Chapter 2Introductory Information and Basic Terms: Basic Paradigm

Population Sample

Statistics

Inference

Parameters

Chapter 2Introductory Information and

Basic TermsBASIC TERMS WE WILL DEFINE

Element (or Observation Unit) Population Sampling Unit Frame Sample

Chapter 2Introductory Information and

Basic Terms

Example

An opinion poll is conducted in a city to determine public sentiment concerning a school construction bond issue that is going to be on the ballot in an upcoming election.

The objective of the survey is to estimate the proportion of the city’s voters that favor the bond issue.

Sampling Design Definitions

An element is an object on which a measurement is taken

• In our example, an element is a registered voter in the community.

• The measurement taken is the voter’s preference concerning the bond issue. (Since measurements are usually numbers, 1 could denote that a voter favors the bond issue and 0 could denote that a voter is not in favor of the bond issue).

Note: “object” is interpreted in the broad sense as something animate or inanimate.

Sampling Design Definitions (cont.) A population is a collection of

elements about which we wish to make an inference.

• In our example, the population is the collection of all registered voters in the city.

• The variable or characteristic of interest for each member of this population is his or her preference on the bond issue.

Note: the population should be carefully defined before collecting the sample.

Sampling Design Definitions (cont.) Sampling units are non-overlapping

collections of elements from the population that cover the entire population.

• In our example, a sampling unit may be a registered voter in the city.

• May be more efficient to sample “households”, which are collections of elements. “Households” must be defined so that no voter in the population can be sampled more than once and each voter has a chance of being selected in the sample.

Sampling Design Definitions (cont.)

Sampling units are non-overlapping collections of elements from the population that cover the entire population.

• Situations arise in which the non-overlapping condition is impossible to achieve.

• For example, in animal habitat studies the field plots are often circular.

Sampling Design Definitions (cont.)

A frame is a list of sampling units.

• In our example, if the individual voter is the sampling unit, a list of registered voters may serve as the sampling frame.

• If “household” is the sampling unit, then a telephone directory, city directory, or list of households from census data can serve as a frame.

• All have inadequacies.• Strive to make gap between population and frame as

small as possible so inferences about the population based on samples from the frame are valid.

Sampling Design Definitions (cont.) A sample is a collection of sampling

units selected from a single frame or from multiple frames.

In our example, if:1.the sampling unit is the individual registered voter, the frame could be a list of registered voters, and the sample is the collection of registered voters in the city whose bond issue preference we obtain2.OR, for example

a. first frame: list of “city blocks”;b. second frame: list of housing units within a city

block;c. third frame: list of registered voters within a

housing unit.

Convenience sampling: Just ask whoever is around.

– Example: “Man on the street” survey (cheap, convenient, often quite

opinionated or emotional => now very popular with TV “journalism”)

Which men, and on which street?

– Ask about gun control or legalizing marijuana “on the street” in Berkeley or in

some small town in Idaho and you would probably get totally different answers.

– Even within an area, answers would probably differ if you did the survey

outside a high school or a country western bar.

Bias: Opinions limited to individuals present.

Sampling methods

Voluntary Response Sampling: Individuals choose to be involved. These samples are very

susceptible to being biased because different people are motivated

to respond or not. Often called “public opinion polls.” These are not

considered valid or scientific.

Bias: Sample design systematically favors a particular outcome.

Ann Landers summarizing responses of readers

70% of (10,000) parents wrote in to say that having kids was not

worth it—if they had to do it over again, they wouldn’t.

Bias: Most letters to newspapers are written by disgruntled people. A

random sample showed that 91% of parents WOULD have kids again.

CNN on-line surveys:

Bias: People have to care enough about an issue to bother replying. This sample

is probably a combination of people who hate “wasting the taxpayers money” and

“animal lovers.”

Another Volunteer Response Sample

http://espn.go.com/sportsnation/polls

Bias-Avoid It!!

• Bias is the bane of sampling—the one thing above all to avoid.

• There is usually no way to fix a biased sample and no way to salvage useful information from it.

To be useful, a sample should be representative, meaning that characteristics of interest in the population can be estimated from the sample with a known degree of accuracy.To achieve this goal, we select individuals for the sample at random. The value of deliberately introducing randomness is one of the great insights of Statistics.

http://abcnews.go.com/blogs/politics/polls/

Randomize• Randomization can protect you against

factors that you know are in the data. – It can also help protect against factors you are

not even aware of.

• Randomizing protects us from the influences of all the features of our population, even ones that we may not have thought about. – Randomizing makes sure that on the average the

sample looks like the rest of the population

– Randomizing enables us to make rigorous probabilistic statements concerning possible error in the sample.

Measurement Error and Measurement Bias

Measurement error occurs when a response in the survey differs from the true value.

Measurement bias occurs when the response has a tendency to differ from the true value in one direction.

Examples of Measurement Error and Bias

People lie (have you shoplifted recently?) People forget People get confused (double negative

question: “Do you oppose a ban not allowing cellphone use while driving?”)

People try to impress the interviewer (“What is your IQ?”)

Interviewers can also impact the results of a survey.

Example: The American Community Survey

The American Community Survey (ACS) is an ongoing survey

… information from the survey generates data that help determine how more than $400 billion in federal and state funds are distributed each year.

… combined into statistics that are used to help decide everything from school lunch programs to new hospitals.

http://www.census.gov/acs/www/

The American Community Survey Element: resident of a housing unit or group

quarters Population: all residents of housing units and

group quarters in the US and Puerto Rico Sampling Units: housing units and group

quarters Frame: master address file (MAF): Census

Bureau’s official inventory of known HU’s, GQ’s and selected nonresidential units in US and PR; for each unit in MAF – Geographic codes, mailing or location address,

physical state, residential or commercial status, lat/long coordinates, and sources for updating the info.

The American Community Survey

American Community Survey Questionnaire

End of Chapter 2