AP Stats - Chapter 4 (Collecting Data)

population

the entire group of individuals we want information about

census

collects data from every individual in the population

sample

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

- when sampling, we can use technology or a Random Digits Table

sample survey

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

convenience sampling

selects individuals from the population who are easy to reach (bias -> poor sampling method)

bias

the design of a study is very likely to underestimate or very likely to overestimate the value you want to know

voluntary response sampling

allows people to choose to be in the sample by responding to a general invitation (bias -> poor sampling method)

random sampling

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

- allows inference about the population from which the individuals were chosen

simple random sample (SRS)

- size n

- chosen in such a way that every group of n individuals in the population has an equal chance to be selected as the sample

- sample without replacement

- label, randomize, select

- best way to reduce sampling bias

sampling without replacement

individual from a population can only be selected once

sampling with replacement

individual from a population can be selected more than once

strata

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

- homogeneous groups

stratified random sampling

- selects a sample by choosing an SRS from each stratum and combining the SRSs into one overall sample ("some from all")

- unbiased & low variability

cluster

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

- ideally heterogeneous groups

cluster sampling

- selects a sample by randomly choosing clusters and including each member of the selected clusters in the sample ("all from some")

- easy to take 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

- don't need to label everyone

undercoverage

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

nonresponse

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

response bias

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

response variable

measures an outcome of a study

explanatory variable

may help explain or predict changes in a response variable

confounding

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 treatments (conditions) on individuals to measure their responses

placebo

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

treatment

- 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

experimental unit

the object to which a treatment is randomly assigned

subjects

human experimental units

factor

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

levels

different values of a factor

control group

- used to provide a baseline for comparing the effects of other treatments

- may be given an inactive treatment (placebo), an active treatment, or no treatment at all depending on the purpose of the experiment

placebo effect

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

double-blind experiment

neither the subjects nor those who interact with them and measure the response variable know which treatment a subject is receiving

single-blind experiment

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

- allows inference about cause and effect

control

keeping other variables constant for all experimental units

replication

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

principles of experimental design

1) comparison

2) random assignment

3) control

4) replication

completely randomized design

the experimental units are assigned to 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

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

matched pairs design

- common experimental design for comparing two treatments that uses blocks of size 2

- in some, two very similar experimental units are paired and the two 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

- larger samples produce more accurate (closer to the true value) estimates

statistically significant

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

margin of error

- creates an interval of plausible values