Chapter 12 Sample Surveys

Vocabulary Population- ALL exp. units that you want to make a conclusion about Note: does not necessarily have to be a large group Sampling frame – list of individuals from which the sample is drawn. Not always the population of interest. Examples: phone book, registered voter list, list of tax returns, school roster, etc. Sample- small group of the population that you do an experiment/study on. Hopefully representative of the population

◦Parameter -A number that describes the population (ex: population mean) -Fixed Value -Often Unknown ◦Statistic -A number that describes the sample of a population (ex: sample mean) -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 Sample is said to be representative if the statistics accurately reflect the population parameters

12% = _________ 15% = __________ Population? Sampling frame? Sample? 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? Parameter of Interest? statistic parameter All American citizens List of tax returns 1500 American citizens selected True % of people who are lactose intolerant

Parameter of interest = 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 = statistic All smokers who intend to quit All people who signed the card 1000 people who signed the card True % of smokers who intend to quit that actually do

14 = _________ 13.8 = __________ Population? Sample? Sampling frame? 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? Parameter of Interest? parameter statistic All ketchup bottles produced at that factory on Tuesday 50 bottles at random from Tuesday’s production All bottles produced at that factory on Tuesday True average amount of ketchup in Tuesday’s bottles

17% = _________ 20% = __________ Population? Sampling frame? Sample? 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? Parameter of Interest? statistic statistic All people who take pain relievers volunteers 100 volunteers True % of people who show relief from medicine 1 and from medicine 2

* Different size samples give us different results SAMPLING VARIABILITY * Different samples give us different results (even if they are from the same population) * Different size 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 of the statistic from each sample (like the mean) True parameter

Sampling errors… Bias vs. Variability: * Bias- consistent, repeated measurements that are not close to the population parameter * Variability- spread of the sampling distribution * We want to keep both of these low! * To reduce bias… use random sampling * To reduce variability… use larger samples!

Bias vs. Variability Bias is the accuracy of a statistic Variability is the reliability of a statistic

Larger samples give smaller variability: * Variability = spread/width of graph Larger samples give smaller variability: Lots of samples of size 100 Lots of samples of size 1000 True parameter True parameter

Label each as high or low for bias and variability True parameter High bias Low variability Low bias High variability True parameter

Label each as high or low for bias and variability High bias High variability True parameter True parameter Low bias Low variability

Another vocab word… Unbiased Estimator: - When the center of a sampling distribution (histogram) is equal to the true parameter. True parameter True parameter BIASED: True parameter True parameter

SAMPLING DESIGNS (HOW to sample a population)

Give every subject in the population a number 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 TRD 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 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.

Example: We want to sample CB South students. However an SRS is too time consuming. How could we use multistage sampling?

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 CHECKING We 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

Last vocab… types of BIAS in samples Undercoverage- Sampling in a way that leaves out a certain portion of the population that should be in your sample Example: Telephone polls, registered voter list, etc. Non-response- 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

Anything in the survey design that influences the responses. Response Bias- Anything in the survey design that influences the responses. Examples: * respondents lying * responses trying to please the interviewer * unwillingness to reveal personal facts or info * leading or confusing questions Voluntary Response Bias 29

Book examples: p. 289 #15, 16, 17, 22, 23