Chapter 2. Sampling Design. How do we gather data?. Surveys Opinion polls Interviews Studies Observational Retrospective (past) Prospective (future) Experiments. the entire group of individuals that we want information about. Population. a complete count of the population. Census.
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The answer is 83!
If using destructive sampling, you would destroy population
Breaking strength of soda bottles
Lifetime of flashlight batteries
Safety ratings for carsWhy would we not use a census all the time?
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!
Since taking a census of any population takes time, censuses are VERY costly to do!
Suppose you wanted to know the average weight of the white-tail deer population in Texas – would it be feasible to do a census?
Use sample to generalize to populationSample
every individual has an equal chance of being selected
every set of n individuals has an equal chance of being selectedSimple Random Sample (SRS)
Suppose we were to take an SRS of 100 PWSH 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!
SRS’s are pulled from each strataStratified random sample
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 PWSH students. Since students are already divided by grade level, grade level can be our strata. Then randomly select 50 seniors and randomly select50 juniors.
randomly select where to begin
Suppose we want to do a systematic random sample of PSWH 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 20th student from there.Systematic random sample
m = 19.41
SRS used at each stageMultistage sample
To use a multistage approach to sampling PWSH 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!
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.
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
digits are independent of each other
Numbers can be read across.Random digit table
Numbers can be read vertically.
The following is part of the random digit table found on page 847 of your textbook:
1 4 5 1 8 5 0 3 3 7 1
2 4 2 5 5 8 0 4 5 7 0
3 8 9 9 3 4 3 5 0 6 3
Numbers can be read diagonally.
1) Aidan 6) Fred 11) Kathy 16) Paul
2) Bob 7) Gloria 12) Lori 17) Shawnie
3) Chico 8) Hannah 13) Matthew 18) Tracy
4) Doug 9) Israel 14) Nan 19) Uncle Sam
5) Edward 10) Jung 15) Opus 20) 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.
Stop when five people are selected. So my sample would consist of :
Aidan, Edward, Matthew, Opus, and Tracy
1 4 5 1 8 0 5 1 3 7 1
2 0 1 5 5 8 0 1 5 7 0
3 8 9 9 3 4 3 5 0 6 3
Usually only people with very strong opinions respondVoluntary response
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:
Produces bias resultsConvenience sampling
The data obtained by a convenience sample will be biased – however this method is often used for surveys & results reported in newspapers and magazines!
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!
People with unlisted phone numbers – usually high-income families
People without phone numbers –usually low-income families
People with ONLY cell phones – usually young adultsUndercoverage
Suppose you take a sample by randomly selecting names from the phone book – some groups will not have the opportunity of being selected!
telephone surveys 70% nonresponseNonresponse
Because of huge telemarketing efforts in the past few years, telephone surveys have a MAJOR problem with nonresponse!
People are chosen by the researchers, BUT refuse to participate.
This is often confused with voluntary response!
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.
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
Response bias occurs when for some reason (interviewer’s or respondent’s fault) you get incorrect answers.
connotation of words
use of “big” words or technical words
– if surveying Podunk, TX, then you should avoidcomplex vocabulary.
– if surveying doctors, then use more complex, technical wording.Wording of the Questions
The level of vocabulary should be appropriate for the population you are surveying
Questions must be worded as neutral as possible to avoid influencing the response.
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)
Convenience sampling – easy way to collect data
Undercoverage – students who buy books from on-line bookstores are included.
Undercoverage – leaves out homes that are not for sale or homes that are listed with different realtors.
(other answers are possible)