AP Statistics: Key Concepts and Definitions for Exam 1

Individuals

are the objects described by a set of data. Individuals may be people, but they may also be animals or things.

Variables

is any characteristic of an individual. A variable can take different values for different individuals.

Data

The actual measurements recorded for individuals.

Census

a sample survey that attempts to include the entire population in the 'sample.'

Subjects

(or participants) are the people in the study.

Treatment

any specific experimental condition applied to the subjects.

Control group

Allows for the researcher to control the effects of lurking variable.

Randomized comparative experiment

compared two (or more) treatments.

Lurking (or confounding variable)

has an effect on the relationship among the variables in a study but is NOT one of the explanatory variables studied.

Confounding variables

Two variables are confounding when their effects on a response variable cannot be distinguished from each other.

Placebo

a dummy treatment (no active pharmacological ingredients).

Placebo effect

someone responds favorably to a placebo because of their expectations.

Single blind

participants doesn't know which conditions they are in but researcher does.

Double blind

neither the participants nor the researcher knows which condition.

Population

the entire group of individuals about which we want information

Sample

part of the population from which we actually collect information and is used to draw conclusions about the whole

Sample Survey

chooses a sample from a specific population and uses the sample to get information about the entire population

Convenience samples

sampling methods that are common but do not produce trustworthy data - these methods are usually biased

Voluntary response samples

sampling methods that are common but do not produce trustworthy data - these methods are usually biased

Parameter

is a number that describes the population; a parameter is a fixed number, but in practice, we don't know its value

Statistic

a number that describes the sample; the value of a statistic is known when we have taken a sample, but it can change from sample to sample

P-hat

the sample proportion (statistic) of those who have the trait/opinion of interest

P

the population proportion (parameter) who have the trait/opinion of interest

Variability

how spread out the values of the statistic are when we take many samples

Bias

consistent, repeated deviation of the statistic from the parameter in the same direction when we take many samples

Sampling Variability

statistics will not be the same from sample to sample (because all samples are going to be a little different from each other)

Random error

repeated measurements on the same individuals give different results (despite true value being the same)

Random Sampling

To reduce bias, use random sampling.

Sample Size

To reduce variability, use a larger sample size.

Margin of Error (MOE)

a value that quantifies the uncertainty in our estimate.

confidence statement

interprets a confidence interval and has two parts: a margin of error & a level of confidence.

Level of Confidence

states what percentage of all possible sample results in a confidence interval which contains the true parameter.

Confidence Interval Formula

Confidence interval formula.

Internal Validity

Internal Validity: a change in the explanatory variable causes changes in the response variable.

External Validity

External Validity: do our conclusions generalize to the wider population.

Predictive Validity

if it can be used to predict things that are related to the property measured.

Stratified Random Sample

Step 1: Divide the sampling frame into distinct groups of individuals, called strata. Step 2: Take a separate simple random sample in each stratum and combine these to make up the complete sample.

Matched Pairs Design

design compares just two treatments.

Block Design

the random assignment of subjects to treatments is carried out separately within each block.

Block

a group of experimental subjects that are known before the experiments to be similar in some way that is expected to affect the response to the treatments.

Variance

Use to determine if the random error is small.

Variance Formula

Σ = sum of, Xi = an individual data point, X̅ = average, n = your sample size.

Measures

A property of a person/thing when a number is assigned to represent it.

Instrument

used to take a measurement.

Units

used to record the measurements.

Example of Measurement

To measure a student's readiness for college, you ask them to take the SAT.

Variable

example: Student's score (in points).

Rate

a fraction, proportion, or percentage at which something occurs.

Count

number of occurrences.