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Small liberal arts college: 1350 undergraduate students Statistician within Department of Math, Stat and CS Class size: Stat 131 (30 students), 5-6 sections per year 3 hours per week in computer or tech- enabled classroom

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What we know about randomization approaches What we don’t What it means

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Tintle et al. flavor (2013 version) ◦ Unit 1. Inference (Single proportion) ◦ Unit 2. Comparing two groups Means, proportions, paired data Descriptives, simulation/randomization, asymptotic ◦ Unit 3. Other data contexts Multiple means, multiple proportions, two quantitative variables Descriptives, simulation/randomization, asymptotic

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Qualitative ◦ Momentum: Attendance at conference sessions, workshops Publishers agreeing to publish the books Class testers/inquiries People doing this in their classrooms (clients, colleagues) Repeat users Appealing “in principle” and based on testimonials to date

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Quantitative assessment Tintle et al. (2011, 2012) ◦ Compare early version of curriculum (2009) to traditional curriculum at same institution as well as national sample ◦ 40 question CAOS test ◦ Results Better student learning outcomes in some areas (design and inference); little evidence of declines

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Post-test answerNational sampleHope -2007Hope-2009 Small p-value68%86%96% Sample sizes: Hope ~200 per group; National Sample 760 P<0.001 between cohorts Pre-test: 50-60% correct Example #1. Proportion of students correctly identifying that researchers want small p-value’s if they hope to show statistical significance

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results 14 instructors, 7 institutions Total combined sample size of 783

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Instructor (Inst, Class size) Pre-testPost-testChangeSample size 1 (LA, Med)70%97%27%33 2 (LA, Med)73%95%22%26 3 (Univ, Med)23%95%72%40 4 (LA, Med)70%96%26%127 5 (LA, Sm)28%92%64%11 6 (Univ, Med)37%96%59%49 7 (Univ, Sm)39%73%34%23 8 (LA, Med)60%97%37%35 9 (LA, Med)29%96%67%95 10 (HS, Med)24%74%50%38 11 (Univ, Large)68%97%29% (LA, Med)63%93%30%92 13 (LA, Med)28%95%68%18 14 (LA, Med)56%97%41%78

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Institutional diversity in student background (pre-test) Post-test performance very good for most (over 90%) A couple of exceptions ◦ Both first time instructors with curriculum who will use it again this year

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Example 1 (continued). First quiz, 2.5 weeks into course; Simulation for a single proportion 119 people played RPS, 11.8% picked scissors Evidence that scissors are picked less than 1/3 of time in long run?

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The following graph shows the 1000 different “could have been” sample proportions choosing scissors for samples of 119 people assuming scissors is chosen 1/3 of the time in the long run.

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Would you consider the results of this study to be convincing evidence that scissors are chosen less often in the long run than expected? No, the p-value is going to be large8% No, the p-value is going to be small2% Yes, the p-value is going to be small77% Yes, the p-value is going to be large9% No, the distribution is centered at 1/3.4%

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Suppose the study had only involved 50 people but with the same sample proportion picking scissors. How would the p-value change? It would not change, the sample proportion was the same 22% It would be smaller11% It would be larger66% Not enough information1% Single instructor (me), on 92 students, across 4 sections and 2 semesters

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Example #2. Moving beyond a specific item to sets of related items and retention Tintle et al (SERJ)+JSE ◦ Improvement in Data collection and Design, Tests of significance, Probability (Simulation) on post-test ◦ Data collection and Design and Tests of significance improvements were retained significantly better than in consensus curriculum

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Retention significantly better (p=0.02)

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Example #3. How are weak students doing?

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GroupPre-testPost-testChange Lowest (n=210; 13 or less) 38%55%17% Middle (n=329; 14-17) 52%60%8% Highest (n=250; 18+) 66%69%3% All changes are highly significant using paired t-tests (p<0.001) **Among those who completed course; anecdotally we’re seeing lower drop out rate now than with consensus curriculum

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Example #4. Understand new data contexts? Old AP Statistics question 10 randomly selected laptop batteries; tested and measured hours they lasted

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To investigate whether the shape of the sample data distribution was simply due to chance or if it actually provides evidence that the population distribution of battery lifetimes is skewed to the right, the engineers at the company decided to take 100 random samples of lifetimes, each of size 10, sampled from a perfectly symmetric normally, distributed population with a mean of 2.6 hours and standard deviation of 0.29 hours. For each of those 100 samples, the statistic sample mean divided by the sample median was calculated. A dotplot of the 100 simulated skewness ratios is shown below.

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What is the explanation for why the engineers carried out the process above? This process allows them to determine the percentage of the time the sample distribution would be skewed to the right 3% This process allows them to compare their observed skewness ratio to what could have happened by chance if the population distribution was really symmetric/normally distributed. 64% This process allows them to determine how many times they need to replicate the experiment for valid results 10% This process allows them to compare their observed skewness ratio to what could have happened by chance if the population distribution was really right skewed. 23%

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Analysis of all (free-response) class tests is ongoing Integrate observed statistic and simulated values to draw a conclusion?

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Summary ◦ Preliminary and current versions showed improved performance in understanding of tests of significance, design and probability (simulation) post-course, and improved retention in these areas ◦ These results appear stable across lower- performing students with older and newer versions of the curriculum ◦ Some evidence of student ability to apply the framework of inference (3-S) to novel situations

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Summary ◦ Some instructor differences, but also preliminary validation of “transferability” of findings across different institutions/instructors; new instructors? ◦ **Note: Some evidence of weaker performance in descriptive stats in this earlier curriculum; substantial changes to descriptive statistics approach to combat this.

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What’s making the change ◦ Content? ◦ Pedagogy? ◦ Repetition? How much randomization before you see a change? Are there differences student performance based on curricula? Are they important?

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What are the developmental learning trajectories for inference (Do they understand what we mean by ‘simulation’)? Other topics? Low performing students; promising---ACT, GPA Does improved performance transfer across institutions/instructors? What kind of instructor training/support is needed to be successful? Using CAOS (or adapted CAOS) questions, but do we still all agree these are the “right” questions? Is knowing what a small p- value means enough? What level of understanding are they attaining? Why do students in both curriculums tend to do poorly on descriptive statistics questions? Or areas where we see little difference in curricula?

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Preliminary indications continue to be positive You can cite similar or improved performance on nationally standardized/accepted/normed tests for the approach Tag line for peers and clients: ◦ We are improving some areas (the important ones?) and doing no harm elsewhere Still lots of room for better understanding and continued improvement of approach Student engagement (talk yesterday) Next steps: Larger, more comprehensive assessment effort coordinated between users of randomization-based curriculum and those that don’t. If you are interested let me know.

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Author team (Beth Chance, George Cobb, Allan Rossman, Soma Roy, Todd Swanson and Jill VanderStoep) Class testers NSF funding

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Tintle NL, VanderStoep J, Holmes V-L, Quisenberry B and Swanson T “Development and assessment of a preliminary randomization-based introductory statistics curriculum” Journal of Statistics Education 19(1), 2011 Tintle NL, Topliff K, VanderSteop J, Holmes V-L, Swanson T “Retention of statistical concepts in a preliminary randomization-based introductory statistics curriculum” Statistics Education Research Journal, 2012.

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