48 terms

AP Statistics - Chapter 4

Sampling and Surveys
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Bias
The design of a statistical study shows bias if it would consistently underestimate or consistently overestimate the value you want to know.
Census
A study that attempts to collect data from every individual in the population.
Cluster sample
To take a cluster sample, first divide the population into smaller groups. Ideally, these clusters should mirror the characteristics of the population. Then choose an SRS of the clusters. All individuals in the chosen clusters are included in the sample.
Convenience sample
A sample selected by taking the members of the population that are easiest to reach; particularly prone to large bias.
Double-blind
An experiment in which neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.
Margin of error
A numerical estimate of how far the sample result is likely to be from the truth about the population due to sampling variability.
Nonresponse
Occurs when a selected individual cannot be contacted or refuses to cooperate; an example of a nonsampling error.
Nonsampling error
The most serious errors in most careful surveys are nonsampling errors. These have nothing to do with choosing a sample—they are present even in a census. Some common examples of nonsampling errors are nonresponse, response bias, and errors due to question wording.
Population
In a statistical study, the population is the entire group of individuals about which we want information.
Random sampling
The use of chance to select a sample; is the central principle of statistical sampling.
Response bias
A systemic pattern of incorrect responses.
Sample
The part of the population from which we actually collect information. We use information from a sample to draw conclusions about the entire population.
Sample survey
A study that uses an organized plan to choose a sample that represents some specific population. We base conclusions about the population on data from the sample. You must 1) say exactly what population you want to describe and 2) say exactly what you want to measure - give exact definitions of the variables.
Sampling frame
The list from which a sample is actually chosen.
Simple random sample (SRS)
The basic random sampling method. An SRS gives every possible sample of a given size the same chance to be chosen. We often choose an SRS by labeling the members of the population and using random digits to select the sample. Common ways to choose an SRS included drawing names out of a hat, technology random number generators or using tables of random digits. You should be able to describe in great detail how to choose an SRS using those methods.
Strata
Groups of individuals in a population that are similar in some way that might affect their responses.
Stratified random sample
To select a stratified random sample, first classify the population into groups of similar individuals, called strata. Then choose a separate SRS from each stratum to form the full sample.
Table of random digits
A long string of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with these properties:
• Each entry in the table is equally likely to be any of the 10 digits 0 through 9.
• The entries are independent of each other. That is, knowledge of one part of the table gives no information about any other part.
Undercoverage
Occurs when some members of the population are left out of the sampling frame; a type of sampling error.
Voluntary response samples
People decide whether to join a sample based on an open invitation; particularly prone to large bias.
Wording of questions
The most important influence on the answers given to a survey. Confusing or leading questions can introduce strong bias, and changes in wording can greatly change a survey's outcome. Even the order in which questions are asked matters.
Block
A group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.
Completely randomized design
When the treatments are assigned to all the experimental units completely by chance.
Confounding
When two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other.
Control group
An experimental group whose primary purpose is to provide a baseline for comparing the effects of the other treatments. Depending on the purpose of the experiment, a control group may be given a placebo or an active treatment.
Double-blind
An experiment in which neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received.
Experiment
Deliberately imposes some treatment on individuals to measure their responses.
Experimental units
The smallest collection of individuals to which treatments are applied.
Explanatory variable
A variable that helps explain or influences changes in a response variable. Also called factors.
Level
A specific value of an explanatory variable (factor) in an experiment. For example, if we were studying effects of advertising an explanatory variable might be lengths of commercials and we could have commercials of varying lengths. 30, 45 and 60 minute commercials would make 3 levels of that one explanatory variable.
Matched pair
A common form of blocking for comparing just two treatments. In some matched pairs designs, each subject receives both treatments in a random order. In others, the subjects are matched in pairs as closely as possible, and each subject in a pair is randomly assigned to receive one of the treatments.
Observational study
Observes individuals and measures variables of interest but does not attempt to influence the responses.
Placebo
An inactive (fake) treatment.
Placebo effect
Describes the fact that some subjects respond favorably to any treatment, even an inactive one (placebo).
Random assignment
An important experimental design principle. Use some chance process to assign experimental units to treatments. This helps create roughly equivalent groups of experimental units at the start of the experiment.
Randomized block design
Start by forming blocks consisting of individuals that are similar in some way that is important to the response. Random assignment of treatments is then carried out separately within each block.
Replication
An important experimental design principle. Use enough experimental units in each group so that any differences in the effects of the treatments can be distinguished from chance differences between the groups.
Response variable
A variable that measures an outcome of a study.
Single-blind
An experiment in which either the subjects or those who interact with them and measure the response variable, but not both, know which treatment a subject received.
Statistically significant
An observed effect so large that it would rarely occur by chance.
Subjects
Experimental units that are human beings.
Treatment
A specific condition applied to the individuals in an experiment. If an experiment has several explanatory variables, a treatment is a combination of specific values of these variables.
Inference about cause and effect
Using the results of an experiment to conclude that the treatments caused the difference in responses. Requires a well-designed experiment in which the treatments are randomly assigned to the experimental units.
Inference about the population
Using information from a sample to draw conclusions about the larger population. Requires that the individuals taking part in a study be randomly selected from the population of interest.
Lack of realism
When the treatments, the subjects, or the environment of an experiment are not realistic. Lack of realism can limit researchers' ability to apply the conclusions of an experiment to the settings of greatest interest.
Basic Principle for Designing Experiments
1. Comparison - Use a design that compares two or more treatments.
2. Random Assignment - Use chance to assign experimental units. Create roughly equivalent groups of experimental units at the start of the experiment to balance the effects of other variables among the treatment groups.
3. Control - Keep other variables that might affect the response the same for all groups. (This is not the same as control group.)
4. Replication - Use enough experimental units in each group so the differences can be distinguished from chance.
Criteria for establishing causation when we can't do an experiment.
1. The association is strong.
2. The association is consistent.
3. Larger values of the explanatory variable are associated with stronger responses.
4. The alleged cause precedes the effect in time.
5. The alleged cause is plausible.
Scope of Inference
1. Inferences about populations are possible when individuals are randomly selected.
2. Inferences about cause and effect are possible when individuals are randomly assigned to groups.