AP Statistics 4.1 (Sampling and Surveys)

Population

The largest group that we hope to learn something about.

Census

Collects data from every member of the population.

Sample

A subset of the population that actually gets examined in an attempt to learn about the population.

Sample survey

A study that uses an organized plan to choose a sample that represents the population.

-The sample can be made of people, animals, or things.

Good sample

A good sample is representative of the population and will provide a good estimate of the value of interest.

Biased sample

Systematically over or under represents a portion of the population and would consistently overestimate or underestimate the value of interest.

-When asked how a sample is biased, be sure to identify the problem with the sampling method and explain how this would lead to an underestimation or an overestimation

Convenience sample

Choosing individuals from the population who are easy to reach.

Voluntary response

Composed of people who choose themselves by responding to a general invite.

-Usually people who choose to voice their opinion on a subject already feel strongly one way or the other about that subject.

-ex) online poll

Random sampling

Uses a chance process to determine which members of a population are included in the process

-chance processes include: flipping a coin, rolling dice, drawing names out of a hat, random number generator, random digit table

-avoids favoritism by the sampler and self-selection by the respondents

Sampling frame

The list of all subject in a population

Simple Random Sampling (SRS)

A simple random sample of size n is chosen in such a way that every group of n individuals in the population has an equal chance to be selected as the sample.

-N = population size

-n = sample size

How to choose a SRS of size n from a population N

1. Assign a unique number between 1 and N to each member of the population.

2. Us randomness (calculator or table) to select n unique numbers, skipping repeated values and values not between 1 and N.

3. The subjects corresponding to the chosen numbers will be in the sample.

Stratified random sampling

Split the sampling frame into homogeneous subgroups (age, gender, etc.) then pick a random sample from each group.

-reduces variability in the sample statistic

-guarantees all subgroups are represented

-allows comparison between subgroups

Cluster sampling

Split the sampling frame into heterogeneous clusters (typically by geographical location), randomly select several clusters, then sample all subjects in the chosen clusters

-can make sampling less expensive by reducing travel time

Systematic sampling

Begin with a randomly selected individual, then use a system to pick the remaining individuals (i.e. Every 7th person)

-can be easier to use than an SRS, especially if the population will be lined up

-ex) the census bureau uses systematic sampling to decide which households get the long form of the census

Inference

Drawing a conclusion about a population based on the data from a sample

Sampling variability

We don't expect the results from a sample to be exactly the same as if we'd measured the entire population, each sample will produce a slightly different result

Why do we use random sampling?

-it helps us avoid bias.

-allows us to use the laws of probability to construct a margin of error.

Undercoverage

Occurrs when a subgroup of the population cannot be chosen in a sample.

-ex) when phone numbers are used to select a sample, those without phones have no chance of being in a sample.

Nonresponse bias

Occurs when a portion of the chosen sample does not respond to the survey

-ex) we son't hear from the stressed/busy people

Response bias

Occurs when the method of the survey influences the response given by the subject

-this can happen in face-to-face interviews, through the wording of a question, or because of the topic being surveyed (alcohol use).