AP Statistics: Chapter 4 - Sampling and Experiments

population

the entire group of individuals we want information about (specifically in a statistical study)

census

collects data from EVERY individual in the population

sample

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

sample survey

a study that collects data from a sample to learn about the population from which the sample was selected

convenience sampling

a sampling method where you select individuals from the population who are easy to reach

bias

the systematic favoring of certain outcomes over others in a study, leading to inaccurate results (overestimation or underestimation of the value)

voluntary response sampling

a sampling method where individuals choose to participate in the survey by responding to a general invitation

random sampling

a sampling method where each individual in the population has an equal chance of being selected

simple random sample (SRS)

a subset (of size n) of the population selected in such a way that every individual has an equal chance of being chosen

sampling without replacement

a sampling method where an individual from a population can only be selected once

sampling with replacement

a sampling method where an individual from a population can be selected multiple times

strata

subgroups within a population that share similar characteristics thought to be associated with the variables being measured in a study, used in stratified sampling

stratified random sampling

a sampling method that involves dividing the population into strata, taking the SRS from each stratum, and combining the SRSs into one overall sample; ideally, the strata should be homogenous, allowing for better representation of the entire population

cluster

a group of individuals in the population that are located near each other

cluster sampling

a sampling method that involves dividing the population into clusters, usually geographically, and then randomly selecting entire clusters to be included in the sample; usually the clusters should be heterogenous, allowing for better representation of the population

systematic random sampling

a sampling method where individuals are selected from a larger population at regular intervals; for example, every nth individual is chosen to be part of the sample (ordered arrangement)

undercoverage bias

a sampling bias when some members of the population are less likely to be chosen or cannot be chosen in a sample

nonresponse bias

a sampling bias when an individual chosen for the sample can’t be contacted or refuses to participate

observational study

a study where researchers observe outcomes/variables of interest without manipulating variables/responses, often used to identify correlations

response variable

a variable that measures an outcome of a study

explanatory variable

a variable that helps to explain or predict changes in a response variable

confounding variable

a variable that occurs when two variables are associated in such a way that their effects on a response variable cannot be distinguished from each other; essentially, you don’t know whether the explanatory variable or the confounding variable is causing changes in the response variable

experiment

deliberately imposes treatments (conditions) on individuals to measure their responses

placebo

a treatment that has no active ingredient, but is otherwise like other treatments (avoid a confounding variable)

treatment

a specific condition (consisting of one or more explanatory variables) applied to individuals in an experiment; if an experiment has >1 explanatory variable, this is a combo of specific values of the explanatory variables

experimental unit

the object to which a treatment is randomly assigned

subjects

a term often used when experimental units are human beings

factor

explanatory variable that is manipulated and may cause a change in the response variable (in an experiment)

levels

the different values of a factor

control group

baseline for comparing the effects of other treatments; depending on the experiment, it may be an active treatment, inactive treatment (placebo), or no treatment at all

placebo effect

some subjects in an experiment will respond favorably to any treatment, even an inactive treatment

double-blind

neither the subjects nor the researchers/ones who interact with them and measure the response variable know which treatment a subject is receiving (removing confounding variables)

single-blind

either the subjects or the people who interact with them and measure the response variable don’t know which treatment a subject is receiving

random assignment

experimental units are assigned to treatments using a chance process (e.g. random number generator, etc.)

control

keeping other variables constant for all experimental units

replication

giving each treatment enough experimental units to ensure a difference in the effects of the treatments can be distinguished from chance variation due to random assignment

completely randomized design

the experimental units are assigned to the treatments completely at random

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

randomized block design

random assignment of experimental units to treatments is carried out separately within each block

matched pairs design

a common experimental design for comparing two treatments that uses blocks of size 2; these blocks are usually very similar and the treatments are randomly assigned within each pair; in others, each experimental unit receives both treatments in a random order

sampling variability

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