Skip to main content
Statistics LibreTexts

Glossary

  1. Last updated
  2. Save as PDF
  • Page ID
    20777

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Example and Directions
    Words (or words that have the same definition) The definition is case sensitive (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages] (Optional) Caption for Image (Optional) External or Internal Link (Optional) Source for Definition
    (Eg. "Genetic, Hereditary, DNA ...") (Eg. "Relating to genes or heredity") The infamous double helix https://bio.libretexts.org/ CC-BY-SA; Delmar Larsen
    Glossary Entries

    Word(s)

    Definition

    		 Image Caption Link Source
    A Glossary from "Introductory Statistics" Schafer and Zhang
    alternative hypothesis A statement that is accepted as true only if there is convincing evidence in favor of it.
    ANOVA F-test a test based on an F

    statistic

    to check whether several population means are equal.
    binomial random variable A

    random variable

    that counts successes in a fixed number of

    independent

    , identical trials of a success/failure experiment.
    Box Plot For a data set, a diagram constructed using the

    five-number summary

    , which graphically summarizes the distribution of the data.
    Chi-Square Goodness of Fit Test A test based on a chi-square

    statistic

    to check whether a

    sample

    is taken from a population with a hypothesized

    probability distribution

    .
    Chi-Square Random Variable A

    random variable

    that follows a chi-square distribution.
    Chi-Square test A test based on a chi-square

    statistic

    to check whether two

    factors

    are

    independent

    .
    Coefficient of Determination A number that measures the proportion of the variability in y that is explained by x.
    Complement of an Event The

    event

    does not occur
    Conditional Probability The probability of the

    event

    A taking into account the fact that

    event

    B is known to have occurred.
    Confidence Interval An interval with endpoints x-±E, computed from the

    sample data

    in such a way that a specified proportion of all intervals constructed by this process will contain the parameter of interest.
    Continuous A

    random variable

    whose possible values contain an interval of decimal numbers.
    Critical Value The number or one of a pair of numbers that determines the

    rejection region

    .
    Data List An explicit listing of all the individual measurements made on a

    sample
    Degrees of Freedom A number that specifies a particular t-distribution and that is computed based on the

    sample

    size.
    Density Function The function f(x) such that probabilities of a

    continuous

    random variable

    X are areas of regions under the graph of y=f(x).
    Descriptive Statistics The organization, display, and description of data.
    Error Using y−y^, the actual y-value of a data point minus the y-value that is computed from the equation of the line fitting the data.
    Event Any set of outcomes.
    Expected Value The mean of a distribution.
    Extrapolation The process of using the

    least squares regression equation

    to estimate the value of y at an x value not in the proper

    range

    .
    F-Distribution A particular

    probability distribution

    specified by two

    degrees of freedom

    , df1 and df2.
    Factors A variable with several qualitative levels.
    F Random Variable A

    random variable

    following an F-distribution.
    Five Number Summary Of a data set, the list {xmin, Q1, Q2, Q3, xmax}.
    Frequency Of a class of measurements, the number of measurements in the data set that are in the class.
    Hypothesis A statement about a population parameter.
    Hypothesis Testing A statistical procedure in which a choice is made between a

    null hypothesis

    and a specific

    alternative hypothesis

    based on information in a

    sample

    .
    Independent Events Events whose probability of occurring together is the product of their individual probabilities.
    Inferential Statistics The process of drawing conclusions about a population based on a

    sample.

    .
    Interquartile Range (IQR) Of a data set, the difference between the first and third

    quartiles.

    .
    Intersection of Events Both events occur.
    Least Squares Regression Equation The equation y^=β^1x+β^0 of the

    least squares regression line

    .
    Least Squares Regression Line The equation y^=β^1x+β^0 of the

    least squares regression line

    .
    Level of Confidence The proportion of confidence intervals which, if under repeated random sampling were always constructed according to the formula of the text, would contain the parameter of interest.
    Level of Significance The probability α that defines an

    event

    as “rare;” the probability that the test procedure will lead to a Type I

    error

    .
    Linear Correlation Coefficient A number computed directly from the data that measures the strength of the linear relationship between the two variables x and y.
    Mutually Exclusive Events that cannot both occur at once.
    Normal Distribution Assignment of probabilities to a

    continuous

    random variable

    using a bell curve for the

    density function

    .
    Normal Random Variable A

    continuous

    random variable

    whose probabilities are determined by a bell curve.
    ANOVA Analysis of variance.
    Null Hypothesis The statement that is assumed to be true unless there is convincing evidence to the contrary.
    Observed Significance or p-value The probability, if H0 is true, of obtaining a result as contrary to H0 and in favor of Ha as the result observed in the

    sample data

    .
    Percentile Rank Of a measurement x, the percentage of the data that are less than or equal to x.
    Population Mean The familiar average of a population data set.
    Population Standard Deviation The variability of population data as measured by the number σ2=Σ(x−μ)^2/N.
    Probability Distribution A list of each possible value and its probability.
    Probability of an Event A number that measures the likelihood of the

    event

    .
    Probability of an Outcome A number that measures the likelihood of the outcome.
    Qualitative Data Measurements for which there is no natural numerical scale.
    Quantitative Data Numerical measurements that arise from a natural numerical scale.
    Quartiles Of a data set, the three numbers Q1, Q2, Q3 that divide the data approximately into fourths.
    Random Variable A numerical value generated by a random experiment.
    Range The variability of a data set as measured by the number R=xmax−xmin.
    Rejection Region An interval or union of intervals such that the

    null hypothesis

    is rejected if and only if the

    statistic

    of interest lies in this region.
    Relative Frequency Histogram A graphical device showing how data are distributed across the

    range

    of their values by collecting them into classes and indicating the proportion of measurements in each class.
    Sample The objects examined.
    Sample Data The measurements from a

    sample

    .
    Sample Mean The familiar average of a

    sample data

    set.
    Sample Median The middle value when data are listed in numerical order.
    Sample Mode The most frequent value in a data set.
    Sample Variance (the square root of which is the sample standard deviation) The variability of

    sample data

    as measured by the number Σ(x−x-)^2/(n−1).
    Sampling Distribution The

    probability distribution

    of a

    sample

    statistic

    when the

    statistic

    is viewed as a

    random variable

    .
    Standard Deviation of the Population The number Σ(x−μ)^2P(x) (also computed using [Σx^2P(x) ]−μ2), measuring its variability under repeated trials.
    Standard Normal Random Variable The

    normal random variable

    with mean 0 and

    standard deviation

    1.
    Standardized Test Statistic The standardized

    statistic

    used in performing the test.
    Statistic A number computed from the

    sample data

    .
    Statistics (as a discipline) Collection, display, analysis, and inference from data.
    Tail The region under a density curve whose area is either P(X<x*) or P(X>x*) for some number x*.
    Type II Error Failure to reject a false

    null hypothesis

    .
    Union of Events One or the other

    event

    occurs.
    Z-score Of a measurement x, the distance of x from the mean in units of

    standard deviation

    .
    1. Back to top
    • Was this article helpful?

    Recommended articles

    1. Article type
      Section or Page
      Show TOC
      no
    2. Tags
      1. columns:three