# Soma Roy, Karen McGaughey (Cal Poly), Soma Roy, Karen McGaughey (Cal Poly)

 Sana 01.04.2018 Hajmi 486 b.

• ## Soma Roy, Karen McGaughey (Cal Poly),

• Alex Herrington (Cal Poly undergrad)

• ## Examples

• Binomial process, randomized experiment- binary, randomized experiment - quantitative response
• Series of lab assignments
• Discussion points

• ## Cobb (2007) – 12 reasons to teach permutation tests…

• Model is “simple and easily grasped”
• Matches production process, links data production and inference
• Role for tactile and computer simulations
• Easily extendible to other designs (e.g., blocking)
• Fisherian logic
• --”The Introductory Statistics Course:
• A Ptolemaic Curriculum” (TISE)

• ## Develop an introductory curriculum that focuses on randomization-based approach to inference

• vs. using simulation to teach traditional inference
• From beginning of course, permeate all topics
• ## Improve understanding of inference and statistical process in general

• More modern (computer intensive) and flexible approach to inferential analysis

• ## Pre-lab

• Background, Review questions submitted in advance

• ## Online instructions

• Directed questions following statistical process
• Embedded applets or statistical software

• ## Can this be done on day one?

• Yes if can motivate the simulation
• Before reveal the data?

• ## Many students can reason inferentially

• “If a choice is made at complete random, then having 13 infants would be highly unlikely”
• “Based on the coin flipping experiment, the results stated that at/over 12 was extremely rare. Therefore, at least 12 infants …
• “Would be around 12-16 because it seems highly unlikely that given a 50-50 option 12-16 would choose the helper toy”

• ## But maybe not as well “distributionally”

• Is it unusual? = “barely over half”
• vs. unusual compared to distribution
• ## Examine language carefully

• “Unlikely that choice is random”
• “Prove”
• “Simulate”, “Repeated this study”
• “At random” = 50/50, “model”

• ## Can this be done on day one?

• Yes if can motivate the simulation
• Before reveal the data?
• Enough understanding of “chance model”?
• Use of class data instead? (“observed” vs. research study)
• Yes, if return to and build on the ideas throughout the course
• So what comes next?

• ## Tactile simulation

• One coin 16 times vs. 16 coins
• ## Population vs process

• Defining the parameter

• ## Timing of final report

• Follow-up in-class discussion

• ## Is Yawning Contagious?

• Modelling entire process: data collection, descriptive statistics, inferential analysis, conclusions
• Parallelisms to first example
• Could random assignment alone produce a difference in the group proportions at least this extreme?
• Card shuffling, recreate two-way table
• Extend to own data

• ## Scaffolding of lab report

• Introductory sentences, labeling of graphs
• Write conclusion to journal
• ## When should “normal-based” methods be introduced

• Alternative approximation to simulation
• Position, method for confidence intervals
• ## Choice of technology

• Applets, Minitab, R, Fathom

• ## Following the lab comparing two groups on a quantitative variable (65 responses)

• Discuss the purpose of the simulation process

• ## Did students address the null hypothesis?

• 33.9% E/ 38.5% P/ 27.7% I
• ## Did students reference the random assignment?

• 36.9% E/ 36.9% P/ 26.2% I
• ## Did students focus on comparing the observed result?

• 64.6% E/ 13.8% P/ 21.5% I
• ## Did students explain how they would link the pieces together and draw their conclusion?

• 24.6% E/ 60% P/ 15% I

• ## Lab 5: Reese’s Pieces (demo)

• Normal approximation, CLT for binary
• Transition to formal test of significance (6 steps)
• ## Lab 6: Sleepless nights (finite population)

• t approximation, CLT for quantitative, conf interval

• ## Instructor A

• Is Yawning Contagious?
• Heart Rates (matched pairs)
• ## Instructor B

• Friend or Foe
• Is Yawning Contagious?
• Reese’s Pieces

• Friend or Foe
• ## Least Helpful (Instructor B):

• Random babies
• Melting away (intro two-sample t, paired)

• ## 35% picked B (usually citing null .75500)

• But some look at shape, or later p-value

• ## Heights of females are known to follow a normal distribution with a mean of 64 inches and a standard deviation of 3 inches. Consider the behavior of sample means. Each of the graphs below depicts the behavior of the sample mean heights of females.

•  a. One graph shows the distribution of sample means for many, many samples of size 10. The other graph shows the distribution of sample means for many, many samples of size 50. Which graph goes with which sample size?

• ## 77% picked B

• Mixture of appealing to smaller SD/outliers, larger sample size means smaller p-value, and thinking in terms of test statistic
• A few choices not internally consistent

• ## CAOS questions (final exam)

• Statistically significant results correspond to small p-values
• Randomization (Hope/CP): 95%/95%
• Recognize valid p-value interpretation
• Randomization (Hope/CP): 60/72%
• p-value as probability of Ho - Invalid
• Randomization (Hope/CP): 80%/89%

• ## CAOS questions (final exam)

• p-value as probability of Ha – Invalid
• Randomization (Hope/CP): 45/67%
• Recognize a simulation approach to evaluate significance (simulate with no preference vs. repeating the experiment)
• Randomization (Hope/CP): 32%/40%

• ## Video game question (Final exam: NCSU, Hope, Cal Poly, UCLA, Rhodes College)

• What is the explanation for the process the student followed?
• Which of the following was used as a basis for simulating the data 1000 times?
• What does the histogram tell you about whether \$5 incentives are effective in improving performance on the video game?
• Which of the following could be the approximate p-value in this situation?

• ## Simulation process

• Fall: over 40% chose “This process allows her to determine how many times she needs to replicate the experiment for valid results.”
• About 70% pick “The \$5 incentive and verbal encouragement are equally effective at improving performance.” as underlying assumption
• Still evidence some look at center at zero or shape as evidence of no treatment effect
• 1/3 to ½ could estimate p-value from graph

• ## A consumer organization would like a method for measuring the skewness of the data. One possible statistic for measuring skewness is the ratio mean/median….

• Calculate statistic for sample data…
• Draw conclusion from simulated data …

• ## Level of student construction

• Ease of changing inputs
• Connect elements between graphs
• ## Carefully designed, spiraling activities

• “Stop!”
• Thought questions

• ## Lab assignments

• Focus on entire statistical process
• Motivating research question
• Follow-up application
• Thought questions
• Screen captures
• Pre-lab questions

• ## Still struggle with more technical understanding

• Under the null hypothesis
• Observed vs. hypothesized value

• ## Begin with class discussion/brain-storming on how to evaluate data before show class results

• Loaded dice, biased coin tossing
• Thought questions
• ## Student data vs. genuine research article

• “the result” vs. “your result”
• ## Choice of first exposure

• Significant?
• Random sampling or random assignment

• ## Scaffolding

• Observational units, variable
• How would you add one more dot to graph?
• At some point, require students to enter the correct “observed result” (e.g., Captivate)
• At some point, ask students to design the simulation?

• ## When connect to normal approximations?

• How make sure traditional methods don’t overtake once they are introduced?
• How much discuss exact methods?
• Confidence intervals

• ## Very promising but also need to be very careful, and need a strong cycle of repetition closely tied to rest of course…

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