Designing Samples Chapter 5 – Producing Data YMS – 5.1

Lots of Vocabulary Observational Study – Does not attempt to influence the responses Experiment – Deliberately imposes some treatment on individuals in order to observe their responses – When goal is to understand cause/effect, experiments are only source of fully convincing data

Statistical Questions from the Classroom TYPE OF STUDY VARIABLE OF INTEREST INFERENCES ABOUT CAUSE EXPERIMENT Randomly assigned Straightforward (if lurking is controlled) OBSERVATIONAL STUDY Built in Difficult or Impossible (5 ways)

Population – Entire group of individuals we want info about – A census attempts to contact everyone Sample – Part of the population we actually examine – Sampling is studying a part in order to gain information about the whole – Done because time, cost, and inconvenience forbid contacting every individual

Sampling Frame – List from which a sample is actually selected Sample Design – Method used to choose sample from population – Poor design can produce misleading conclusions Bias – Systematically favoring certain outcomes

Types of Samples Voluntary Response – People who choose themselves by responding (usually have strong negative opinions) Convenience – Choose the individuals that are easiest to reach Simple Random (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

Stratified Random – Divide the population into groups (strata), take an SRS of each group, combine results Systematic Random – Randomly choose a starting point and select remaining individuals systematically Multistage Sampling Design – Select successively smaller groups (state, county, city, neighborhood, block) Probability – A sample chosen by chance – Must know every possible sample

Beware! Undercoverage – groups in the population are left out of the process of choosing the sample – When sampling frame is smaller than population Nonresponse – individual chosen can’t be contacted or doesn’t cooperate Response Bias – Occurs due to behavior of interviewer or respondent Wording of Questions – Most important influence on the answers given to a sample survey

Random Digits Table Each entry is equally likely to be any of the digits 0-9 Entries are independent of each other Choosing an SRS – Label & Table – Label with the fewest digits possible (i.e. 01 to 99 instead of 001 to 100) – Clearly identify labeling method – very important step for any simulation

Inference About Population Larger random samples give more accurate results than smaller samples BUT we have to beware of compromising independence. Sampling with or without replacement 5.1 Practice/Homework: p273 #5.2, , , 5.13, 5.15, , , Graded Activity/Classwork: Poker Analysis and Numb3rs “Traffic” episode

YMS – 5.2 Designing Experiments

Vocabulary for Experiments Experimental Unit – Individuals on which the experiment is being done Subject – When units are human beings Factor – Explanatory variables in an experiment Level – Possible combination of factors Treatment – Experimental condition applied to the units Placebo – Dummy treatment

Placebo Effect – Favorable response just because it’s a treatment – Mind over body Double-Blind – Neither the subject nor the researcher knows which treatment any subject has received Comparative Experiments – Using a control group to compare several treatments in the same environment Statistical Significance – An observed effect so large that it would rarely occur by chance – AKA The entire second semester of this class

Principles of Experimental Design Control – Effects of lurking variables Randomize – Treatments Replicate – On many units to reduce chance variation

Block Design Blocks are groups of experimental units known before the experiment to be similar in some way that is expected to affect the response to the treatments Random assignment of treatments is carried out separately within a block

p303 – Blocks allow us to draw separate conclusions about each block, i.e. men and women… – A wise experimenter … Matched Pairs – Blocking design which compares two treatments by choosing blocks of units that are as closely matched as possible – Order of treatment is assigned randomly

5.2 Practice/Homework p293 # P303 # P306 #5.50, 5.52, Classwork Read “Healthier and Happier” Article, News clips M*A*S*H clip, Blocking with Dogs AP Practice questions and p308 #5.56

YMS – 5.3 Simulating Experiments

Vocabulary Simulation – Imitation of chance behavior Independent Events – The result of one event has no effect or influence on another

Steps of a Simulation State the problem or describe the experiment. State the assumptions. Assign digits to represent outcomes. Simulate many repetitions. State your conclusions. 5.3 Practice/Homework: p314 # , 5.86 Ch 5 Review: p319 #5.74, 5.76,