Randomization workshop

MAY 22 , 2014ECOTS WORKSHOP

PRESENTERS: NATHAN TINTLE AND BETH CHANCEHOUR #2

Randomization workshop

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

I N T R O D U C T I O N T O S TAT I S T I C A L I N V E S T I G AT I O N S

A U T H O R S : T I N T L E , C H A N C E , C O B B , R O SS M A N, R O Y, S WA N S O N, A N D VA N D E R S T O E P

P R E L I M I N A RY E D I T I O N AVA I L A B L E V I A W I L E Y FA L L 2 0 1 4

The ISI curriculum

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

Six Step Process

Students have been able to consider the entire statistical process:Can dolphins

communicate?Performance of

Buzz/DorisAssessing statistical

significanceDraw 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


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


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


4. Integration of exposition, explorations, and examples.

Overview of each section in the book

Common introduction

ExplorationExample

Common conclusion


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


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. 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 55.1: Descriptive statistics for 2 proportions5.2: Inference with Simulation-Based Methods5.3: 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 peopleRandomly 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

Yawn seed planted Yawn seed not planted

Total

Subject yawnedSubject did not yawnTotal

The researchers found 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:


Results

Yawn seedNo yawn

seedTotal

Yawned 11 (32.4%) 3 (18.8%) 14

Didn’t yawn 23 13 36Total 34 16 50

Yawn seed No yawn seed0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Didn't yawnYawned

Did subject get randomly assigned to yawn seed group?

Did

subje

ct

yaw

n?


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


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


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


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.


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!


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


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, implementation and assessment

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.


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.


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


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


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, class testing, ongoing discussion

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!

http://math.hope.edu/isi

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

Randomization workshop

Documents

Transcript of Randomization workshop