Chapter 2 Sampling Design

How do we gather data? SurveysSurveys Opinion pollsOpinion polls InterviewsInterviews StudiesStudies –Observational –Retrospective (past) –Prospective (future) ExperimentsExperiments

Population the entire group of individuals that we want information aboutthe entire group of individuals that we want information about

Census a complete count of the populationa complete count of the population

How good is a census? Do frog fairy tale... The answer is 83!

Why would we not use a census all the time? 1)Not accurate 2)Very expensive 3)Perhaps impossible 4)If using destructive sampling, you would destroy population Breaking strength of soda bottlesBreaking strength of soda bottles Lifetime of flashlight batteriesLifetime of flashlight batteries Safety ratings for carsSafety ratings for cars Look at the U.S. census – it has a huge amount of error in it; plus it takes a long to compile the data making the data obsolete by the time we get it! Suppose you wanted to know the average weight of the white-tail deer population in Texas – would it be feasible to do a census? Since taking a census of any population takes time, censuses are VERY costly to do!

Sample A part of the population that we actually examine in order to gather informationA part of the population that we actually examine in order to gather information Use sample to generalize to populationUse sample to generalize to population

Sampling design refers to the method used to choose the sample from the populationrefers to the method used to choose the sample from the population

Sampling frame a list of every individual in the populationa list of every individual in the population

Jelly Blubber Activity Select 10 Jelly blubbers that you think are representative of the population of blubbers in regards to length.Select 10 Jelly blubbers that you think are representative of the population of blubbers in regards to length. Find the mean length of your sampleFind the mean length of your sample

consist of n individuals from the population chosen in such a way thatconsist of n individuals from the population chosen in such a way that –every individual has an equal chance of being selected –every set of n individuals has an equal chance of being selected Simple Random Sample (SRS) Suppose we were to take an SRS of 100 SHS students – put each students’ name in a hat. Then randomly select 100 names from the hat. Each student has the same chance to be selected! Not only does each student has the same chance to be selected – but every possible group of 100 students has the same chance to be selected! Therefore, it has to be possible for all 100 students to be seniors in order for it to be an SRS!

Stratified random sample population is divided into homogeneous groups called stratapopulation is divided into homogeneous groups called strata SRS’s are pulled from each stratumSRS’s are pulled from each stratum Homogeneous groups are groups that are alike based upon some characteristic of the group members. Suppose we were to take a stratified random sample of 100 SHS students. Since students are already divided by grade level, grade level can be our strata. Then randomly select 50 seniors and randomly select 50 juniors.

Systematic random sample select sample by following a systematic approachselect sample by following a systematic approach randomly select where to beginrandomly select where to begin Suppose we want to do a systematic random sample of SHS students - number a list of students (There are approximately 2000 students – if we want a sample of 100, 2000/100 = 20) Select a number between 1 and 20 at random. That student will be the first student chosen, then choose every 20 th student from there.

Cluster Sample based upon locationbased upon location randomly pick a location & sample all thererandomly pick a location & sample all there Suppose we want to do a cluster sample of SHS students. One way to do this would be to randomly select 10 classrooms during 2 nd period. Sample all students in those rooms!

For the Jelly Blubber colony:  = 19.41

Multistage sample select successively smaller groups within the population in stagesselect successively smaller groups within the population in stages SRS used at each stageSRS used at each stage To use a multistage approach to sampling SHS students, we could first divide 2 nd 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!

SRS AdvantagesAdvantages –Unbiased –Easy DisadvantagesDisadvantages –Large variance –May not be representative –Must have sampling frame (list of population)

Stratified AdvantagesAdvantages –More precise unbiased estimator than SRS –Less variability –Cost reduced if strata already exists DisadvantagesDisadvantages –Difficult to do if you must divide stratum –Formulas for SD & confidence intervals are more complicated –Need sampling frame

Systematic Random Sample AdvantagesAdvantages –Unbiased –Ensure that the sample is spread across population –More efficient, cheaper, etc. DisadvantagesDisadvantages –Large variance –Can be confounded by trend or cycle –Formulas are complicated

Cluster Samples AdvantagesAdvantages –Unbiased –Cost is reduced –Sampling frame may not be available (not needed) DisadvantagesDisadvantages –Clusters may not be representative of population –Formulas are complicated

Identify the sampling design 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

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. Identify the sampling design Cluster sampling

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 10 th customer after them, to fill it out before they leave. Identify the sampling design Systematic random sampling

Random digit table each entry is equally likely to be any of the 10 digitseach entry is equally likely to be any of the 10 digits digits are independent of each otherdigits are independent of each other The following is part of the random digit table found on page 847 of your textbook: Row Numbers can be read across. Numbers can be read vertically. Numbers can be read diagonally.

Suppose your population consisted of these 20 people: 1) Aidan6) Fred 11) Kathy16) Paul 2) Bob7) Gloria 12) Lori 17) Shawnie 3) Chico8) Hannah 13) Matthew18) Tracy 4) Doug9) Israel14) Nan19) Uncle Sam 5) Edward10) Jung 15) Opus20) Vernon Use the following random digits to select a sample of five from these people. We will need to use double digit random numbers, ignoring any number greater than 20. Start with Row 1 and read across. Row Ignore. 18) Tracy 5) Edward 13) Matthew 1) Aidan 15) Opus Ignore. Stop when five people are selected. So my sample would consist of : Aidan, Edward, Matthew, Opus, and Tracy

Bias A systematic error in measuring the estimateA systematic error in measuring the estimate favors certain outcomesfavors certain outcomes Anything that causes the data to be wrong! It might be attributed to the researchers, the respondent, or to the sampling method!

Sources of Bias things that can cause bias in your samplethings that can cause bias in your sample cannot do anything with bad datacannot do anything with bad data

Voluntary response People chose to respondPeople chose to respond Usually only people with very strong opinions respondUsually only people with very strong opinions respond An example would be the surveys in magazines that ask readers to mail in the survey. Other examples are call- in shows, American Idol, etc. Remember, the respondent selects themselves to participate in the survey! Remember – the way to determine voluntary response is: Self-selection!!

Convenience sampling Ask people who are easy to askAsk people who are easy to ask Produces bias resultsProduces bias results An example would be stopping friendly-looking people in the mall to survey. Another example is the surveys left on tables at restaurants - a convenient method! The data obtained by a convenience sample will be biased – however this method is often used for surveys & results reported in newspapers and magazines!

Undercoverage some groups of population are left out of the selection processsome groups of population are left out of the selection process Suppose you take a sample by randomly selecting names from the phone book – some groups will not have the opportunity of being selected! People with unlisted phone numbers – usually high-income families People without phone numbers – usually low- income families People with ONLY cell phones – usually young adults

Nonresponse occurs when an individual chosen for the sample can’t be contacted or refuses to cooperateoccurs when an individual chosen for the sample can’t be contacted or refuses to cooperate telephone surveys 70% nonresponsetelephone surveys 70% nonresponse People are chosen by the researchers, BUT refuse to participate. NOT NOT self-selected! This is often confused with voluntary response! Because of huge telemarketing efforts in the past few years, telephone surveys have a MAJOR problem with nonresponse! One way to help with the problem of nonresponse is to make follow contact with the people who are not home when you first contact them.

Response bias occurs when the behavior of respondent or interviewer causes bias in the sampleoccurs when the behavior of respondent or interviewer causes bias in the sample wrong answerswrong answers 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 answers? Response bias occurs when for some reason (interviewer’s or respondent’s fault) you get incorrect answers.

Wording of the Questions wording can influence the answers that are givenwording can influence the answers that are given connotation of wordsconnotation of words use of “big” words or technical wordsuse of “big” words or technical words Questions must be worded as neutral as possible to avoid influencing the response. The level of vocabulary should be appropriate for the population you are surveying – if surveying Podunk, TX, then you should avoid complex vocabulary. – if surveying doctors, then use more complex, technical wording.

Source of Bias? 1) Before the presidential election of 1936, FDR against Republican ALF Landon, the magazine Literary Digest predicting Landon winning the election in a 3-to-2 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, telephone directories, etc. Undercoverage – since the Digest’s survey 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 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 during lunch one day. Convenience sampling – easy way to collect data or Undercoverage – students who buy books from on-line bookstores are included.

3) To find the average value of a home in Fort Smith, 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)

4) A new and somewhat controversial polling procedure that replaces the phone with the Internet is being used to conduct surveys. One criticism is that Internet users as a whole are still too highly educated and urban to produce results that accurately reflect all Americans.

5) “More than half of California’s doctors say they are so frustrated with managed care they will quit, retire early, or leave the state.” This statement comes from a survey conducted by the California Medical Association in which surveys were sent to 19,000 doctors and 2000 completed surveys were returned.