AP统计术语词典

GLOSSARY

Alternative hypothesis—the theory that the researcher hopes to confirm byrejecting the null hypothesis

Association —when some of the variability in one variable can be accounted forby the other

Bar graph—graph in which the frequencies of categories are displayed withbars; analogous to a histogram for numerical data

Bimodal —distribution with two (or more) most common values; see mode Binomial distribution—probability distribution for a random variable X in a

binomial setting;

where n is the number of independent trials, p is the probability of successon each trial, and x is the count of successes out of the n trials

Binomial setting (experiment)—when each of a fixed number, n , of

observations either succeeds or fails, independently, with probability p Bivariate data—having to do with two variables

Block —a grouping of experimental units thought to be related to the response tothe treatment

Block design—procedure by which experimental units are put into

homogeneous groups in an attempt to control for the effects of the group on theresponse

Blocking —see block design

Boxplot (box and whisker plot)—graphical representation of the five-numbersummary of a dataset. Each value in the five-number summary is located overits corresponding value on a number line. A box is drawn that ranges from Q1to Q3 and “whiskers” extend to the maximum and minimum values from Q1and Q3.

Categorical data—see qualitative data

Census —attempt to contact every member of a population

Center —the “middle” of a distribution; either the mean or the median

Central limit theorem—theorem that states that the sampling distribution of asample mean becomes approximately normal when the sample size is large

Chi-square (χ2) goodness-of-fit test—compares a set of observed categoricalvalues to a set of expected values under a set of hypothesized proportions for

the categories;

Cluster sample—The population is first divided into sections or “clusters.”Then we randomly select an entire cluster, or clusters, and include all of themembers of the cluster(s) in the sample.

Coefficient of determination (r 2) —measures the proportion of variation in theresponse variable explained by regression on the explanatory variable

Complement of an event—set of all outcomes in the sample space that are notin the event

Completely randomized design—when all subjects (or experimental units) arerandomly assigned to treatments in an experiment

Conditional probability—the probability of one event succeeding given thatsome other event has already occurred

Confidence interval—an interval that, with a given level of confidence, islikely to contain a population value; (estimate) ± (margin of error)

Confidence level—the probability that the procedure used to construct aninterval will generate an interval that does contain the population valueConfounding variable—has an effect on the outcomes of the study but whoseeffects cannot be separated from those of the treatment variable

Contingency table—see two-way table

Continuous data—data that can be measured, or take on values in an interval;the set of possible values cannot be counted

Continuous random variable—a random variable whose values are continuousdata; takes all values in an interval

Control —see statistical control

Convenience sample—sample chosen without any random mechanism; choosesindividuals based on ease of selection

Correlation coefficient (r ) —measures the strength of the linear relationship

between two quantitative variables;

Correlation is not causation—just because two variables correlate stronglydoes not mean that one caused the other

Critical value—values in a distribution that identify certain specified areas ofthe distribution

Degrees of freedom—number of independent data-points in a distributionDensity function—a function that is everywhere non-negative and has a totalarea equal to 1 underneath it and above the horizontal axis

Descriptive statistics—process of examining data analytically and graphicallyDimension —size of a two-way table; r × c

Discrete data—data that can be counted (possibly infinite) or placed in orderDiscrete random variable—random variable whose values are discrete dataDotplot —graph in which data values are identified as dots placed above theircorresponding values on a number line

Double blind—experimental design in which neither the subjects nor the studyadministrators know what treatment a subject has received

Empirical Rule (68-95-99.7 Rule)—states that, in a normal distribution, about68% of the terms are within one standard deviation of the mean, about 95%are within two standard deviations, and about 99.7% are within threestandard deviations

Estimate —sample value used to approximate a value of a parameter

Event —in probability, a subset of a sample space; a set of one or more simpleoutcomes

Expected value—mean value of a discrete random variable

Experiment —study in which a researcher measures the responses to a treatmentvariable, or variables, imposed and controlled by the researcher

Experimental units—individuals on which experiments are conductedExplanatory variable—explains changes in response variable; treatmentvariable; independent variable

Extrapolation —predictions about the value of a variable based on the value ofanother variable outside the range of measured values

First quartile—25th percentile

Five-number summary—for a dataset, [minimum value, Q1, median, Q3,maximum value]

Geometric setting—independent observations, each of which succeeds or failswith the same probability p ; number of trials needed until first success isvariable of interest

Histogram —graph in which the frequencies of numerical data are displayedwith bars; analogous to a bar graph for categorical data

Homogeneity of proportions—chi-square hypothesis in which proportions of acategorical variable are tested for homogeneity across two or more

populations

Independent events—knowing one event occurs does not change theprobability that the other occurs; P(A) = P(A|B )

Independent variable—see explanatory variable

Inferential statistics—use of sample data to make inferences about populationsInfluential observation—observation, usually in the x direction, whoseremoval would have a marked impact on the slope of the regression lineInterpolation —predictions about the value of a variable based on the value ofanother variable within the range of measured values

Interquartile range—value of the third quartile minus the value of the firstquartile; contains middle 50% of the data

Least-squares regression line—of all possible lines, the line that minimizesthe sum of squared errors (residuals) from the line

Line of best fit—see least-squares regression line

Lurking variable—one that has an effect on the outcomes of the study butwhose influence was not part of the investigation

Margin of error—measure of uncertainty in the estimate of a parameter;(critical value) · (standard error)

Marginal totals—row and column totals in a two-way table

Matched pairs—experimental units paired by a researcher based on somecommon characteristic or characteristic

Matched pairs design—experimental design that utilizes each pair as a block;one unit receives one treatment, and the other unit receives the other treatmentMean —sum of all the values in a dataset divided by the number of valuesMedian —halfway through an ordered dataset, below and above which lies anequal number of data values; 50th percentile

Mode —most common value in a distribution

Mound-shaped (bell-shaped)—distribution in which data values tend to clusterabout the center of the distribution; characteristic of a normal distributionMutually exclusive events—events that cannot occur simultaneously; if oneoccurs, the other doesn’t

Negatively associated—larger values of one variable are associated withsmaller values of the other; see associated

Nonresponse bias—occurs when subjects selected for a sample do not respondNormal curve—familiar bell-shaped density curve; symmetric about its mean;defined in terms of its mean and standard deviation;

Normal distribution—distribution of a random variable X so that P(a

Null hypothesis—hypothesis being tested—usually a statement that there is noeffect or difference between treatments; what a researcher wants to disproveto support his/her alternative

Numerical data—see quantitative data

Observational study—when variables of interest are observed and measuredbut no treatment is imposed in an attempt to influence the response

Observed values—counts of outcomes in an experiment or study; comparedwith expected values in a chi-square analysis

One-sided alternative—alternative hypothesis that varies from the null in onlyone direction

One-sided test—used when an alternative hypothesis states that the true valueis less than or greater than the hypothesized value

Outcome —simple events in a probability experiment

Outlier —a data value that is far removed from the general pattern of the dataP (A and B)—probability that both A and B occur; P(A and B ) = P (A) · P (A|B)P (A or B)—probability that either A or B occurs; P(A or B ) = P (A) + P (B) –P(A and B )

P value—probability of getting a sample value at least as extreme as thatobtained by chance alone assuming the null hypothesis is true

Parameter —measure that describes a population

Percentile rank—proportion of terms in the distributions less than the valuebeing considered

Placebo —an inactive procedure or treatment

Placebo effect—effect, often positive, attributable to the patient’s expectationthat the treatment will have an effect

Point estimate—value based on sample data that represents a likely value for apopulation parameter

Positively associated—larger values of one variable are associated with largervalues of the other; see associated

Power of the test—probability of rejecting a null hypothesis against a specificalternative

Probability distribution—identification of the outcomes of a random variable

together with the probabilities associated with those outcomes

Probability histogram—histogram for a probability distribution; horizontal axisshows the outcomes, vertical axis shows the probabilities of those outcomesProbability of an event—relative frequency of the number of ways an eventcan succeed to the total number of ways it can succeed or fail

Probability sample—sampling technique that uses a random mechanism toselect the members of the sample

Proportion —ratio of the count of a particular outcome to the total number ofoutcomes

Qualitative data—data whose values range over categories rather than valuesQuantitative data—data whose values are numerical

Quartiles —25th, 50th, and 75th percentiles of a dataset

Random phenomenon—unclear how any one trial will turn out, but there is aregular distribution of outcomes in a large number of trials

Random sample—sample in which each member of the sample is chosen bychance and each member of the population has an equal chance to be in thesample

Random variable—numerical outcome of a random phenomenon (randomexperiment)

Randomization —random assignment of experimental units to treatmentsRange —difference between the maximum and minimum values of a datasetReplication —repetition of each treatment enough times to help control forchance variation

Representative sample—sample that possesses the essential characteristics ofthe population from which it was taken

Residual —in a regression, the actual value minus the predicted value

Resistant statistic—one whose numerical value is not influenced by extremevalues in the dataset

Response bias—bias that stems from respondents’ inaccurate or untruthfulresponse

Response variable—measures the outcome of a study

Robust —when a procedure may still be useful even if the conditions needed tojustify it are not completely satisfied

Robust procedure—procedure that still works reasonably well even if the

assumptions needed for it are violated; the t -procedures are robust against theassumption of normality as long as there are no outliers or severe skewness.Sample space—set of all possible mutually exclusive outcomes of a probabilityexperiment

Sample survey—using a sample from a population to obtain responses toquestions from individuals

Sampling distribution of a statistic—distribution of all possible values of astatistic for samples of a given size

Sampling frame—list of experimental units from which the sample is selectedScatterplot —graphical representation of a set of ordered pairs; horizontal axisis first element in the pair, vertical axis is the second

Shape —geometric description of a dataset: mound-shaped; symmetric, uniform;skewed; etc.

Significance level (α) —probability value that, when compared to the P -value, determines whether a finding is statistically significant

Simple random sample (SRS)—sample in which all possible samples of thesame size are equally likely to be the sample chosen

Simulation —random imitation of a probabilistic situation

Skewed —distribution that is asymmetrical

Skewed left (right)—asymmetrical with more of a tail on the left (right) than onthe right (left)

Spread —variability of a distribution

Standard deviation

—square root of the variance;

Standard error—estimate of population standard deviation based on sampledata

Standard normal distribution—normal distribution with a mean of 0 and astandard deviation of 1

Standard normal probability—normal probability calculated from the standardnormal distribution

Statistic —measure that describes a sample (e.g., sample mean)

Statistical control—holding constant variables in an experiment that mightaffect the response but are not one of the treatment variables

Statistically significant—a finding that is unlikely to have occurred by chanceStatistics —science of data

Stemplot (stem-and-leaf plot)—graph in which ordinal data are broken into“stems” and “leaves”; visually similar to a histogram except that all the dataare retained

Stratified random sample—groups of interest (strata) chosen in such a way thatthey appear in approximately the same proportions in the sample as in thepopulation

Subjects —human experimental units

Survey —obtaining responses to questions from individuals

Symmetric —data values distributed equally above and below the center of thedistribution

Systematic bias—the mean of the sampling distribution of a statistic does notequal the mean of the population; see unbiased estimate

Systematic sample—probability sample in which one of the first n subjects ischosen at random for the sample and then each n th person after that is chosenfor the sample

t -distribution —the distribution with n – 1 degrees of freedom for thet statistic

—

Test statistic

—

Third quartile—75th percentile

Treatment variable—see explanatory variable

Tree diagram—graphical technique for showing all possible outcomes in aprobability experiment

Two-sided alternative—alternative hypothesis that can vary from the null ineither direction; values much greater than or much less than the null provideevidence against the null

Two-sided test—a hypothesis test with a two-sided alternative

Two-way table—table that lists the outcomes of two categorical variables; thevalues of one category are given as the row variable, and the values of theother category are given as the column variable; also called a contingencytable

Type-I error—the error made when a true hypothesis is rejected

Type-II error—the error made when a false hypothesis is not rejected

Unbiased estimate—mean of the sampling distribution of the estimate equalsthe parameter being estimated

Undercoverage —some groups in a population are not included in a samplefrom that population

Uniform —distribution in which all data values have the same frequency ofoccurrence

Univariate data—having to do with a single variable

Variance —average of the squared deviations from their mean of a set of

observations;

Voluntary response bias—bias inherent when people choose to respond to asurvey or poll; bias is typically toward opinions of those who feel moststrongly

Voluntary response sample—sample in which participants are free to respondor not to a survey or a poll

Wording bias—creation of response bias attributable to the phrasing of aquestion

z -score

—number of standard deviations a term is above or below the mean;