Chapter 2 Introductory Information and Basic Terms: Basic Paradigm Population Sample Statistics Inference Parameters

Chapter 2 Introductory Information and Basic Terms BASIC TERMS WE WILL DEFINE Element (or Observation Unit) Population Sampling Unit Frame Sample

Chapter 2 Introductory Information and Basic Terms Example An opinion poll is conducted at a large university to determine student sentiment concerning a proposed change to the method for determining what students receive tickets to basketball games. The objective of the survey is to estimate the proportion of students that favor the proposed change.

Sampling Design Definitions An element (or observation unit) is an object on which a measurement is taken In our example, an element is a student at the university. The measurement taken is the student’s preference concerning the proposed change in the ticket distribution method. (Since measurements are usually numbers, 1 could denote that a student favors the change and 0 could denote that a student is not in favor of the change). Beginning of lecture unit 2 in coursepack 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 students at the university. The variable or characteristic of interest for each member of this population is his or her preference concerning the proposed change in the ticket distribution policy. Population definition and the measurements to be taken are interrelated. For example, since the population is registered voters, may want to obtain information on whether the sampled voter plans to vote in upcoming election. Not always possible to sample from target population. For example, if population available is a list of residents, then information about whether the person is in fact a registered voter will have to be collected. 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 an individual student at the university. If every student is required to have a “major” (math, history, etc.), then “major” could be a sampling unit. “Majors” are collections of elements. Only 1 major should be designated for each student so that no student in the population can be sampled more than once and each student 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: Categorizing students by those taking face-to-face lecture classes and those taking online classes 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 student is the sampling unit, a list of students from Reg.& Records may serve as the sampling frame. If “major” is the sampling unit, then a list of majors from the Division of Academic Affairs can serve as a frame. Most frames 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: the sampling unit is the individual student, the frame could be an alphabetic list of students from Reg. & Records, and the sample is the group of students selected from the Reg. & Records. OR, for example first frame: randomly choose some “majors” from a list of “majors” available at the university; second frame: randomly select students from the majors selected in part a. (make sure a double-major student not selected twice)

Sampling methods 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.

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.” Examples: Ann Landers - 80% of people would not have kids if had to do over again. CNN website, intecepting people on the street or at the mall.

Another Volunteer Response Sample Another place you might have seen volunteer response samples are at web sites like CNN.com or ESPN.com where they ask for a “quick vote” on a particular issue Many web sites use these opinion polls to try and get your viewers involved in their website. Unfortunately these types of opinion polls are not good at judging the opinions the entire population. These “quick votes” are often biased because the individuals that take the time to fill them out have a strong opinion about the topic. Individuals that bother to fill out the survey on a sports website like ESPN.com tend to be fans of one of the teams or at least fans of that sport. 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.

https://poll.qu.edu/national/release-detail?ReleaseID=2562 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. https://poll.qu.edu/national/release-detail?ReleaseID=2562

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 $500 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