sample surveys. population- all exp. units that you want to make a conclusion about sampling frame...
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Population- all exp. units that you want to make a conclusion about
Sampling frame – list of individuals from whom the sample is drawn. Not always the population of interest.
Sample- small group of the population that you do an experiment/study on.
Vocabulary
◦Parameter -Describes the population-Fixed Value-Often Unknown
◦Statistic-Describes the sample of a population-Changes from sample to sample-Use the statistics from repeated samples to
estimate the value of the parameter
Value Parameter Statistic
Mean
Standard Deviation
Proportion
x s
Sample is said to be representative if the statistics accurately reflect the population parameters
EXAMPLE 1:A polling agency takes a sample of 1500
American citizens from a list of tax returns and asks them if they are lactose intolerant. 12% say yes. This is interesting, since it has been shown that 15% of the population is lactose intolerant.
12% = _________ 15% = __________
Population? Sampling frame? Sample?
EXAMPLE 2:A random sample of 1000 people who signed a card saying they intended to quit smoking were contacted a year after they signed the card. It turned out that 210 (21%) of the sampled individuals had not smoked over the past six months.
21% = _________ Population = Sampling frame= Sample = Parameter of interest =
EXAMPLE 3:On Tuesday, the bottles of tomato ketchup filled in a plant were supposed to contain an average of 14 ounces of ketchup. Quality control inspectors sampled 50 bottles at random from the day’s production. These bottles contained an average of 13.8 ounces of ketchup.
14 = _________ 13.8 = __________
Population? Sample? Sampling frame?
EXAMPLE 4:A researcher wants to find out which of two pain relievers works better. He takes 100 volunteers and randomly gives half of them medicine #1 and the other half medicine #2. 17% of people taking medicine 1 report improvement in their pain and 20% of people taking medicine #2 report improvement in their pain.
17% = _________ 20% = __________Population? Sampling frame? Sample?
HW answers:
3) A website asks visitors to its site “Do you ever use emoticons when you type online?” Of the 87,262 respondents, 27% said NO.
(a) What kind of sample?(b) How confident are you in this result?
4) MLB decides to select a team at random and test all 40 of its players.
(a) What kind of sample?(b) Is the sample appropriate?
5) Results based on telephone interviews with 1,008 national adults, conducted April 2 – 5, 2007. In addition to sampling error, question wording and practical diificulties can lead to error and bias.
(a) population?(b) sampling frame?(c) what problems?
11) The EPA took soil samples at 16 locations near a former industrial waste dump and checked each for evidence of toxic chemicals. They found no elevated levels of any harmful substances.
(a) population?(b) parameter of interest?(c) sampling frame?(d) sample?(e) sampling method?(f) sources of bias?
Some more vocab….
Bias VS. Variability:
* Bias- consistent, repeated measurements that are not close to the population parameter
* Variability- basically like reliability
* To reduce bias… use random sampling
* To reduce variability… use larger samples!
* We want to keep both of these low!
Bias is the accuracy of a statistic Variability is the reliability of a statistic
Bias vs Variability
SAMPLING VARIABILITY
* Different samples give us different results
* Bigger samples are better!!
* Sampling distribution: If we take lots of samples of the same size and make a graph
* Different size samples give us different results
True parameter
* Variability = spread/width of graph
Larger samples give smaller variability:
Lots of samples of size 100
True parameter True parameter
Lots of samples of size 1000
Another vocab word…
• Unbiased Estimator:
- When the center of a sampling distribution (histogram) is equal to the true parameter.
True parameter
True parameter
GOOD Sampling Designs:
1) Simple Random Sample (SRS) - Every experimental unit has the same chance of being picked for the sample and every possible sample has the same chance of being selected
• Give every subject in the population a number
• Use the table of random digits and read across to select your sample
• Ignore repeats
EXAMPLE:
Take an SRS of 5 from the following list. Start at line 31 in the table.
Smith Jones Holloway
DeNizzo David Adams
Schaefer Gray Capito
Meyers Gingrich Card
Dietrich Moreland Hall
Walsh Whitter Jordan
EXAMPLE:
Take an SRS of 4 from the following list. Start at line 18 in the table.
McGlone McCuen Wilson
Szarko Bellavance Woodring
Stotler Kelly Wheeles
Timmins Arden McNelis
Gemgnani O’Brien Robinson
Lorenz Lake Bainbridge
2) Stratified Random Sample- (not SRS)
* Divide population into groups with something in common (called STRATA)
Example: gender, age, etc.
* Take separate SRS in each strata and combine these to make the full sample
- can sometimes be a % of each strata
Example:We want to take an accurate sample of CB
South students. There are 540 sophomores, 585 juniors, and 530 seniors. Take a stratified random sample.
3) Systematic Random Sample – The first exp. unit is selected at random. Each additional exp. unit is selected at a predetermined interval.
Examples:
- Surveying every 5th person that walks thru the back door of CB South.
- Selecting a random person to start with (like person #4) and then taking every 10th person on the list after that (person #14, person #24, person #34, etc.)
4) Cluster Sample – Population is broken into groups. All members in one or more groups are taken as the sample.
5) Multistage Sample - - Used for large populations Example: sampling the population of the USA
Example:The government wants to survey the entire
population. However they cannot just give every person a number and do an SRS. So they follow this process:
* Randomly select 5 counties from each state
* In each of those counties, randomly select 6 towns/cities
* In each town/city, randomly select 4 streets
* On each street, select 3 houses, and interview the head of the household.
BIASED SAMPLING METHODS:
1) Voluntary Response Samples
• Chooses itself by responding to a general appeal.
• Call-in, write-in, etc.
2) Convenience Samples
• Selecting individuals that are the easiest to reach/contact
JUST CHECKINGWe need to survey a random sample of 30 passengers on a flight from San Francisco to Tokyo. Name each sampling method described below:
• Pick every 10th passenger that boards• From the boarding list, randomly choose 5 people flying first class, and 25 of the other passengers• Randomly generate 30 seat numbers and survey the passengers who sit there
• Randomly select a seat position (right window, left window, right aisle, etc.) and survey all
people in those seats
HW answers:
8) (a) population = all Americans?(b) parameter = true percent of people who want marijuana legalized for medicinal reasons(c) sampling frame = people who visit the website(d) sample = all people who responded to the question on the website(e) method = voluntary response sample(f) biases = voluntary response bias
undercoverage- not everyone visits the site and sees the question
HW answers:
10) (a) population = all voters(b) parameter = issues that voters are
interested in(c) sampling frame = blocks in the city’s
election districts(d) sample = all residents that the staff
members can find that day(e) method = stratified, then convenience
within each strata (f) biases = voluntary response bias
nonresponse bias
HW answers:
17) (a) Voluntary response sample
(b) Cluster sample
(c) census, and voluntary response sample
(d) Stratified random sample
Last vocab… types of BIAS in samples
Example: Telephone polls, registered voter list, etc.
• Nonresponse- Bias introduced when a large amount of those sampled do not respond.
Example: people don’t answer phone, don’t mail back questionnaires, refuse to answer
questions
• Undercoverage-
Sampling in a way that leaves out a certain portion of the population that should be in your sample
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