AP Stat - Chapter 4: Collecting Data

population

in a statistical study is the entire group of individuals we want

census

collects data from every individual in the population

sample

a subset of individuals in the population from which we actually collect data

statistic

a numerical measurement describing some characteristic of a sample

parameter

a numerical measurement describing some characteristic of a population

sample survey

a study that collects data from a sample that is chosen to represent a specific population (observational study)

convenience sample

choosing individuals who are easiest to reach (produces unrepresentative data)

voluntary response

sampling design where individuals can choose on their own whether to participate in the sample (biased because people with strong opinions, especially negative opinions, are most likely to respond)

random sampling

involves using a chance process to determine which members of a population are included in the sample

simple random sample (SRS)

of size n consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance to be the sample actually selected

strata

groups of individuals in a population who share characteristics thought to be associated with the variables being measured in a study

stratified random sampling

selects a sample by choosing an SRS from each stratum and combining the SRSs into one overall sample

advantages/disadvantages of stratified sampling

A: best when individuals within each stratum are homogenous and there are large differences between stratum

D: time consuming and expensive

cluster

a group of individuals that are "near" one another

advantages/disadvantages of cluster sampling

A: best when individuals in each cluster are heterogenous; saves time or money

D: if individuals in each cluster are homogenous, could give imprecise results

cluster sampling

selects a sample randomly choosing clusters and including each member of the selected cluster in the sample

systematic random sampling

selects a sample from an ordered arrangement of the population by randomly selecting one of the first k individuals and choosing every kth individual thereafter

advantages/disadvantages of systematic sampling

A: simple to use; suitable for large samples

D: only random if list is random; could have bias

undercoverage

occurs when some groups in the population are less likely to be chosen or cannot be chosen in a sample

nonresponse

occurs when an individual chosen for the sample can't be contacted or refuses to participate

response bias

occurs when there is a systematic pattern of inaccurate answers to a survey question

observational study

observes individuals and measures variables of interest but does not attempt to influence the responses

confounding

occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other

experiment

deliberately imposes some treatment on individuals to measure their responses

placebo

a treatment that has no active ingredient, but is otherwise like other treatments

treatment

a specific condition applied to the individuals in an experiment

experiment unit

the object to which a treatment is randomly assigned

factor

a variable that is manipulated and may cause a change in the response variable

levels

different values of the factor

placebo effect

describes the fact that some subjects in an experiment will respond favorably to any treatment, even an inactive treatment

double-blind

experiment in which neither the subjects nor those who interact with them and measure the response variable know which treatment a subject received; avoids unconscious bias

single-blind

experiment in which either the subjects don know which treatment they are receiving or the people who interact with them and measure the response variable don know which subjects are receiving which treatment

random assignment (in an experiment)

means that experimental units are assigned to treatments using a chance process

comparison

first principle for designing experiments; use a design that compares two or more treatments

random assignment

second principle for designing experiments; use chance to assign experimental units to treatments (doing so helps create roughly equivalent groups of experimental units by balancing the effects of other variables among the treatment groups)

control

third principle for designing experiments; keep other variables the same for all groups, especially variables that are likely to affect the response variable (helps reduce confounding variables)

replication

fourth principle for designing experiments; giving each treatment to enough experimental units so that any differences in the effects of the treatments can be distinguished from chance differences between groups

sampling variability

refers to the fact that different random samples of the same size from the same population produce different estimates

statistically significant

when the observed results of a study are too unusual to be explained by chance alone