Chapter 12 Sample Surveys

At the end of this chapter, you should be able to Take a simple random sample from a population. Understand and use the principles of sampling. Know the most common statistics and parameters. Identify the common problems in sampling.

Who will win the Presidential Election in November? Won’t know until Election Night (maybe!) Polls try to determine the answer to this question. Do they talk to all voters?

Idea I: Take a Sample _______________ –Group of people we want information from. –Generally, _________________. –Impractical or prohibitively expensive to talk to everyone

Sample Surveys –_______________ Smaller group of people from population. – Group we get information from. –Want sample to be representative of population. Ex:

Idea 2: Select the sample Randomly Controls for factors you know in data. – –Race – Controls for factors you don’t know in data. Allows you to make ________ about ________. – Without random selection, your sample does not tell you anything about population.

Idea 3: Sample Size Matters How many people should you talk to? Depends on population size, right? Size of ________ matters. –Usually need a couple of hundred. Size of __________ doesn’t. –Fraction of population sampled not important.

Terminology Information –Percentage of Registered Voters that would vote for a candidate. –Mean age of ISU undergraduates. Population – Sample –

Parameters and Statistics NameStatisticParameter Meanμ Standard Deviationsσ Proportionp Correlationrρ

How do you sample randomly? Might want every population member to have equal chance of being selected. –Ex. Population of 200 people – 100 males and 100 females. –Flip a coin Heads – sample = 100 females Tails – sample = 100 males –Not a representative sample of population

How do you sample randomly? Make every combination of population members have equal chance of being selected. _______________________ (SRS) –Get a sampling frame (list of names of pop.) –Assign a number to each person on sampling frame. –Use random numbers to select sample.

Selecting a SRS Population = 30 firms. Sample = 4 firms. –Number the firms 01,02,…,09,10,11,12,…,30. –Go to random number table and write down numbers by twos. –Throw out 00 and 31 through 99. –Throw out repeats. –First 4 numbers are sample.

Selecting a SRS Random numbers By twos Throw out 00 and 31 through 99 Throw out repeats Sample = Firms

Stratified Random Sample Large populations will be made up of smaller homogenous groups. Make sure each group included in sample. –Usually in proportion of population. Divide population into groups. Take SRS from each group. Combine SRSs = Stratified Random Sample

Stratified Random Sample 120 men and 80 women are in company. Opinions on policy of arrival of children. Sample 20 people –Stratify into men and women –Sample 12 men and 8 women

Cluster Sampling Difficult to get sampling frame for large population. Sample group or cluster first. Then take SRS from each clusters. Combined SRSs = Cluster Sample

Cluster Sample Opinion of Catholics church goers in Boston. –Cluster = Catholic churches –Take SRS of churches. –Take SRS of members of selected churches.

Gallup Major polling organization –Presidential polling –Opinion polling Multi-stage sampling –Combination of SRS, stratified and cluster sampling.

What can go Wrong? Biased Samples – Ex. CNN Quick Poll Ex. Ann Landers – Ex. Mall poll Ex. Internet Company database

What can go Wrong? ________________ – Need a good sampling frame. Household Surveys – homeless, students, prison inmates, etc. Phone Surveys – 6% of population with no phone. __________________ – People elect not to participate in survey. Can reach 30% or more.

What can go Wrong? _________________ – People will lie. Illegal or unpopular behavior. Leading questions from interviewer. Faulty Memory. _______________________. Confusing wording – use of negatives. Leading questions.

Inference about Population Biased samples tell us nothing about the population. –You can’t fix a bad sample. Good samples have sampling variability. –Statistics will be different for each sample. –Statistics will be different from population parameters. These differences obey certain laws of probability but only for random samples. Larger samples give more accurate results.