AP Statistics Study Guide Flashcards

Flashcards covering key vocabulary and concepts from an AP Statistics course, based on provided study guide notes. These flashcards are optimized for vocabulary review.

Statistics

The science and art of collecting, analyzing, and drawing conclusions from data.

Individual

Object described in a set of data.

Variable

Aspect that can take different values for different individuals.

Distribution

Pattern of variation of a variable.

Descriptive Statistics

Analyzing data.

Inferential Statistics

Making inferences / drawing conclusions from data.

Nominal Variable

No certain order.

Ordinal Variable

No order *could be numbers if they don’t measure anything (eg. cell phone digits)

Discrete Variable

Fixed set of possible values with gaps between them, whole numbers or defined intervals, countable or countably infinite.

Continuous Variable

Infinite possibilities, decimals / fractions, any value in an interval on the number line.

Basic Statistic Vocab

Also known as cases / observational units.

Frequency Table

Shows what values the variable takes & how often it takes them types of statistics.

Two-way table

Summarizes data on relationship between two categorical variables for a group of individuals.

Side-by-side bar graph

Bars showing the distribution of a categorical variable for each value of another categorical variable (grouped side-by-side).

Segmented bar graph

Distribution of a categorical variable as segments of a whole (bars stacked on top of each other & proportional to relative frequencies).

Mosaic plot

The width of the bars proportional to number of individuals in that category.

Association

Knowing the value of one variable allows you to predict value of the other.

Back-to-back stemplot

Quantitative data that’s split into two groups.

Mean

Average.

Median

Middle value.

Mode

Most common value.

IQR

Interquartile range (middle 50% of values).

Standard deviation

Typical distance from mean.

Resistant Measure

Not sensitive to skewness / outliers.

Statistic

A value that describes a characteristic of a sample.

Parameter

A value that describes a characteristic of a population.

Percentile

pth percentile is value with p% observations less than or equal to it.

Cumulative relative frequency graphs / ogives

Plots points corresponding to the percentile of a value in the distribution & points connected with line segments to create the graph.

Standardized scores (z-scores)

How many standard deviations from the mean a value is (& what direction).

Density curve

Simplified model of a distribution of a quantitative variable, always on or above horizontal axis, has an area of exactly 1 underneath it.

Normal distributions

Bell shaped & symmetric & unimodal distribution approximated with a normal curve (density curve).

Extrapolation

Using a regression line to make predictions way outside of the interval of x-values used to generate the line (beyond the scope of your data).

Least-squares regression line

Line that minimizes sum of squared residuals.

Residuals

Actual value – predicted value (based on line).

Residual plots

Scatterplot that plots residuals against explanatory variable, determines whether a linear model is appropriate (check for random scatter & no leftover curved pattern).

Standard deviation of residuals (s)

Measures typical residual (distance between predicted & actual).

Coefficient of determination (r2)

Square of correlation r when finding r from r2, make sure to consider direction of correlation!

Influential points

Points that, if removed, substantially change the slope, y-int, r, r2 , or s *these are very often influential (but not automatically guaranteed to be).

Transforming to achieve linearity

Applying a function to a quantitative variable (changes the scale of measurement) in order to make the scatterplot more approximately linear (in order to use linear regression methods).

Sampling

Selecting a random group of people out of a whole population (that’s representative of the population).

Sampling frame

The group of members from the population from which we select our sample.

Sampling survey

Collects data from the individuals in the sample (to learn about the population).

SRS (Simple Random Sample)

Every group of n individuals has an equal chance of being selected.

Stratified Sample

SRS selected from each strata. Strata: group w similar characteristics assumed to be associated with the variables being measured.

Clustered Sample

Randomly selecting entire clusters, Clusters: diff responses between (hopefully representative of population).

Systematic Sample

Randomly select starting point & select every kth individual after.

Convenience Sampling

Individuals who are easy to reach.

Voluntary Response Sampling

Allows individuals to choose to be in sample.

Bias

Likely to systematically overestimate or underestimate the value.

Undercoverage

Certain individuals less likely / cannot be chosen in a sample.

Nonresponse

Individual chosen for sample can’t be contacted / doesn’t participate.

Response Bias

Systematic pattern of inaccurate answers to a survey question.

Observational Studies

Observes individuals & measures variables of interest (does not influence responses).

Experiments

Imposes a treatment on individuals & measures their responses.

Placebo

No active ingredient.

Treatment

Condition imposed on individuals.

Experimental unit

Individual to which treatment applied, subject: human experimental unit.

Factor

Explanatory var that’s manipulated (may cause change in response var).

Levels

Diff possible values of a factor.

Confounding

When variables are associated so that their effects on a response variable can’t be distinguished from one another.

Control group

Provides a baseline for comparison.

Replication

Use enough subjects (diff in effects can be distinguished from chance variation).

Double blind

Neither subjects nor the ppl measuring know the treatment.

Single-blind

Only one of the groups (above) knows.

Completely randomized design

Experimental units assigned to treatments completely at random.

Randomized block design

Random assignment within each block. Block: group of experimental units known to be similar in some way that could affect their response to the treatments.

Matched pairs design

A type of RBD where blocks are pairs.

Statistical significance

Observed diff is larger than can be attributed to chance alone.

Statistical inference

Generalizing results to population, assuming sample is representative of population (ensured by random sample).

Sampling variability

Diff random samples (same size, same population) produce diff estimates.

Random process

Generates outcomes purely by chance.

Probability

Likelihood of an event to happen.

Law of large numbers

More trials means proportion approaches true probability (more accurate).

Simulation

Imitates random process such that simulated outcomes are consistent with real-world outcomes.

Probability model

Description of a random process that includes a list of all possible outcomes & the probability for each outcome.

Sample space

List of all outcomes.

Event

Any collection of outcomes from a random process.

Complement

The probability that an event does not occur.

Intersection

P(A and B) = A ∩ B (both A and B must be true).

Union

P(A or B) = A ⋃ B (at least one–either A or B, or both–must be true).

Mutually exclusive events

Cannot occur simultaneously (no outcomes in common) (also known as disjoint).

Non-mutually exclusive events

Can occur simultaneously.

Conditional probability

Probability that an event happens given that another event is known to have happened: P(A | B).

Independent events

Knowing whether or not one event has occurred does not change the probability that the other event will happen P(A | B) = P(A | BC) = P(A).

Random variable

Takes numerical values that describe the outcomes of a random process.

Discrete Random Variable

Fixed set of values with gaps between them can be described using probability distributions & histograms (each bar a value).

Continuous Random Variable

Any value in an interval on the number line probability distribution: density curve.

Binomial Random Variable

Use acronym BINS to check for binomial setting.

Geometric random variable

Number of trials it takes to get a success in a geometric setting.

Sampling distribution

The distribution of a statistic in all possible samples of the same size from the population.

Unbiased Estimator

Mean of sampling distribution of a statistic equal to true value of parameter same as accuracy check center (unbiased estimator).

Biased Estimator

Statistics consistently do not match parameters same as precision check variability choose an estimator with low bias & low variability.

Confidence interval

An interval of plausible values for an unknown population parameter based on sample data.

Confidence Level

Success rate / capture rate of the method that produces the interval accounts for sampling variability & increases confidence that our parameter value is correct.

Power of a test

Probability that a test will find convincing evidence for Ha when a specific alternative value of the parameter is true (probability that you avoid a type II error).

Chi square tests for goodness of fit

To check whether a hypothesized distribution seems valid.

Chi-square test for homogeneity

Compares distributions of a single cat var over multiple populations / treatments (multiple independent samples).

Chi-square test for independence & association

Compares distributions of two cat var (association) in a single population (one sample).