1STA 291 - Lecture 3 1STA 291Lecture 3• Data type:– Categorical/Qualitative and – Quantitative/Numericalwithin categorical (nominal and ordinal)within quantitative (discrete and continuous)• How data are collected?experiments and surveys (polls)Example of experiment: clinical trials testing the effectiveness of a new drug.Example of survey: opinion polls.STA 291 - Lecture 3 2STA 291 - Lecture 3 3In both methods, a key ingredient is randomness. “randomly select people to interview ” (in survey)“randomly divide patients into two groups” (in experiment)Observational Study = Survey2STA 291 - Lecture 3 4Methods of Collecting Data I Observational Study• An observational study observes individuals and measures variables of interest but does not attempt to influence the responses.• The purpose of an observational study is to describe/compare groups or situations.• Example: Select a sample of men and women age 18 and over and ask whether he/she smoke cigarette.STA 291 - Lecture 3 5Methods of Collecting Data II Experiment• An experiment deliberately imposes some treatment on individuals in order to observe their responses.• The purpose of an experiment is to study whether the treatment causes a change in the response.• Example: Volunteers, divided randomly into two groups. One group would take aspirin daily, the other would not. After 3 years, determine for each group the proportion of people who had suffered a heart attack. (This is an actual study)STA 291 - Lecture 3 6Methods of Collecting Data Observational Study/Experiment• Observational Studies are passive data collection• We observe, record, or measure, but don’t interfere• Experiments are active data production• Experiments actively intervene by imposing some treatment in order to see what happens• Experiments can tell what caused the change, if any.3• Why random? • To eliminate bias.STA 291 - Lecture 3 7STA 291 - Lecture 3 8Collecting data for a pollSimple Random Sampling• Each possible sample has the same probability of being selected.• The sample size is usually denoted by n.STA 291 - Lecture 3 9Example: Simple Random Sampling• Population of 4 students: Adam, Bob, Christina, Dana• Select a simple random sample (SRS) of size n=2to ask them about their smoking habits• 6 possible samples of size n=2: (1) A+B, (2) A+C, (3) A+D(4) B+C, (5) B+D, (6) C+D4STA 291 - Lecture 3 10Q: How to choose a SRS?A: “Label and table”• Give each unit in the population a unique label (usually a number, like SSN, SID, or phone number etc) (product serial #)• Go to random number table to see which label (unit) should be selected as sample. [this step often done by computer now] STA 291 - Lecture 3 11Q: How to choose a SRS?A: “Label and table”• Each of the six possible samples has to have the same probability of being selected• For example, roll a die (or use a computer-generated random number) and choose the respective sample• Online random number Applet acts like a tableSTA 291 - Lecture 3 12How not to choose a SRS?• Ask Adam and Dana because they are in your office anyway– “convenience sample”• Ask who wants to take part in the survey and take the first two who volunteer– “volunteer sampling”5STA 291 - Lecture 3 13Problems with Volunteer Samples• The sample will poorly represent the population • Misleading conclusions• BIAS – and no way to pin it down (how much is the bias?)• Examples: Mall interview, Street corner interview, internet click survey, TV show audience phone-in the opinion.STA 291 - Lecture 3 14Famous Example• 1936 presidential election• Alfred Landon vs. Franklin Roosevelt• Literary Digest sent over 10 million questionnaires in the mail to predict the election outcome• More than 2 million questionnaires returned• Literary Digest predicted a landslide victory by Alfred LandonSTA 291 - Lecture 3 15• George Gallup used a much smaller random sample and predicted a clear victory by Franklin Roosevelt (modern technique were able to reduce the sample size n to 1500 or so)• Roosevelt won with 62% of the vote• Why was the Literary Digest prediction so far off?6Terminology• Population• Sample• Parameter• Estimator STA 291 - Lecture 3 16STA 291 - Lecture 3 17Other Examples• TV talk show, radio call-in polls• “should the UN headquarters continue to be located in the US?”• ABC poll with 186,000 callers: 67% no• Scientific random sample with 500 respondents: 28% no• The smaller randomsample is much more trustworthy because it has less biasSTA 291 - Lecture 3 18• Cool inferential statistical methods can be applied to state that “the true percentage of all Americans who want the UN headquarters out of the US is between 24% and 32% etc.”• These methods cannot be applied to a volunteer sample.7• http://www.pollster.com/pollster-faq/• http://abcnews.go.com/PollingUnit/• http://en.wikipedia.org/wiki/Clinical_trialSTA 291 - Lecture 3 19STA 291 - Lecture 3 20Collecting Data II --- Experiments• Example: testing of new treatments or drugs via clinical trials.• Testing a new product, etc.STA 291 - Lecture 3 21• Clinical trial: Double blinded, placebo controlled, randomized.• recruit volunteers that met specific requirements (have certain conditions). Statistician will decide how many subjects is enough. (usually from a few hundreds to a few thousands, depending on what you are looking for, what is the budget, how certain the result need be ….)8STA 291 - Lecture 3 22• Randomly decide if a volunteer is given the new drug or placebo (sugar pill). Usually 50%-50% chance.• Neither the subject nor the attending doctor know which is given to the subject. (to minimize psychological effects, also called placebo effects)• Only a high level committee know.STA 291 - Lecture 3 23• The idea is to match as closely as possible the subjects of the two groups. The only difference is the drug.• The phrase “if everything else remain the same, the use of the drug for XXX patients can reduce the 5 year mortality rate by X%”STA 291 - Lecture 3 24• Resulting data are analyzed by statistical procedure. (will cover later)• Conclusion might be “proven beyond reasonable doubt that the new drug is better”. Or …• Inconclusive…either no effect or the results too noisy (effect too small) that you do not see it clearly, or• Clearly No effect.9STA 291 - Lecture 3 25• More than 40% of