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.
the entire group of individuals that we want information about
a complete count of the population
The answer is 83!
If using destructive sampling, you would destroy population
Breaking strength of soda bottles
Lifetime of flashlight batteries
Safety 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!
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?
A part of the population that we actually examine in order to gather information
Use sample to generalize to population
refers to the method used to choose the sample from the population
a list of every individual in the population
consist 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
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!
population is divided into homogeneous groups called strata
SRS’s are pulled from each strata
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.
select sample by following a systematic approach
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.
based upon location
randomly pick a location & sample all there
Suppose we want to do a cluster sample of PSWH students. One way to do this would be to randomly select 10 classrooms during 2nd period. Sample all students in those rooms!
For the Jelly Blubber colony:
m = 19.41
select successively smaller groups within the population in stages
SRS used at each stage
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!
May not be representative
Must have sampling frame (list of population)
More precise unbiased estimator than SRS
Cost reduced if strata already exists
Difficult to do if you must divide stratum
Formulas for SD & confidence intervals are more complicated
Need sampling frame
Don’t need sampling frame
Ensure that the sample is spread across population
More efficient, cheaper, etc.
Can be confounded by trend or cycle
Formulas are complicated
Cost is reduced
Sampling frame may not be available (not needed)
Clusters may not be representative of population
Formulas are complicated
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
each entry is equally likely to be any of the 10 digits
digits are independent of each other
Numbers can be read across.
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.
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.
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
A systematic error in measuring the estimate
favors certain outcomes
Anything that causes the data to be wrong! It might be attributed to the researchers, the respondent, or to the sampling method!
things that can cause bias in your sample
cannot do anything with bad data
People chose to respond
Usually 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:
Ask people who are easy to ask
Produces bias results
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!
some groups of population are left out of the sampling process
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
Suppose you take a sample by randomly selecting names from the phone book – some groups will not have the opportunity of being selected!
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 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.
occurs when the behavior of respondent or interviewer causes bias in the sample
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 can influence the answers that are given
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.
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)
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
Undercoverage – students who buy books from on-line bookstores are included.
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)