Chapter 12 - Sampling

Chapter 12 - Sampling - Chapter 12 Chapter Sampling Design...

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Unformatted text preview: Chapter 12 Chapter Sampling Design How do we gather data? How • Surveys Surveys • Opinion polls • Interviews • Studies – – – Observational Retrospective (past) Prospective (future) • Experiments Population Population • the entire group of the individuals that we want information about want Census Census • a complete count of the complete population population How good is a census? census? Do frog fairy tale . . . The answer is 83! Why would we not use a census all the time? census 1) 2) 3) 4) Not accurate Very expensive Perhaps impossibleat the U.S. census – it Look has a huge amount of error If using destructive sampling, you would in If Since taking takes a to know Suppose it census of any it; plus destroy population youawanted long to • • • population takes time, t ompile the weight of the che average data making the Breaking strength of soda bottles cwhite-tail are VERY costly to ensuses deer population in data obsolete by the time we Lifetime of flashlight batteries d et it! Texas – wouldo! be feasible to git Safety ratings for cars do a census? Sample Sample • A part of the population that part we actually examine in order to gather information order • Use sample to generalize to Use population population Sampling design design • refers to the method refers method used to choose the sample from the population population Sampling frame Sampling • a list of every list every individual in the population population Jelly Blubber Activity Jelly • Select 5 Jelly blubbers that you think Select are representative of the population of blubbers in regards to length. of • Find the mean length of your sample Simple Random Simple Suppose we were to take an SRS of 100 BHS students – put each Samplestudent has the Samplein(SRS) Not only does each students’ name a hat. Then • sconsist of nto ndividuals–from very consist select 100 namesbut e the ame chance i be selected randomly from the possible group of 100 students has the population chosen in suchsame hat. Each student has the a way same chance to be selected! Therefore, c that to behance to be selected! that it has possible for all 100 students to be seniors in order for it to be an – every individual has an equal every SRS! chance of being selected chance – every set of n individuals has an every equal chance of being selected equal Stratified random sample sample Homogeneous groups are groups that are alike based upon some characteristic of the a stratified Suppose we were to takegroup members. random sample of 100 BHS students. • population are already divided by population is divided Since students grade level, grade level can be our strata. intohen randomly select 25 seniors, T homogeneous randomly select 25 juniors, randomly groups sophomores, and randomly groups called strata select 25 select 25 freshmen. • SRS’s are pulled from SRS’s each strata each Systematic random sample random Suppose we want to do a systematic random sample of BHS students - number a list of students (There are approximately 2000 students – if we want a sample of 100, 2000/100 = 20) • selecta sample by 1 and 20 at select number between Select random. That the first fsollowing student will beevery 20 a systematic tudent chosen, then choose student approach from there. approach • randomly select where to randomly begin begin th Cluster Sample Cluster Suppose we want to do a cluster sample of BHS students. One way to do this would be to randomly select 10 classrooms during 2nd period. Sample all students in those rooms! • based upon location • randomly pick a randomly location & sample all all there there For the Jelly Blubber colony: colony: µ = 19.41 19.41 Multistage sample sample To use a multistage approach to sampling BHS students, we could first divide 2nd period classes by level (AP, Honors, Regular, etc.) and randomly select 4 second period classes from each group. Then we could randomly select 5 students from each of those classes. The selection process is done in stages! • select successively select smaller groups within the population in stages the • SRS used at each stage SRS SRS •Advantages – Unbiased – Easy •Disadvantages – Large variance – May not be representative – Must have sampling frame (list of population) Stratified Stratified • Advantages •Disadvantages – More precise – Difficult to do if you unbiased estimator must divide stratum than SRS – Formulas for SD & – Less variability confidence intervals are more complicated – Cost reduced if strata already exists – Need sampling frame Systematic Random Sample Sample •Advantages •Disadvantages – Unbiased – Don’t need sampling frame – Ensure that the sample is spread across population – More efficient, cheaper, etc. – Large variance – Can be confounded by trend or cycle – Formulas are complicated Cluster Samples Cluster •Advantages – Unbiased – Cost is reduced – Sampling frame may not be available (not needed) •Disadvantages – Clusters may not be representative of population – Formulas are complicated Identify the sampling design Identify 1)The Educational Testing Service (ETS) needed a sample of colleges. ETS first divided all colleges into groups of similar types (small public, small private, etc.) Then they randomly selected 3 colleges from each group. Stratified random sample Identify the sampling design 2) A county commissioner wants to survey people 2) A county commissioner wants to survey people in her district to determine their opinions on a particular law up for adoption. She decides to randomly select blocks in her district and then survey all who live on those blocks. Cluster sampling Identify the sampling design 3) A local restaurant manager wants to survey 3) A local restaurant manager wants to survey customers about the service they receive. Each night the manager randomly chooses a number between 1 & 10. He then gives a survey to that customer, and to every 10th customer after them, to fill it out before they leave. Systematic random sampling Random digit table table Numbers can be read across. Numbers can the random digit The following is part of be read vertically. table found on page A-117 ofdiagonally. Numbers can be read your textbook: • each entry is equally each Row 1 likely 8 5 be3any of the 4 5 1 to 0 371 24255804570 10 digits 10 38993435063 • digits are independent digits of each other of Suppose your population consisted of these 20 people: Suppose We will need to use double 1) Aidan 6) Fred 11) Kathy 16) Paul 1) Aidan digit 2) Bob 7) Gloria 12) Lori random numbers, 17) Shawnie 3) Chico 8) Hannah ignoring any 18) Tracy greater 13) Matthew number 13) Matthew 18) Tracy t14) Nan Start with Row 1 han 20. 4) Doug 9) Israel 19) Uncle Sam 5) Edward 10) Jung 15) Opus and read across. 20) Vernon Ignore. Ignore. Ignore. Ignore. Use the following random digits to select a sample of five from these people. Row 14 20 38 Stop when five people are selected. So 5 1 my sample would consist of : 8051371 155801570 9 Aidan, Edward, Matthew, Opus, and 93435063 Tracy Bias Bias • A systematic error in systematic measuring that causes the measuring the estimate Anything data to be wrong! It might • favors certain outcomes be attributed to the researchers, the respondent, or to the sampling method! Sources of Bias Bias • things that can cause things can bias in your sample bias • cannot do anything cannot with bad data with Voluntary response response •People chose to respond in An example would be the surveys Remember – the way to magazines that ask readers to mail in determine voluntary •tUsually only people with very he survey. Other examples are call-in shows, Americanis: etc. response Idol, strong opinions respond Remember, the respondent selects themselves to participate in the survey! Self-selection!! Convenience sampling sampling The data obtained by a convenience sample will be biased – however this method is often used for surveys & results reported in newspapers and An example would be stopping magazines! friendly-looking people in the mall to survey. Another example is the surveys left on tables at restaurants - a convenient method! •Ask people who are easy to ask •Produces bias results Undercoverage Undercoverage People with unlisted phone numbers – usually high-income families •some groups of population People without phone numbers – Suppose you take a are left out of the usually lowsample by randomly income families selecting names from sampling process the phone book – some groups will not have the opportunity of being selected! People with ONLY cell phones – usually young adults Nonresponse Nonresponse •occurs when an individual chosen for the sample can’t be contacted or refuses to cooperate •telephone surveys 70% nonresponse Because of huge telemarketing efforts in the past few years, telephone surveys have a MAJOR People roblem with by the researchers, One p are to help with the problem way chosen nonresponse! BUT refuse o to make follow of nonresponse tis participate. contact with the people who are NOT N when you first contact not homeOT self-selected! them. This is often confused with voluntary response! Suppose we wanted to survey high school students on drug abuse and we used a uniformed police officer to interview each student in our sample – would we get honest Response bias occurs when for answers? some reason (interviewer’s or respondent’s fault) you get incorrect answers. Response bias Response •occurs when the behavior of respondent or interviewer causes bias in the sample •wrong answers Wording ofbethe The level of vocabulary should appropriate for the population as Questions must be worded Questions Questions nyou ares possible to avoid eutral a surveying influencing the response. •wording can influence the – if surveying Podunk, TX, then you answers that are given should avoid complex vocabulary. •connotation of words – if surveying doctors, •use of “big” words or technical then use more complex, words wording. technical Response bias refers to anything in the survey design that influences the responses. Source of Bias? Source 1) Before the presidential election of 1936, FDR against Republican ALF Landon, the magazine Literary Digest predicting Landon winning the election in a 3­to­2 victory. A survey of 2.8 million people. George Gallup surveyed only 50,000 people and predicted that Roosevelt would win. The Digest’s survey came from magazine subscribers, car owners, Undercoverage – since the Digest’s survey telephone directories, etc. comes from car owners, etc., the people selected were mostly from high-income families and thus mostly Republican! (other answers are possible) 2) Suppose that you want to estimate 2) Suppose that you want to estimate the total amount of money spent by students on textbooks each semester at SMU. You collect register receipts for students as they leave the bookstore Convenience sampling – easy way to during lunch one day. collect data or Undercoverage – students who buy books from on-line bookstores are included. 3) To find the average value of a 3) To find the average value of a home in Plano, one averages the price of homes that are listed for sale with a realtor. Undercoverage – leaves out homes that are not for sale or homes that are listed with different realtors. (other answers are possible) ...
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This note was uploaded on 12/09/2011 for the course STATS 221 taught by Professor Nielson during the Fall '10 term at BYU.

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