AP Stats Unit 1

stratified random samples

break down larger more complicated populations into strata

strata

smaller subgroups

what is the statistical advantage of stratified samples over SRS?

helps ensure representation from population of interest & should create more precise estimates of the truth of the population

cluster sample

groups of individuals in the population that are located near eachother

systematic random sample

randomly select a starting point, then sample every nth individual from there

pros of SRS

easy design, hopefully unbiased

cons of SRS

usually has large variation

pros of stratified sampling

helps ensure a representative sample, hopefully unbiased

cons of stratified sampling

extra steps, must stratify correctly

pros of cluster sampling

get a lot of sample quickly

cons of cluster sampling

estimates might be extreme or biased if you have low numbers of clusters, can’t guarantee a representative sample

cons of systematic sampling

if nth selection is too small/large, you might have undercover bias, run the risk of undercovering a portion of the population

pros of systematic sampling

easy design, get a lot of samples quickly

sampling frame

list of individuals to sample from

undercoverage

when sampling, a portion of the population is left out. caused by sampling designs

nonresponse

occurs when the individuals chosen for the sample can’t be reached or refuse to participate. can impact overall estimate

how can nonresponse be reduced?

better designs & anonymous surveys

what is nonresponse vs. voluntarily response?

underestimate, overestimate

response bias

when respondents purposefully lie or don’t know how to answer truthfully; could be because of surroundings or slanted survey questions

observational study

observes individuals & measures variables of interest without attempting to influence the response variable

retrospective observational study

uses existing data

prospective observational study

follows individuals into the future

explanatory variable

may help us explain/predict changes in a response variable; potential cause

response variable

measures the outcomes of a study; potential effect

association

knowing the value of 1 variable can help predict the other

confounding

happens often in observational studies when a change in response variable is caused from multiple explanatory variables

when are 2 variables confounded?

if it’s impossible to determine which variable is causing a change in the response variable

experiment

when we delberately impose treatments onto subjects in order to observe a change in the response variable

benefit of experiments

we can begin to establish cause & effect through random assignment & well designed experiments

placebo

a dummy treatment made to be seemingly identical to the real treatment; no active ingredient. use for control/comparison groups

treatment

what we randomly assign to experimental units.;specific treatments are applied to individuals. explanatory variable; may be more than 1 treatment or multiple treatment groups

experimental unit/subject

the object to which a treatment is randomly assigned. if it’s a human we call them subjects

factor

is what may be causing a change in the response variable

level

the different values of a factor

control group

provides a baseline for comparison

placebo affect

describes the fact some subjects in an experiment will respond favorably to any treatment, even a placebo.

single blind experiment

either the subjects or the people who interact with them & measure the response variable don’t know which treatment has been assigned/assessed

double blind experiment

neither subjects nor people interacting with them know the treatment assigned/assessed

why are blindness procedures important?

they reduce placebo effect & keep studies as honest as possible

what does it mean to control other variables?

holding other variables constant for each member of both treatment groups. benefits to this is reducing variability in the response variable

replication

use enough subjects. ensuring there are an adequate number of units in each treatment group so that 2 groups are equivalent as possible. can also refer to repeating the experiment with different subjects

how can we determine if evidence is convincing?

compare the observed difference with what could happen by random change alone & a well controlled, replicated, & randomized experiment or a simulation

statistifcally significant

convincing evidence; results are s.s. if they are unlikely to happen by random chance alone.

what is associated with sampling & experiment?

bias, confounding

blocking

a way to establish cause & effect that accounts for a source of variability similar to stratifying

what variables are best for blocking?

we want to use variables that are most strongly associated with the response variable?

what is the difference between blocking & stratifying?

blocking goes to experiments (treatments), stratifying goes to sampling (surveying)

matched pairs design

a special type of block design where an individual gets both treatments & acts as their own control/comparison

inference

using info from sampling/experiments/simulations to draw conclusions about a population or treatment

sampling variability

from sample to sample we should expect to get different results even though we’re sampling in the same population of interest

margin of error (moe)

how far, on average, we expect our estimate to be from the truth of the population

what’s the benefit to increasing sample size?

increasing n increases precision; decreases margin of error but doesn’t counteract a bad sampling design. doesn’t increase accuracy.