Chapter 5 Producing Data 5.1 Designing Samples 5.2 Designing Experiments 5.3 Simulating Experiments

CHAPTER 5.1 SIMPLE RANDOM SAMPLE OBSERVATIONAL STUDY RANDOM DIGITS PROBABILITY SAMPLE STRATIFIED RANDOM SAMPLE STRATA MULTISTAGE SAMPLE UNDERCOVERAGE NONRESPONSE RESPONSE BIAS WORDING EFFECTS SAMPLING FRAME OBSERVATIONAL STUDY EXPERIMENT SIMULATION STATISTICAL INFERENCE POPULATION SAMPLE SAMPLING CENSUS VOLUNTARY RESPONSE SAMPLE CONVENIENCE SAMPLING BIASED

Chapter 5.2-5.3 EXPERIMENTAL UNITS SUBJECTS TREATMENT FACTOR LEVEL PLACEBO PLACEBO EFFECT CONTROL GROUP CONTROL RANDOMIZE REPLICATE STATISTICALLY SIGNIFICANT COMPLETELY RANDOMIZED DESIGN DOUBLE BLIND LACK OF REALISM MATCHED PAIRS DESIGN BLOCK BLOCK DESIGN SIMULATION INDEPENDENT

5.1 Designing Samples Observational study: observes individuals and measures variables of interest but does not attempt to influence the responses. Experiment: deliberately imposes some treatment on individuals in order to observe their responses. Simulation: provides an alternative method for producing data. Statistical Inference: answers specific questions with a known degree of confidence.

5.1 Designing Samples Population: entire group of individuals that we want information about is called the population. Sample: part of the population that we actually examine in order to gather information; larger samples give more accurate results than smaller samples. Sampling: studying a part in order to gain information about the whole. Sampling Frame: the list of individuals from which a sample is actually selected. Census: attempts to contact EVERY individual in the entire population.

5.1 Sampling Design Sample Design: the method used to choose the sample from the population. Voluntary Response Sample: consists of people who choose themselves by responding to a general appeal; biased because people with strong opinions (especially negative) are most likely to respond. Convenience Sampling: chooses individuals easiest to reach. Biased: if the design systematically favors certain outcomes.

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5.1 Simple Random Samples Simple Random Sample (SRS): consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected. Random Digits: each entry in the table is equally likely to be any of the 10 digits 0 to 9; entries are independent of each other.

5.1 Choosing an SRS Step 1) Label: assign a numerical label to every individual in the population. 50/50: evens/odds; 1-5/6-10 (or 0) 80/20: 1-8/9-10 (or 0) 85/15: 01-85/86-100 (or 00) Step 2) Table: Use Table B to select labels at random. Can use “zero trick” when have sample sizes that are powers of 10 (10, 100…) Be careful of repeated numbers: Use repeats if assigning outcomes/responses Don’t use repeats if assigning people/objects

5.1 Other Designs Probability Sample: sample chosen by chance (not necessarily equal chance). Stratified Random Sample: divide the population into groups of similar individuals (called strata) then choose a separate SRS in each stratum. Multistage Sample: choose sample in stages (big to small, ex: US to houses)

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5.1 Cautions about sample surveys Undercoverage: occurs when some groups in the population are left out of the process of choosing the sample. Nonresponse: occurs when an individual chosen for the sample can’t be contacted or does not cooperate. Response Bias: behavior or characteristic of the respondent or of the interviewer causes bias in sample results. Wording Effects: confusing or leading questions; minor changes in wording (ex. page 282)

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5.2 Designing Experiments Experimental units: individuals on which the experiment is done. Subjects: when the units are human beings. Treatment: specific experimental condition applied to the units. Factor: explanatory variables in an experiment. Level: each treatment is formed by combining a specific value of each factor.

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5.2 Comparative Experiments Placebo: dummy/fake treatment Placebo effect: response to a dummy treatment Control group: the group of patients who received the placebo; enables us to control the effects of outside variables on the outcome.

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5.2 Principles of Experimental Design 1. CONTROL the effects of lurking variables on the response by comparing two or more treatments. 2. RANDOMIZE by using impersonal chance to assign experimental units to treatments. 3. REPLICATE each treatment on many units to reduce chance variation in the results.

5.2 Experimental Design Completely Randomized Design: when all experimental units are allocated at random among all treatments. Show the design by the diagrams shown on pages 295 and 297. Statistically significant: an observed effect so large that it would rarely occur by chance; tells you that the investigators found good evidence for the effect they were seeking.

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5.2 Experiment Design Double-blind: neither the subjects nor the people who have contact with them know which treatment a subject received. Matched pairs: compare two treatments on one unit (randomly assign order of treatments) OR compare two units that are closely matched (randomly assign which unit gets what treatment) Block: group of units that are known before the experiment to be similar in some way that is expected to affect the response to the treatment. Block Design: random assignment of units to treatments is carried out separately within each block.

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5.2 Cautions Block vs. Strata? Lack of realism: when the subjects or treatments or setting of an experiment may not realistically duplicate the conditions we really want to study; makes generalizations difficult.

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5.3 Simulating Experiments Simulation: imitation of chance behavior, based on a model that accurately reflects the experiment under consideration. 1. State/describe the problem 2. State the assumptions 3. Assign digits to represent outcomes 4. Simulate many repetitions 5. State your conclusions Independent: the result of one trial (toss, roll) has no effect or influence over the next trial.

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5.3 Simulation with calculator Random Integer Table (like Table B): Math/Prb 5: randInt(from, to, n) Dice: randInt(1,6,#) Coin: randInt(0,1,#) Children: randInt(1,2,#) Integers: randInt(1,10,#) Seeding calculator: tells it a starting point; #STO>rand

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