AP Statistics Vocabulary

A complete sequence of AP Statistics vocabulary terms, providing definitions and relevant statistical notation for each concept found in the lecture notes.

Alternative Hypothesis

States that a treatment has had an effect or caused a change in the population

Bias

Describes a study which systematically favors certain outcomes

Binomial Distribution

The distribution of the probabilities of $X$ successes out of $n$ trials, calculated using $p$ as the probability of any single success – $B(n, p)$

Blind

Describes an experiment in which the subjects do not know which treatment they are getting

Blocking

A statistical design which creates groups that are similar in some way, and then randomizes the treatments within each block

Central Limit Theorem

States that when an SRS is drawn from a population with mean $\mu$ and standard deviation $\sigma$, the sampling distribution for the sample mean will be approximately normally distributed, and have a mean $\mu$ and a standard deviation $\frac{\sigma}{\sqrt{n}}$

Chi-Square Distributions

A family of skewed-right distributions which take on only positive values and are defined by their degrees of freedom – the specific shape of the Chi-Square Distribution changes as the sample size changes

Chi-Square Goodness-of-Fit Test

Used to determine if a population has a certain hypothesized distribution

Chi-Square Test for Homogeneity

Used to determine if every category in the population has the same population

Chi-Square Test for Independence

Used to determine if there is a relationship between two categorical variables – also known as Chi-Square Test for Association

Coefficient of Determination

Tells what percent of the change in the response variable can be attributed to the change in the explanatory variable – symbolized as $r^2$

Complement of an Event

The set of all outcomes not defined as successful outcomes for any event

Conditional Probability

The probability of an event occurring if it is known that another specific event has already occurred

Confidence Interval

An interval estimate of a parameter calculated using a sample from that population

Confidence Level

The probability that the desired parameter will fall into a confidence interval if many intervals were calculated from samples of the same size

Confounding Variable

A variable which could affect the result of a statistical test but has not been controlled for

Continuous Random Variable

A random variable which takes on all values in an interval of numbers

Control Group

Any group of subjects who receive either a placebo or no treatment at all during an experiment

Correlation

Measures the direction and strength of the linear relationship between two quantitative variables – symbolized as $r$

Critical Value

A value (z-score, t-score, or $\chi^2$ value) used in a hypothesis test to help determine if the null hypothesis should be rejected

Cumulative Distribution Function

A function which calculates the sum of the probabilities for each possible value for any random variable $X$

Degrees of Freedom

A value used to help determine significance for a t-test or a Chi-Square test – measured as $n-1$ in most cases, or $(r-1)(c-1)$ when dealing with two-way tables

Dependent Trials

Trials whose probability is affected by the outcome of previous trials

Density Curve

A curve used to represent a distribution; always on or above the horizontal axis and has a total area of exactly $1$ underneath it

Discrete Random Variable

A random variable with countable outcomes

Mutually Exclusive Events

Events which cannot occur at the same time

Distribution

A list of what values a variable takes on and how often it takes on each one of those values

Double Blind

Describes an experiment in which neither the subjects nor the researcher know which treatment each subject is getting

Empirical Rule

Also known as the $68-95-99.7$ rule – is used as an approximation for what percent of the data falls within $1$, $2$, or $3$ standard deviations of the mean in any normal distribution

Expected Value/ Mean

The 'average' of a data set

Experimental Units/Subjects

The individuals on which an experiment is conducted

Explanatory/Independent Variable

Attempts to explain the observed outcomes in a statistical study

Exploratory Data Analysis

Uses graphs and numerical summaries to describe the variables in a data set and the relationships among them

Factor

Any explanatory variable in an experiment

Five Number Summary

A method to describe a data set using the minimum, first quartile, median, third quartile, and maximum points in the data set

Geometric Distribution

A distribution of probabilities of when the first successful outcome occurs in a probability experiment

Hypothesis/Significance Test

A type of inference used to determine the feasibility of an assumed population parameter

Independent Trials

Trails whose probabilities are not affected by the outcome of previous trials

Individuals

People or objects described by a set of data

Inference

The statistical process of drawing conclusions about a population by examining data from a sample

Influential Point

A point which, if removed from the data set, would markedly change the regression equation for that data set

Interquartile Range (IQR)

The difference between the third and first quartiles of a data set

Law of Large Numbers

States that as increased numbers of observations are drawn from any population, the mean of the observations eventually approaches the mean of the population as closely as we would like to estimate it, and remains that close or closer

Least Squares Regression Line

A regression line which makes the sum of the squares of the vertical distances from the data points to the line as small as possible

Level

A numerical value of a factor of an experiment

Matched Pairs

A statistical design which compares two treatments – this is usually done with one sample receiving each treatment over a different time period

Median

The point at which $50\%$ of the data is above and $50\%$ of the data is below

Nonresponse

A type of bias that occurs when an individual chosen for a sample cannot be contacted or chooses not to participate

Normal Distribution

A symmetric, bell-shaped distribution in which approximately $68\%$ of the data lies within one standard deviation of the mean, $95\%$ lies within two standard deviations, and $99.7\%$ lies within three standard deviations – defined by mean and standard deviation

Null Hypothesis

States that either a treatment has had no effect on a population, or that the population has not changed

Observation

Any single point from a data set

Outlier

An individual observation that falls outside the pattern of the data set – often defined as any number that is $1.5(IQR)$ outside of $Q1$ or $Q3$

P-value

The probability that the observed outcome would take on a value as extreme or more extreme than observed if the null hypothesis were true

Parameter

A number that describes a population

Percentile

Tells what percent of a data set falls below the given observation

Placebo

A false treatment which should have no effect on an experiment

Pooled Procedures

Occurs when separate samples are combined into a single sample for analysis – done only if population variances are equal

Population

The entire group of individuals that we want information about

Power of a Hypothesis Test

The probability that the test will reject the null hypothesis when the null hypothesis is false – equal to $1 - P(\text{Type II error})$

Probability

The proportion of times an outcome would occur over a large number of trials

Probability Distribution Function

A function which assigns a probability for each possible value for any discrete random variable $X$

Proportion

Tells what percent of a data set falls into a given category

Qualitative Variable

A variable which takes on a non-numeric description

Quantitative Variable

A variable which takes on a numeric value

Quartiles

Observations which fall at the $25\text{th}$, $50\text{th}$, and $75\text{th}$ percentiles of a data set

Range

The difference between the maximum and minimum values of a data set

Random

When individual outcomes are uncertain, but there is a pattern to the distribution of the outcomes over time

Random Variable

A variable whose value is a numeric outcome of a random phenomenon

Randomization

Using the laws of probability to select members for a sample or assign treatments to samples in experiments

Regression Line

A straight line that describes how a response variable changes as the explanatory variable changes

Residual

The difference between and observed value of a response variable and its predicted value from a regression equation

Response/Dependent Variable

Measures the outcome of a statistical study

Robustness

A measure of how much the P-value of a test is affected if the conditions of the hypothesis test are not met

Sample

A part of the population used to gather information about the entire population

Sample Space

A list of all possible outcomes for a random event

Sampling Distribution

A distribution of values taken by a statistic in all possible samples of the same size from the same population

Sampling Frame

A list from which a sample is chosen – ideally consists of the entire population

Significance Level

The point at which it will be determined that a result is statistically significant

Simple Random Sample (SRS)

A sample in which every member and every group of size $n$ has the same probability to be chosen

Simulation

A method for collecting data which uses the laws of probability to represent all possible outcomes of an experiment

Skewed

Describes a distribution whose histogram extends much farther to one side of the mean than the other in the direction of the 'tail'

Standard Deviation

Square root of the variance – used as a common measure of spread for a data set

Standard Error

The standard deviation of a sampling distribution – measures the amount of expected error per standard deviation from the mean

Standard Normal Distribution

A normal distribution with a mean of zero and a standard deviation of one

Statistic

A number that describes a sample

Statistically Significant

An observed effect so far removed from the mean that it would be unlikely to occur by chance alone

Stratified Random Sample

A sample chosen by splitting the population into several well-defined groups, then taking an SRS from each group

Symmetric

Describes a distribution whose histogram has its left and right sides as mirror images of each other

t-Distributions

A family of symmetric, bell-shaped distributions with a standard deviation larger than that of the standard normal distribution – defined by degrees of freedom

Treatment

A specific experimental condition applied to an experimental unit or subject

Treatment Group

A group of subjects who receive an actual treatment during an experiment

Type I Error

When the null hypothesis is rejected but it is in fact true

Type II Error

When the null hypothesis is not rejected but it is in fact false

Unbiased Statistic

A statistic from a sampling distribution whose mean must be equal to the mean of the population

Undercoverage

A type of bias that occurs when some groups of a population are left out of the selection process for the sample

Variability

Describes the spread of a data set

Variable

Any characteristic of an individual

Variance

The average of the squares of the deviations of the observation from their mean – used as a measure of spread

Voluntary Response Sample

Consists only of people who choose to participate – a poor method for collecting meaningful data

z-Score

A measure used to tell how many standard deviations above or below the mean an observation lies – also known as a Standardized Score