AP Stats Unit 1B Vocab

explanatory variable

the factor you measure that is believed to cause an outcome

response variable

the outcome of the explanatory variable

confounding variable

a variable that is associated with both explanatory and response variable AND creates doubt about a true causal connection between the two variables

observational study

a study in which variables are observed without imposing any conditions or treatments; these cannot eliminate confounding or draw causal conclusions

prospective observational study

observational study analyzing data gathered now and into the future

retrospective observational study

observational study analyzing data that was already collected in the past

direct observation

observational study analyzing data measured through observation or records of observations

survey

observational study analyzing data gathered from responses to questions

experiment

study in which conditions, or treatments, are imposed on experimental units

treatments

different categories or levels of an explanatory variable that are imposed on experimental units

simple random sample

a sampling method in which every possible group of n individuals in the population has an equal chance of selection

stratified random sampling

 divide the population into non-overlapping homogenous groups called strata, then pick random samples from each of the strata, and combine these individual samples into the stratified random sample.

cluster random sampling

divides the population into non-overlapping heterogenous groups called clusters, each similar to each other, and then picking everyone or everything in a random selection of one or more of the clusters

systematic sampling

simple and quick sampling method in which you list the population in some order (ex. alphabetically), choose a random point to start, and then pick every tenth, hundredth, or kth person from the list. gives a reasonable sample as long as the original order of the list isn’t related to the variables being considered

convenience sampling

choose individuals that are easiest to reach to survey

census

measuring all items or individuals in a population

generalizability

when individuals are randomly selected from target population, results can be generalized to the whole population

causality

when individuals are randomly assigned to treatment, explanatory variable can be deemed causal to response variable

simple statistic

numerical value that describes a characteristic of a sample, which is a subset of the population; we use this to estimate population parameter

population parameter

numerical value that describes a characteristic of the entire population; we use sample statistic to estimate this

z score

measures how many standard deviations a data value is above/below the mean

z score formula

data value - mean / standard deviation

bias

flaw in sampling or measurement procedure that leads to systematically overestimating or underestimating a parameter value

key to eliminating bias

sampling randomly from the whole population of interest

undercoverage bias

sampling bias when part of the population is excluded or less likely to be selected for a sample

nonresponse bias

sampling bias when individuals who do not respond to surveys substantially differ from responders

voluntary response bias

sampling bias when a sample consists of entirely volunteers who differ from the general population

4 steps when writing about sampling bias on FRQs

identify the population of interest, identify the sample, identify the observational units excluded and how they differ, and explain how that exclusion leads to an overestimate or underestimate of the parameter

response bias

when responses to a survey differ from the true value; can happen even when sample is well chosen without sampling biases; has two formations called question wording bias and self reporting bias

question wording bias

response bias when survey questions are confusing or leading

self-reporting bias

when individuals inaccurately report their own traits

four principles of experimental design

comparison of at least two treatment groups, random assignment of treatments to experimental units, replication with many experimental units in each treatment group, and direct control of extraneous variables

random assingment

doing this with variables in an experiment balances extraneous variables and prevents confounding

control group

comparison group that is not given the treatment of interest

placebo effect

when belief of receiving treatment leads to a measured response, even though the treatment is inactive

single-blind/masked study

either the subjects or the researchers who interact with them are unaware of who receives the active treatment vs. the placebo

double blind/masked study

study when both the subjects and the researchers are unaware of who receives the active treatment vs. the placebo

completely randomized experimental design

involves experimental units being assigned to treatments completely at random (no pre-grouping); simplest experimental design

randomized block design

experimental units are grouped in blocks based on an extraneous variable, then units are randomly assigned to treatment and compared within each block

matched pairs design

a randomized block experiment in which either: 1) each block is composed of two similar experimental units (a matched pair) or 2) the same experimental unit receives both treatments and the order of the treatments is randomized