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Section 5.1 Sample Design Continued
Observational Study – observes individuals and measures variables of interest but does not attempt to influence responses. • Experiment – deliberately imposes some treatment on individuals in order to observe their responses.
Population – the entire group of individuals that we want information about • Info on college students • Info on seniors at kphs • Sample – part of the population that we actually examine in order to gather information • Seniors, 18-24 yr olds • Sampling vs census
Design of a Sample – refers to method used to choose a sample from the population • Biased – the design of a study is biased if it systematically favors certain outcomes • Confounding – two variables (explanatory or lurking) are confounded when their effects on a response variable cannot be distinguished from each other • Statistical Inference – provides ways to answer specific questions from data with some guarantee that answers are good ones.
Types of Samples: • Voluntary Response Sample – consists of people who choose themselves by responding to a general appeal. • Convenience Sampling – chooses individuals easiest to reach • Simple Random Sample (SRS) – of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance of being the sample actually selected
Chance • Choosing by chance attacks bias • Drawing from a hat, flipping a coin • Table of Random Digits – Table B • Is a long string of digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 • Each entry in the table is equally likely to be any of the digits 0 to 9 • The entries are independent of each other
Example 5.4 page 276 • 30 Business clients • Labeled 01- 30 could choose 00-29 • Use line 120 to find the 1st 5 clients she should choose.
When Choosing a SRS • Label – assign a numerical label to every individual in the population • Table – use Table B to select labels at random
Probability Sample – gives each member of the population a known chance (>0) to be selected. (ex: SRS)
Stratified Random Sample – Divide the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRSs to form the full sample. • Mrs. B wants to randomly select 12 students from KPHS to receive 12 tickets. The classes are stratified (frosh, soph, etc.) to make sure all classes are represented and then randomly chooses 4 students from each strata. • This is NOT a SRS of 12 KPHS students, why?
Choose the strata based on facts known before sample is taken. • A strata design can produce more exact information than an SRS of the same size by taking advantage of the fact that individuals in the same stratum are similar to one another • Election District • *Urban area * Suburban *Rural
Multistage Sample Design – Select successively smaller groups within a population by stages • Ex: Population – Residents of Texas • Select randomly 20 counties • Select randomly 5 cities/towns in each county • Select randomly 100 individuals from phone listings in each town/city • Most opinion polls and other national samples are done by multistage
Cautions about Sample Surveys • Undercoverage – Some groups in the population are left out in the process of choosing the sample • EX: opinion poll conducted by phone will miss 7-8% of Americans who do not have phones. • Nonresponse – occurs when an individual choosen for the sample can’t be contacted or refuses to cooperate • More serious source of bias • Higher in urban areas
Cautions about Sample Surveys • Response Bias – a variety of things that can lead to incorrect or false responses. • Behavior of interviewer; race/sex of interviewer; dress of interviewer; memory of respondent • Wording of Questions – most important influence on the answers given to a sample survey. • V1: Do you think there should be an amendment to the Constitution prohibiting abortion? • V2: Do you think there should be an amendment to the Constitution protection the life of an unborn child?
Closing • Properly designed samples avoid systematic bias, but their results are rarely exactly correct and vary from sample to sample • The results of random sampling don’t change haphazardly from sample to sample • Larger samples give more accurate information than smaller samples.