve the goals • 4. Integration of exposition, explorations, and examples. Overview of each section in the book Common introduction Exploration Example Common conclusion
6 distinctive features to achieve the goals • Lots of flexibility with how to walk through material within each section • Key idea: Examples and explorations do not depend on each other; for example, definition boxes are in both
6 distinctive features to achieve the goals • 5. Easy to use technology throughout • Freely available suite of web-applets • Visualizing simulation and randomization • Integration of simulation and theory-based approaches • Pasting datasets • Allows for supplementing with a traditional software package
6 distinctive features to achieve the goals • 6. Real data from genuine studies • Taken from a variety of fields of interest; popular appeal • Real, published research in many cases; some student gathered datasets as well • Exercises, in-depth investigations, research articles
Content sequencing • Traditional Stat 101 • 1. Descriptive statistics and study design • 2. Probability and sampling distributions • 3. Inference • Our Stat 101 • Unit 1. Introduction to the four pillars of statistical inference • Unit 2. Comparing two groups • Unit 3. Analyzing more general situations
Content sequencing • Unit 1. Four pillars • Preliminaries. Statistical thinking (6-steps), Variability, and Probability (Long-run frequency) • Chapter 1. Significance (3-S process, chance model); one proportion • Chapter 2. Generalization (To whom can we generalize?); one proportion, one mean; types of errors • Chapter 3. Confidence (Range of plausible values; 2SD); one proportion, one mean • Chapter 4. Causation (Is cause-effect possible?)
Content sequencing • The following chapters all have a similar flow • Descriptive statistics • Simulation/Randomization approach • Theory-based approach • Unit 2. Comparing two groups • Chapter 5. Comparing two proportions • Chapter 6. Comparing two group on quantitative response (means or medians) • Chapter 7. Comparing two paired groups (on quantitative response; and, one sample t-test) • Unit 3. More general situations • Chapter 8. Comparing more than two groups using proportions • Chapter 9. Comparing more than two groups using means • Chapter 10. Analyzing two different quantitative variables
Content sequencing • Comments • Descriptive statistics are “just in time”; chapters are focused more on type of data (allows for the application of all 6-steps) • Probability and sampling distributions come up throughout the book using tactile and computer simulations to estimate sampling distributions; no formal rules of probability needed • Theory-based approaches are merely convenient alternatives to simulation which predict what would happen if you simulated, assuming certain conditions are met
Pedagogy • Built a course from the ground up that was based on GAISE principles • Statistical literacy and thinking • Conceptual • Active • Real data • Technology to drive understanding • Assessments for continuous improvement
Is it working? • Preliminary evidence is positive • Students, instructors enjoy it and appear to be learning more • We’ve documented learning gains in a number of key areas with preliminary versions of the curriculum (Tintle et al. 2011), with little to no evidence of declines vs. the standard curriculum in other areas • These gains are retained longer by students in this curriculum than with the traditional curriculum (Tintle et al. 2012) • Still are actively gathering assessment data across multiple institutions every semester with a long-term vision of continual improvement to maximize student learning MORE LATER THIS HOUR
Comparisons with other curricula CATALST—focus on modelling Lock5 – different content ordering; bootstrapping **Note: Others are under-development
Final remarks • Why so much time on proportions and not quantitative? • Easiest place to start • Cover 4-pillars, 6-steps and 3-S then apply them all, everywhere
Comparing Two Proportions Chapter 5 5.1: Descriptive statistics for 2 proportions5.2: Inference with Simulation-Based Methods 5.3: Inference with Theory-Based Methods
Exploration 5.2: Is yawning contagious? http://www.discovery.com/tv-shows/mythbusters/videos/is-yawning-contagious-minimyth.htm
Is yawning contagious? Are people who see someone yawn more likely to yawn themselves? Mythbusters recruited 50 people Randomly assigned to 3 rooms; 2 with yawn seed planted, one without
Example questions from guided discovery ‘exploration’ • Think about why the researchers made the decisions they did. • Why did the researchers include a group that didn’t see the yawn seed in this study? In other words, why didn’t they just see how many yawned when presented with a yawn seed? • Why did the researchers use random assignment to determine which subjects went to the “yawn seed” group and which to the control group? • Is this an observational study or a randomized experiment? Explain how you are deciding. • The researchers clearly used random assignment to put subjects into groups. Do you suspect that they also use random sampling to select subjects in the first place? What would random sampling entail if the population was all flea market patrons?
Example questions The researchersfound that 11 of 34 subjects who had been given a yawn seed actually yawned themselves, compared with 3 of 16 subjects who had not been given a yawn seed. Organize this information into the following 2×2 table:
Is yawning contagious? Results
Is yawning contagious? • The difference in proportions of yawners is 0.324 – 0.188 = 0.136. • There are two possible explanations for an observed difference of 0.136. • A genuine tendency to be more likely to yawn with seed • The 14 subjects who yawned were going to yawn regardless of the seed and random chance assigned more of these yawners to the “yawn seed” group
Is yawning contagious? Null hypothesis: Yawn seed doesn’t make a difference • Yawn seed or not has no association with whether someone yawns • seed =no seed or seed no seed = 0 Alternative hypothesis: Yawn seed increases chances of yawning • Yawn seed increases the probability of someone yawning; association • seed >no seed or seed no seed > 0
Is yawning contagious? The parameter is the (long-run) difference in the probability of yawning between yawn seed and no seed groups Our statistic is the observed difference in proportions 0.324 – 0.188 = 0.136
Is yawning contagious? If the null hypothesis is true (yawn seed makes no difference) we would have 14 yawners and 36 non-yawners regardless of the group they were in. Any differences we see between groups arise solely from the randomness in the assignment to the groups.
Is yawning contagious? • We can perform this simulation with index cards. • 14 blue cards represent the yawners • 36 green cards represent the non-yawners • We assume these outcomes would happen no matter which treatment group subjects were in. • Shuffle the cards and put 34 in one pile (yawn seed) and 16 in another (no seed) • An yawner is equally likely to be assigned to each group • In class we do this!
Is yawning contagious? • First simulation • 9 blue (yawners) and 25 green (non-yawners) in yawn seed group • 5 blue (yawners) and 11 green (non-yawners) in no yawn seed group • Difference in proportions? • 9/34 – 5/16 = -0.048 • “Chance” value of the statistic • Repeat many times
Is yawning contagious? • Confession • We tweaked the data! • Actually 10/34 yawners in seed group • 4/16 in control group • Difference is only 4.4%! • By this time our students realize that’s not enough to be statistically significant (even though Adam and Jamie didn’t)
Cautions • The good; Question on small p-values • National sample (not randomization) • Pre-test: 50%, Post-test: 69% • Fall 2013, dozen institutions using ISI text • Pre-test: 44%, Post-test 84% (some nearly 100%) • SERJ article (2012) • Retention of this concept is good 4 months later • Not going to solve all of your problems! • Assessment data is positive, but doesn’t mean everything is better (concepts some better, much the same; attitudes similar)
Cautions • Biggest misconceptions we create with this approach: 1. Need multiple samples in real life to analyze data Solution: Emphasize reality vs. pretend world where null is true 2. Thinking you have proven /gotten evidence for the null hypothesis Solution: focus on the idea of the assumptions behind the simulation and the idea of modelling in general 3. Still get a little dependent on mean/proportion Solution: We are hoping to show more transfer questions so they can use any statistic they come up with 4. Assuming too much student background? Solution: Have included the preliminary chapter for those who want a real quick introduction to “background” ideas
How to convince others • Focus on what they get • Better understanding of logic and scope inference • Focus on 6-steps (scientific reasoning) • Real studies/research • Still coverage of the theory based test or tests you know • Still coverage of descriptive statistics topics • Conceptual understanding of probability and sampling distributions • Good transition to applied second course (stat/math dept or client dept.
How to convince others Content re-ordering and re-focus more than content change What are your needs? It will still meet them, and likely do even better at meeting them then the current course.
How to convince others • Embracing active, guided discovery pedagogy which engages students and improves student learning (Guidelines of Assessment and Instruction in Statistics Education; GAISE) • “How do you do this all in one semester?” • Efficiency of approach/similarities between framework of inference • More accessible • Focusing more on the important stuff (inference) • Topics we don’t emphasize: • Reading probabilities from a table • Notation (doing more and more “in words”) • Using a random number table • More getting less on data cleaning, other sampling methods and other subtleties
How to convince others • But what about probability? What about the central limit theorem? • Not core to our approach • Some are supplementing for AP • More questions from math/stat colleagues than clients • Does it really work? • Published assessment data
How to convince others • But what about the second course? • Developing second course materials that flows out of this • Segway to research methods or other ‘traditional’ second courses fine • But what about a large class/online? • Nathan and Beth both have done/are doing online/hybrid • Applets are good outside of class; demo in class, use outside of class • But what about other text/software • Integration has been done many ways so far (R, SPSS, Minitab, etc.); just explorations as ‘labs’ with traditional text • But what about more ‘mathy’ students • Faster • More formulas
Next steps • What first? • Examine different curricula • Think about an action plan. Try a day? Try a course? Talk with colleagues? Talk with an author? What are your learning goals? How are you doing on them? • Participate in a longer workshop • Chicago, Sioux Center (IA), San Luis Obispo, Flagstaff and Boston (all this summer). See http://math.hope.edu/isi for details. • Lots of differences? Lots of options—what’s correct? • No consensus • Would like to make decisions based on assessment • YOU have something to offer here!
Next steps • Sign up for copy of the book (on the post-workshop evaluations) • You will be contacted soon (mid-late summer) re: • Participation in blog • Questions/discussion on randomization • Monthly themes • Stipend • We will be up and running soon • Assessment project—could use your/colleagues students; we’ll provide reports. Especially non-randomization users!! • We are happy to help you work with your institution/colleagues to assist in implementation/discussions