AP Statistics Important Vocabulary Terms

AP Statistics Important Vocabulary Terms

Alternative Hypothesis

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

Bias

• Describes a study that systematically favors certain outcomes.

Binomial Distribution

• Distribution of the probabilities of X successes out of n trials.
• Denoted as B(n, p) where p is the probability of a single success.

Blind

• Experiment where subjects do not know which treatment they are receiving.

Blocking

• Statistical design that creates groups that are similar in some way, then randomizes treatments within each block.

Central Limit Theorem

• States that when a simple random sample (SRS) is drawn from a population with mean  and standard deviation 00, the sampling distribution for the sample mean will be approximately normally distributed with a mean of 0B and standard deviation of rac{00}{ ext{√}n}.

Chi-Square Distributions

• Family of skewed-right distributions defined by their degrees of freedom and taking only positive values.
• Shape changes with sample size.

Chi-Square Goodness-of-Fit Test

• Used to determine if a population has a certain hypothesized distribution.

Chi-Square Test for Homogeneity

• Determines if every category in the population has the same distribution.

Chi-Square Test for Independence

• Assesses if there is a relationship between two categorical variables; also known as Chi-Square Test for Association.

Coefficient of Determination

• Indicates the percentage of change in the response variable attributed to the change in the explanatory variable, symbolized as r^2.

Complement of an Event

• Set of all outcomes not defined as successful outcomes for any event.

Conditional Probability

• Probability of an event occurring given that another specific event has already occurred.

Confidence Interval

• Interval estimate of a parameter calculated using a sample from that population.

Confidence Level

• Probability that the desired parameter falls into a confidence interval if multiple intervals were calculated from samples of the same size.

Confounding Variable

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

Continuous Random Variable

• Takes on all values in an interval of numbers.

Control Group

• Group of subjects who receive either a placebo or no treatment during an experiment.

Correlation

• Measures direction and strength of a linear relationship between two quantitative variables, symbolized as r.

Critical Value

• Value (z-score, t-score, or 0 value) used in hypothesis testing to determine if the null hypothesis should be rejected.

Cumulative Distribution Function

• Function that calculates the sum of probabilities for each possible value of a random variable X.

Degrees of Freedom

• Value used to determine significance for a t-test or a Chi-Square test, measured generally as n-1; for two-way tables, (r-1)(c-1).

Dependent Trials

• Trials whose probability is affected by the outcomes of previous trials.

Dependent Variable

• Also referred to as Response Variable.

Density Curve

• Represents a distribution, always on or above the horizontal axis with total area of exactly 1 underneath.

Discrete Random Variable

• Random variable with countable outcomes.

Disjoint Events

• Events that cannot occur simultaneously; also known as Mutually Exclusive Events.

Distribution

• A list of the values a variable takes on and their frequencies.

Double Blind

• Experiment where neither the subjects nor the researchers know which treatment each subject receives.

Empirical Rule

• Also known as the 68-95-99.7 rule, used for approximating data that falls within 1, 2, or 3 standard deviations of the mean in any normal distribution.

Expected Value

• Synonymous with Mean.

Experimental Units

• Individuals on which an experiment is conducted.

Explanatory Variable

• Explains observed outcomes in a statistical study; also known as Independent Variable.

Exploratory Data Analysis

• Uses graphs and numerical summaries to characterize variables in a data set and their relationships.

Factor

• Any explanatory variable in an experiment.

Five Number Summary

• Describes data using the minimum, first quartile, median, third quartile, and maximum points.

Geometric Distribution

• Distribution of probabilities regarding the number of trials until the first successful outcome.

Hypothesis Test

• Inference type used to determine the feasibility of an assumed population parameter; also referred to as Significance Test.

Independent Trials

• Trials whose probabilities are not influenced by prior outcomes.

Independent Variable

• Also referred to as Explanatory Variable.

Individuals

• People or objects described in a data set.

Inference

• Process of drawing conclusions about a population based on sample data.

Influential Point

• Point whose removal markedly changes the regression equation.

Interquartile Range (IQR)

• Difference between the third and first quartiles of a data set.

Law of Large Numbers

• As the number of observations increases, the mean of those observations approaches the population mean closely.

Least Squares Regression Line

• Regression line minimizing the sum of squared vertical distances of points to the line.

Level

• Numerical value of a factor in an experiment.

Matched Pairs

• Statistical design comparing two treatments, often with one sample receiving each treatment over different time periods.

Mean

• The average of a data set; also known as Expected Value.

Median

• The middle value where 50% of data is above and 50% is below.

Mutually Exclusive Events

• Events that cannot occur together; synonymous with Disjoint Events.

Nonresponse

• Type of bias when individuals chosen for a sample cannot be contacted or choose not to participate.

Normal Distribution

• A symmetric, bell-shaped distribution where approximately 68% of data lies within one standard deviation, 95% within two, and 99.7% within three standard deviations of the mean.

Null Hypothesis

• States that a treatment has no effect or that the population has not changed.

Observation

• A single point from a data set.

Outlier

• An individual observation that deviates significantly from the overall pattern of data, defined as any number that is 1.5 IQR outside of Q1 or Q3.

P-value

• Probability that the observed outcome is as extreme or more extreme than observed if the null hypothesis is true.

Parameter

• A number describing a population.

Percentile

• Indicates what percent of a data set falls below a given observation.

Placebo

• A treatment with no expected effect, designed to appear the same as the actual treatment.

Pooled Procedures

• Combining separate samples into one sample for analysis, applicable only if variances are equal.

Population

• The entire group of individuals from which information is sought.

Power of a Hypothesis Test

• Probability of rejecting the null hypothesis when it is false, calculated as 1 minus the probability of a Type II error.

Probability

• Proportion of times an outcome occurs over a large number of trials.

Probability Distribution Function

• Assigns probabilities for each possible value of a discrete random variable X.

Proportion

• Percentage of a data set that falls within a given category.

Qualitative Variable

• Takes on non-numeric descriptions.

Quantitative Variable

• Takes on numeric values.

Quartiles

• Observations falling at the 25th, 50th, and 75th percentiles of a data set.

Range

• Difference between maximum and minimum values of a data set.

Random

• Individual outcomes are uncertain but follow a pattern over time.

Random Variable

• Variable whose value is a numeric outcome of a random phenomenon.

Randomization

• Using probability laws for sample selection and treatment assignments in experiments.

Regression Line

• Describes how a response variable changes as the explanatory variable changes.

Residual

• Difference between observed and predicted values of a response variable.

Response Variable

• Measures the outcome of a statistical study; also known as the Dependent Variable.

Robustness

• Measures how much the P-value is affected if the conditions of the hypothesis test are not met.

Sample

• A part of the population used for information gathering.

Sample Space

• List of all possible outcomes for a random event.

Sampling Distribution

• Distribution of values taken by a statistic across all possible samples of the same size from the same population.

Sampling Frame

• List from which a sample is chosen, ideally consisting of the entire population.

Significance Level

• The threshold point for determining statistical significance.

Significance Test

• Another term for Hypothesis Test.

Simple Random Sample (SRS)

• A sample where every population member has an equal chance of being chosen.

Simulation

• Method for collecting data using laws of probability to represent all possible outcomes of an experiment.

Skewed

• Description of a distribution whose histogram extends farther on one side of the mean; skewed in the direction of the tail.

Standard Deviation

• Square root of variance; commonly measures the spread of a data set.

Standard Error

• Standard deviation of a sampling distribution, representing expected error per standard deviation from the mean.

Standard Normal Distribution

• A normal distribution with a mean of 0 and standard deviation of 1.

Standardized Score

• Another term for z-Score.

Statistic

• A number describing a sample.

Statistically Significant

• An effect unlikely to occur by chance alone.

Stratified Random Sample

• Sample chosen by defining subsets within the population, then taking an SRS from each subset.

Subjects

• Also referred to as Experimental Units.

Symmetric

• Describing a distribution that has mirror-image histograms on either side.

t-Distributions

• Family of symmetric, bell-shaped distributions with a larger standard deviation than the standard normal distribution, defined by degrees of freedom.

Treatment

• A specific condition applied to an experimental unit or subject.

Treatment Group

• Group of subjects receiving an actual treatment in an experiment.

Type I Error

• Rejecting the null hypothesis when it is true; probability is the significance value for the test.

Type II Error

• Not rejecting the null hypothesis when it is false; probability must be calculated for a specific alternative.

Unbiased Statistic

• Statistic whose mean equals the population mean.

Undercoverage

• Bias occurring when certain population groups are omitted from the selection process.

Variability

• Describes the spread of a data set.

Variable

• Any characteristic of an individual.

Variance

• Average of the squares of deviations from the mean, used as a measure of spread.

Voluntary Response Sample

• Sample that consists only of people who opt to participate, generally a poor method for data collection.

z-Score

• Indicates how many standard deviations an observation lies above or below the mean; also called Standardized Score.