Chapter 12Sample Surveys

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

Label each as high or low for bias and variability

True parameter

True parameter

Label each as high or low for bias and variability

True parameter

True parameter

Another vocab word…

• Unbiased Estimator:

- When the center of a sampling distribution (histogram) is equal to the true parameter.

True parameter

True parameter

SAMPLING DESIGNS

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

Complete the Sampling Rectangles activity

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

Examples:

* respondents lying

* responses trying to please the interviewer

* unwillingness to reveal personal facts or info

* leading or confusing questions

• Response Bias-

Anything in the survey design that influences the responses.