5.1: Designing Samples

Important Distinction Observational Study – observe individuals and measure variables but do not attempt to influence the responses. Experiment – deliberately impose some treatment on individuals in order to observe responses.

Designing Samples Population – entire group of individuals we want information about. Sample – part of the population we actually examine. Samples are used due to constraints such as time, cost, and inconvenience.

Census vs. Sampling Census – contacting every individual in the entire population. Sampling – studying a part in order to gain information about the whole.

Sampling Methods Voluntary Response Sample – people who choose themselves by responding to a general appeal (question, etc.). Bias - those with strong (especially negative) opinions are most likely to respond. Remember Ann Landers? Write-in, Call-in, and online polls are not very reliable! Convenience Sample – choosing individuals who are easiest to reach. Bias – Mall samples are convenient. However, they are more likely to include teenagers, retirees, and wealthier segments of the population.

REAL ESTATE DEVELOPMENT PROJECT

What is BIAS? Bias occurs when a sampling method systematically favors certain outcomes. “Personal Choice” (by a responder to a VRS or the interviewer of a CS) produces bias. The statistician’s remedy? CHANCE!

I. Simple Random Samples Simple Random Sample (SRS) – every member of a population has an equal chance of being selected. Ex) Names in a hat (population) are drawn out with in a handful (sample). NOTE: larger random samples give more accurate results than smaller samples. Random Digits Table (Table B: Back of Book) Each entry is equally likely to be any of the 10 digits 0 through 9. Entries are independent of each other.

Using Table B DPS would like to interview a sample of 5 students to find ways to improve teacher quality. To avoid bias, DPS will use a SRS of size 5. Steps: Label: Give each student a numerical label. Two digits are needed in our class. For example, 01 to 26. Table B: Enter anywhere. Let’s try line 130.    Students 05, 16, 17, 20, 19 are selected  It’s good practice to start at a different row every time you use Table B

If only I had my Table B…

TI Alternative MATH, PRB, randInt(1,26), hit ENTER five times ENTER again if you get repeats MATH, PRB, randInt(1,26,5), ENTER Works well unless you get repeats

Other Sampling Methods Probability Sample – a sample chosen by chance The use of chance to select the sample is the ESSENTIAL principle of statistical sampling. Stratified Random Sample - First, divide the population into strata (groups of individuals) that are similar in some way. Next, choose a separate SRS in each stratum and combine to for the full sample. Ex) Divide a population of high schools into public, Catholic, and other private schools

…Continued Cluster Sampling – First, divide the population into groups, or clusters. Next, clusters are randomly selected. ALL individuals in the chosen clusters are selected for the sample. Ex) Do students feel they have enough time for AP Statistics free response questions?  Randomly select a few schools from a comprehensive list featuring every school that administers the AP exam.  Every student at the selected schools is asked about the time limits.  The students interviewed would constitute a cluster sample.

Take Caution… Undercoverage occurs when some groups are left out of the sample selection process. Household surveys miss the homeless, inmates, and students in dormitories. Telephone polls miss the 8% of homes without residential lines. Nonresponse occurs when a selected individual can’t be contacted or does not cooperate.

…More Caution Examples of Response Bias Respondents may lie if asked about illegal or unpopular behavior. In a recent poll, 72% said they voted when just 56% actually did vote. An interviewer’s race or gender may influence responses regarding racism or sexism. Faulty memories “Telescoping” Example – “Have you visited a dentist in the last 6 months?” will often elicit a “Yes” from someone who went 8 months ago.

…More Caution The Wording of Questions is the most important influence on the answers given to a sample survey. Ex) 1992 Opinion Poll by American Jewish Commission “Does it seem possible or does it seem impossible to you that the Nazi extermination of the Jews never happened?”  22% responded “possible” “Does it seem possible to you that the Nazi extermination of Jews never happened, or do you feel certain that it happened?”  1% responded “possible”

Before You Trust a Poll… Know the… Exact questions asked Rate of nonresponse Date and method of the survey