# Math W50: How do they know my opinion? # January, 2000 Monday, January 3 Note: No Class Tuesday, January 4 Note: No Class Wednesday, January 5 Note: No Class Thursday, January 6 Topic: Introduction Topic: 7 Critical Components @ overheads/seven-critical.shtml Topic: Measurement Act: Survey 1 @ data/survey01.shtml Act: Survey 2 @ data/survey02.txt Read: Utts 1-3 Vocab: Vocab: statistics, 7 critical components, %% individual (unit), variable, value of variable, %% categorical variable, measurement variable, %% discrete, continuous, validity, reliabilty, bias, variability #Note: Class begins 2pm in NH 295 course intro, student intros, why you are in the course Def of stats get student ideas (on board) more than one use of word statistics descriptive (summary measures) inferential Video - FAPP #6 beginning to about 4:00 in diner some defs (primarily of inferential statistics) Utts: a collection of procedures and principles for gaining information in order to make decisions when faced with uncertainty Amabile: a way of taming uncertainty, of turning raw data into arguments that can resolve profound questions Moore: the science of gaining information from numerical data Garfunkel: the science of drawing conclusions from data with the aid of the mathematics of probability dictionary: the mathematics of the collection, organization, and interpretation of numerical data, especially the analysis of a population's characteristics by inference from sampling etymology: latin: statisticus - of state affairs political right down to etymology key elements data uncertainty information/decision-making ability science or math? Video - Against All Odds #1: beginning thru about 13:30, 26:00 to end [whole thing if time -- but probably not] Three phases of a statistical study (and outline of course) 1) collect data (statistical design) 2) organize data (data analysis) 3) draw conclusions from data (statistical inference) Survey 1: Have students add to existing list collect data from students, have them gather 2 more each Quiz 0: info about students ----------- Break ----------- Fill out survey 1 and survey 2 7 critical components that determine soundness of statistical studies 1) source of funding (why was it done?) 2) researcher contact 3) individuals studied and how selected 4) measurements made (quesitons asked) 5) setting 6) extraneous differences (other explanations for effect) 7) magnitude of claimed effect example: drug to cure excessive barking in dogs (page 22) example: US Voters Focus on Selves, Poll says (from Moore S:C&C) example: most women unhappy in their choice of husbands (page 24) didn't do this one How data are organized: units/individuals/subjects variables values of variables immagine a grid layout Some terminology categorical vs. measurement variables continuous vs. discrete validity (proxies) reliability bias -- systematically off in same direction variability pictures of variability/bias possibilities (target) Some things are not easily or obviously measured: happiness (happiness newpaper article) Apply terminology to Survey 1 Summary -- Measuring is a difficult task example: finding cheapest grocery store Survey 2: Wording issues did questions 1 and 2 in class data: 1) 6-0; 0-6 in expected direction 2) 2-4; 2-4 in expected direction Wording Pitfalls Bias (Intentional or unintentional) Elian Gonzalez Do you agree that he should be returned to his father in Cuba? [with US Immigration and Naturalization Service] Do you agree that he should be allowed to remain with his relatives in Florida? [agree with boy's attorneys] Confidentiality and Anonymity (people may lie) positive AIDS test? financial and sexual issues a methods to ask sensitive questions (some answers random) Desire to Please "How much do you smoke?" vs. cigarette sales didn't discuss this particular pair, put on quiz for tomorrow Unneccessary complexity, misunderstandings 1992 American Jewish Committee [NY Times July 8, 1994] Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened? (22% possible) Does it seem possible to you that the Nazi extermination of the Jews never happened, or do you feel certain that it happened? (1% possible) -------------- only got this far -------------------- "do you own stock?" cartoon Asking the uninformed will see an example in a video 1975 Public Affairs Act [didn't exist] (page 35) in 1978 1/3 expressed opinion in 1995 nearly 1/2 expressed opinion with leading political bias, 53% expressed opinion and tended to go with political leanings Ordering of questions, additional information peer pressure example (34) Open/closed questions museum example Levi jeans example (page) Defining your terms adolescent sex: increasing or decreasing? (page 37) unemployment changes have been made to survey questsions - define week as sunday to saturday so people don't underreport weekend work - redesign questions so definitions of 'work', 'looking for work', 'on layoff' are uniform - emphasize difference between 'on layoff' and 'fired' - also split long questions into series of short questions "The Truth but not the Whole Truth" Friday, January 7 Topic: Sampling Topic: Observation and Experimentation Act: Random Samples of %% Circles @ http://www.calvin.edu/~rpruim/cgi-bin/random-digits.cgi Act: What comes to mind @ data/words.txt Read: Utts 4 Read: Utts 5 Due: HW #1 @ hw01.shtml Vocab: Vocab: observational study, experiment, %% unit, population, sample, sampling frame, sample survey, %% census, margin of error, "1 Over Root n Rule", %% simple random sampling, stratified random sampling, %% cluster sampling, systematic sampling, %% random digit dialing, %% multi-stage sampling, convenience sample, response rate, %% treatment, explanatory variable, %% response variable (outcome variable), control, %% interaction, %% confounding, placebo, placebo effect, Hawthorne effect, %% experimenter effect, double-blind, single-blind %% Basic categories of studies sample survey -- ask a bunch of people a question experiment -- looking for relationships, cause/effect key: treatment observational study -- looking for relationship, but no treatment meta-analysis case study (popular in media -- clip from ABC news?) First 3 all have something in common: you don't measure every unit To conduct a study properly 1) get a representative sample 2) get a large enough sample 3) decide between observational study and experiment Sampling terminology: unit, population, sample, sampling frame, sample survey, census, margin of error sampling vs. census: samples are often possible, faster, accurate SRS: sampling circles using random digits Video -- Against All Odds #14: skip 35:20-41:10 [14 without bead sampling, 21 minutes with] Sampling Methods -- make sure they understand SRS stratified random sampling cluster sampling systematics sampling random-digit dialing multistage sampling Sampling difficulties wrong sampling frame not reaching selected individuals low response rate volunteer sample haphazard or convenience sample Literary Digest poll (1936) Alf Landon predicted to get 3-2 victory volunteer response to sample from poor frame George Gallup Quiz 1 ------------------------------------- Break: do the three words experiment ------------------------------------- Experiment terminology and set-up treatment, explanatory variable, response variable, control can't get cause/effect from observational study alone individual divided into groups each group gets different treatment measurements taken and comparison made between groups looking for cause/effect: treatment -> response Video -- FAPP segment on Physicians Health Study Problems with experiments Placebo effect Gastric freezing to relieve ulcer pain (34% in gf group, 38% in placebo group) Lack of control, confounding variables -- randomize 1940 propaganda experiment [Germany occupied France] Interaction -- measure and report possible variables can turn possible confounding variables into possible interaction variables by mesureing nicotine patch and smokers at home Hawthorne effect -- not always possible to avoid this problem new curricula Experimentor Bias -- blindness Ecological validity/generalizability what is the population, was setting a factor? over weekend: how many words come to mind from 4 others == Monday, January 10 Topic: Statistical Summaries Topic: Distributions Read: Utts 7 Read: Utts 8 Act: How Many Raisins? Due: HW #2 @ hw01.shtml Vocab: mean, median, mode, outlier, range, stemplot, histogram, %% shape, symmetric, bell-shaped, unimodal, bimodal, skewed, %% five-number summary, quartile, boxplot, interquartile range, %% variance, standard deviation, frequency curve, normal curve, %% proportion, percentile, standardized score, z-score, %% standard normal distribution, "68-95-99.7 Rule" Ethics of experiments informed consent use of doctors in physicians health study kids in art experiment human subjects & review boards Stanley Milgram (Yale): shock and memory done 1960's, probably not doable today Penny's data collection in grad school risk: cost/benefit analysis reasonable hope, reasonable doubt criteria for clinical trials (did friday) Some specific examples and issues Nazi data give them article (2 versions) and then discuss twins studies -- ideal matched pairs? PHS used only middle-aged men, what about women? minorities 1 in 5 men has heart attack before age 65 1 in 17 women has heart attack before age 65 (did friday) AIDS and slow process of clinical trials measuring easier but less reliable things pressure to release drugs before effectiveness demonstrated (mentioned friday, mention again) domestic violence: warn and release or arrest can a randomized experiment be done? [no informed consent] Tuesday, January 11 Topic: Pictures of Data Topic: Relationships between Categorical Variables Topic: Chi-Squared Read: Utts 9 Act: Golf Balls in the Yard Due: HW #3 @ hw02.shtml Vocab: pie chart, bar chart, pictogram, line graph, scatter plot Common problems with plots, graphs, and pictures 1) missing labels 2) scale doesn't start at 0 3) changes in labeling along an axis 4) misleading units 5) poor information Picture Checklist overall impression 1) is message clear? 2) is purpose clear? 10) is there any clutter? source 3) is source given? 4) is source reliable? labeling 5) is labeling clear? 6) do axes start at 0? 7) is scale constant? 8) are there any breaks along axis? are they easy to spot? 9) was inflation adjustment made? Banner chart and follow-up letters Utts, Figure 9.9 (page 149) and fixed version Read: Utts 12 Vocab: contingency table, cell, row, column, conditional percentage, %% rate, test statistic, chi-sqaured statistic, p-value, %% statistical significance, proportion, odds, relative risk, %% odds ratio, Simpson's paradox %% Golf ball distribution and test statistics Chi-squared statistic (on golf ball data again) what should we expect if there is no association? how can we adjust our measurement to account for sample size? Relative Risk Misrepresenting risk 1) no baseline risk given 2) no time period given 3) unclear population (may not apply to you) Simpson's Parodox hospital example (Utts chapter 12, pages 213-215) give combined results first, then separate discrimination example (Utts, chapter 12, pages 215-217) get graduate school acceptence data from Moore Wednesday, January 12 Topic: Probability and Randomness Read: Utts 15 Vocab: probability, relative frequency, personal probability, coherent, Vocab: mutually exclusive events, independents events, Vocab: cummulative probability, expected value, four probability rules Due: HW #4 @ hw02.shtml axiomatic method Read: Utts 16 Thursday, January 13 Topic: More Probability Topic: Sampling Distributions Read: Utts 17 Read: Utts 18 Due: HW #5 Friday, January 14 Topic: Inference for Proportions Read: Utts 19 Read: Utts 20 Due: HW #6 == Monday, January 17 Topic: Inference for Proportions Topic: Chi-Squared Again Read: Utts 21 Read: Utts 22 Due: HW #7 Tuesday, January 18 Topic: More about Inference Topic: Significance and Importance Read: Utts 23 Due: HW #8 Wednesday, January 19 Topic: Risk Assessment Read: Utts 12.3-12.4 Due: HW #9 Greatest Risks (problem 11.4 on page 191 of Utts) have students rank risks of 10 to 30 different items discuss how to measure relative risk Act: Video: Are We Scaring Ourselves to Death? Thursday, January 20 Topic: Test Friday, January 21 Topic: TBA == Monday, January 24 Topic: Inference for Measurement Variables Due: HW #10 Tuesday, January 25 Topic: Wrap-Up Due: HW #11 Wednesday, January 26 Topic: Test Thursday, January 27 Note: no class Friday, January 28 Note: no class == end of calendar Read: Utts 13, 14 Vocab: CPI, price index numbers, leading economic indicator, Vocab: coincident economic indicator, lagging economic indicator, Vocab: time series, long-term trend, seasonal adjustment