Stat 217 – Day 10 Review

Last Time Judging “spread” of a distribution “Empirical rule”: In a mound-shaped symmetric distribution, roughly 68% of observations fall within one standard deviation of the mean, 95% within two standard deviations of the mean  2SD = width of middle 68% of distribution Z-scores measure the relative position of an observation and provide us a unitless measuring stick for how far an observation falls from mean  Very useful for comparing values from different distributions Boxplots – visual display of five number summary  Helpful for comparing distributions (spread, center)

Comments on HW 2 Problem 2: Identify terms  Sampling frame is the list of the population used to select the sample Does not include the response variable information! (b) average number of words on a page of a textbook (d) tend to gain an average of 15 lbs?

Comments on HW 2 Act 5-14: Studies from Blink  (a) and (b) only had response variables, observational studies  (c) and (d) had 2 variables and the explanatory variable was randomly assigned, experiments  So in (c) and (d) can potentially draw cause and effect conclusions  “Generalizability” means can you take information from sample and apply it to the larger population? “There was not a significance difference in SAT performance in the sample so I don’t think there is in the population as well” Yes if have random sample, so maybe only in (a)

Comments on HW 2 Question 4: Hand hold (b) Can the status of the EV be determined by Ashleigh? Gender of participant vs. gender of researcher  Random sampling vs. random assignment

Comments on HW 2 Cause and effect vs. generalizing to population YesNo Yes No Were groups randomly assigned? Were obs units randomly selected? Can draw cause-and- effect conclusions Can generalize to larger population

Comments on HW 2 Question 5: AIDS testing  Most of you got the table right but then read the wrong proportion from the table Of those who tested positive, what proportion had AIDS = 4885/78515 =.062 Of those who have AIDS, what proportion test positive = 4885/5000 =.977 (sensitivity) Positive testNegative testTotal Carries AIDS virus(2) 4885(2) 115(1) 5000 Does not carry AIDS(3)73630(3) (1) 995,000 Total(4) 78515(4) ,000,000

Lab 2 Notes (model online) Comparing groups  Are people yawning a lot vs. does the yawn seed group yawn more often Overall proportion vs. Difference in conditional proportions  4.4% vs. 4.4 percentage points  Yawned “a lot more” vs. “yawned a lot more often” Interpreting p-value vs. conclusions from p- value  Probably want to explicitly compare p-value to some cut-off

Lab 2 Notes Interpretation of p-value  If those subjects were going to yawn, regardless of which condition they were in, how often would the random assignment process alone lead to such a large difference in the conditional proportions? Each dot represents one (fake) random assignment Observation units = 1000 fake random assignments Variable = difference in conditional proportions Roughly 51% of fake random assignments (null model) saw a difference at least this large Don’t consider this a small p-value since >.05

Lab 2 Notes Effect of sample size

Challenge Question Why was “random assignment” used in the study? Why did we shuffle the cards and deal them into 2 groups?

Lab 3 Randomization distribution  If everyone was going to remember the same number of letters regardless of which sequence they got, how often would the random assignment process alone lead to such a big difference in the group means? Each dot represents one random assignment Observation units = 1000 fake random assignments Variable = difference in group means Where is the observed difference in means in this distribution?

About Exam 1 50 minutes, 50 points  Will include one of the self-check activities Bring calculator, pencil, eraser  Could be asked to use Minitab and/or to interpret Minitab output  No cell phone calculators (square root) One 8.5x11 sheet of own notes  Both sides ok I will supply paper

Some advice for studying Review handout, problems online  See also p. 627? Review lecture notes, text, hws, labs  See me for old homework, inclass activities Work problems Start with ideas that we have emphasized more often

Some advice during exam If you get stuck on a problem, move on  later parts, later problems Try to hit the highlights in your answer (e.g., not all sources of bias, just the most serious)  Be succinct (think before you write) Read the question carefully Show all of your work, explain well  communication points Read entire question before writing anything

Some big, big ideas Observational units, variable Random assignment vs. random sampling  Implementation  Purpose  Consequence (Scope of conclusions) What see in sample vs. saying something beyond the sample  Statistic vs. Parameter  Statistical significance Interpretations, reasoning  Properties, “what if” questions… How are you deciding this?

Activity 4-19: Voter Turnout (p. 70) Statistic:.682 proportion claiming to vote Parameter:.490 proportion claiming to vote What are some possible explanations for why these values differ?  Those in sample do not represent population  Those in sample were not honest  Statistics vary from sample to sample and may differ from parameter by chance Which of these explanations can we eliminate?

No longer believe it was just “by chance”…

Questions?