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Stat 301 – Statistics 1

Stat 301 – Statistics 1

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Stat 301 – Statistics 1

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  1. Stat 301 – Statistics 1 Day 2: p-values

  2. Recap – Technology issues • Studio usage rules • PolyLearn page • Initial course survey

  3. Recap – Syllabus Issues • Calendar • Office hours • Textbook • Glossary links • Investigation solutions

  4. Last Time • Study looked at the choices made by 16 infants, 14 picked the “helper” toy • Possible explanations • Something to the theory that infants have a more positive reaction to the social interaction • Something about the color, size, position of the helper toy – but this was “balanced” out in the study design • Random chance/coincidence/fluke

  5. Last Time • To help us decide whether this could believably be a fluke outcome, we need to know what fluke outcomes look like • How many infants pick the helper when they are just picking randomly between the two? • What is the typical “chance variation” in those results? • “Null model”

  6. Last Time • We can evaluate the “fluke” explanation by simulating the study using the model that infants were picking at random equally between the two toys (50/50) • Know will center at 8, but how rare is 14? • Our coin flip results (16 tosses each) indicated that 14 heads was a bit unusual  Strong evidence to rule out the “fluke” explanation

  7. Improving the simulation • But we only did this a few times. • How can we get a better estimate of how often 14 heads happens “just by chance”? • Practice Problem 1 • The probability of an event is the long-run proportion of times the event will happen if the same random process is repeated infinitely man times

  8. Random Babies applet

  9. Improving the simulation • So how do we run thousands of repetitions of the coin tossing model? • One Proportion Inference Applet • Textbook applets page or Course Schedule page • Set Number of tosses to 16 and press Toss Coin • Uncheck “animate” box and press Toss Coins 4 more times • Answer questions (q) and (s) – 1000 repetitions

  10. One Proportion Inference applet • This distribution by itself tells us nothing! Key is that it tells us how to evaluate the extremeness of the observed result. • One way to measure how extreme an observation is to calculate how often you get results at least as extreme as the one observed. • p-value

  11. Evaluating the p-value • p-value conveys the strength of evidence against the null model • Small p-values are evidence against the claim about the world (just by chance) • Statistically significant • How small? (p. 15)

  12. But can we get an exact p-value? • Binomial probability • Using technology • Minitab • R • RStudio

  13. Investigation 1.2 • Data collection • Answer questions (a)-(c)

  14. Quick Survey • You will be shown two pictures. • Decide which face belongs to “Tim” and which to “Bob”

  15. To do for Wednesday • Practice problem 1.1 (p. 17) • In PolyLearn, under Assignments • Read Terminology Detour (p. 15) and Summary (p. 17) • Review online solutions to Inv 1.1 • Be working on HW 1 (due Thursday/Friday)