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Glossary of Statistical Terms

spread, measure of
    Also inter-quartile range, range, and standard deviation
inter-quartile range, range, and standard deviation;
inter-quartile range, range, and standard deviation
    spread, measure of;
    change of units or variables
      Also transformation
    class interval
      In plotting a histogram, one starts by dividing the range of values into a set of non-overlapping intervals, called class intervals, in such a way that every datum is contained in some class inter... bin; класса интервал;
    binomial coefficient
    1. Combinations

    2. Биномиальный коэффициент
      The number of combinations of n things taken k at a time is the number of ways of picking a subset of k of the n things, without replacement, and without regard to the order in which the elements ... binomial coefficient;
    mutually exclusive
    1. Disjoint events or disjoint sets

    2. Взаимоисключающий
    disjoint events or disjoint sets;
    disjoint events or disjoint sets
      mutually exclusive;
      element of a set
      standard normal curve
        Normal curve
      normal curve;
      normal curve
        The normal curve is the familiar "bell curve:," illustrated on this page. the mathematical expression for the normal curve is y = (2×pi)−½e−x2/2, where pi is the ratio of the... standard normal curve;
      frequency theory of probability
        Probability, theories of
      probability, theories of;
      probability, theories of
        A theory of probability is a way of assigning meaning to probability statements such as "the chance that a thumbtack lands point-up is 2/3." that is, a theory of probability connects the mathemati... frequency theory of probability;
      lower quartile (lq)
        There are three quartiles. the first or lower quartile (lq) of a list is a number (not necessarily a number in the list) such that at least 1/4 of the numbers in the list are no larger than it, an... lower quartile (lq); upper quartile (uq);
      upper quartile (uq)
      random event
      1. Random experiment

      2. Случайное событие
      random experiment;
      random experiment
        An experiment or trial whose outcome is not perfectly predictable, but for which the long-run relative frequency of outcomes of different types in repeated trials is predictable. note that "random... random event;
      sample survey
      1. A survey based on the responses of a sample of individuals, rather than the entire population.

      2. Выборочное обследование; выборочное наблюдение, см. sampling; sampling observation, sa... survey;
      affine transformation
      post hoc ergo propter hoc
        "after this, therefore because of this." a fallacy of logic known since classical times: inferring a causal relation from correlation. don`t do this at home!
      1. A "dummy" treatment that has no pharmacological effect; e.g., a sugar pill.

      2. Placebo

      3. A tablet which appears to be a drug, but has no medicinal substance in it comment: pla... placebo; плацебо;
      independent and identically distributed (iid)
        A collection of two or more random variables {x1, x2, … , } is independent and identically distributed if the variables have the same probability distribution, and are independent.
      controlled, randomized experiment
        A controlled experiment in which the assignment of subjects to the treatment group or control group is done at random, for example, by tossing a coin.
      cross-sectional study
        A cross-sectional study compares different individuals to each other at the same time—it looks at a cross-section of a population. the differences between those individuals can confound with the e...
      skewed distribution
        A distribution that is not symmetrical.
      multimodal distribution
        A distribution with more than one mode. the histogram of a multimodal distribution has more than one "bump."
      fair bet
        A fair bet is one for which the expected value of the payoff is zero, after accounting for the cost of the bet. for example, suppose i offer to pay you $2 if a fair coin lands heads, but you must ...
      game theory
      1. A field of study that bridges mathematics, statistics, economics, and psychology. it is used to study economic behavior, and to model conflict between nations, for example, "nuclear stalemate"... теория игр;
      monotone, monotonic function
        A function is monotone if it only increases or only decreases: f increases monotonically (is monotonic increasing) if x > y, implies thatf(x) ≥ f(y). a function f decreases monotonically (is...
      secular trend
        A linear association (trend) with time.
      секулярный тренд;
      logical argument
        A logical argument consists of one or more premises, propositions that are assumed to be true, and a conclusion, a proposition that is supposed to be guaranteed to be true (as a matter of pure log...
      sound argument
        A logical argument is sound if it is logically valid and its premises are in fact true. an argument can be logically valid and yet not sound—if its premises are false.
      denying the antecedent
        A logical fallacy that argues from the premise a → b and the premise !a that therefore, !b. the name comes from the fact that the operation denies (i.e., asserts the negation of) the anteced...
      affirming the consequent
        A logical fallacy that argues from the premise a → b and the premise b that therefore, a is true. the name comes from the fact that the argument affirms (i.e., asserts as true) the consequen...
      appeal to ignorance
        A logical fallacy: taking the absence of evidence to be evidence of absence. if something is not known to be false, assume that it is true; or if something is not known to be true, assume that it ...
      compound proposition
      1. A logical proposition formed from other propositions using logical operations such as !, |, xor, &, → and ↔.

      2. Сложное высказывание; составное высказывание
      proposition, logical proposition
        A logical proposition is a statement that can be either true or false. for example, "the sun is shining in berkeley right now" is a proposition. see also &, ↔, →, |, xor, converse, con...
      location, measure of
        A measure of location is a way of summarizing what a "typical" element of a list is—it is a one-number summary of a distribution. see also arithmetic mean, median, and mode.
      subject, experimental subject
        A member of the control group or the treatment group.
      venn diagram
        A pictorial way of showing the relations among sets or events. the universal set or outcome space is usually drawn as a rectangle; sets are regions within the rectangle. the overlap of the regions... диаграмма венна;
      class boundary
        A point that is the left endpoint of one class interval, and the right endpoint of another class interval.
      nearly normal distribution
        A population of numbers (a list of numbers) is said to have a nearly normal distribution if the histogram of its values in standard units nearly follows a normal curve. more precisely, suppose tha...
      premise, logical premise
        A premise is a proposition that is assumed to be true as part of a logical argument.
      probability histogram
        A probability histogram for a random variable is analogous to a histogram of data, but instead of plotting the area of the bins proportional to the relative frequency of observations in the class ...
      qualitative variable
        A qualitative variable is one whose values are adjectives, such as colors, genders, nationalities, etc. c.f. quantitative variable and categorical variable.
      continuous variable
        A quantitative variable is continuous if its set of possible values is uncountable. examples include temperature, exact height, exact age (including parts of a second). in practice, one can never ...
      discrete variable
        A quantitative variable whose set of possible values is countable. typical examples of discrete variables are variables whose possible values are a subset of the integers, such as social security ...
      quota sample
        A quota sample is a sample picked to match the population with respect to some summary characteristics. it is not a random sample. for example, in an opinion poll, one might select a sample so tha...
      chance variation, chance error
        A random variable can be decomposed into a sum of its expected value and chance variation around its expected value. the expected value of the chance variation is zero; the standard error of the c...
      random variable
      1. A random variable is an assignment of numbers to possible outcomes of a random experiment. for example, consider tossing three coins. the number of heads showing when the coins land is a rando... rv; случайная величина;
      residual plot
        A residual plot for a regression is a plot of the residuals from the regression against the explanatory variable.
      convenience sample
        A sample drawn because of its convenience; it is not a probability sample. for example, i might take a sample of opinions in berkeley (where i live) by just asking my 10 nearest neighbors. that wo... выборка;
      probability sample
        A sample drawn from a population using a random mechanism so that every element of the population has a known chance of ending up in the sample.
      вероятностная выборка; выборка;
      frame, sampling frame
        A sampling frame is a collection of units from which a sample will be drawn. ideally, the frame is identical to the population we want to learn about; more typically, the frame is only a subset of...
        A scatterplot is a way to visualize bivariate data. a scatterplot is a plot of pairs of measurements on a collection of "individuals" (which need not be people). for example, suppose we record the... график рассеяния;
      converge, convergence
        A sequence of numbers x1, x2, x3 … converges if there is a number x such that for any number e>0, there is a number k (which can depend on e) such that |xj − x| < e whenever j > k. if such a...
      convergence in probability
      1. A sequence of random variables x1, x2, x3 … converges in probability if there is a random variable x such that for any number e>0, the sequence of numbers

      2. Сходимость по вероятности<...
      countable set
      1. A set is countable if its elements can be put in one-to-one correspondence with a subset of the integers. for example, the sets {0, 1, 7, −3}, {red, green, blue}, {…,−2, −1, ...
      1. A set is uncountable if it is not countable.

      2. Несч

      3. A неисчисляемый (ант. countable) noun
      multivariate data
        A set of measurements of two or more variables per individual. see bivariate.
      simple random sample
        A simple random sample of n units from a population is a random sample drawn by a procedure that is equally likely to give every collection of n units from the population; that is, the probability... выборка;
      no causation without manipulation
        A slogan attributed to paul holland. if the conditions were not deliberately manipulated (for example, if the situation is an observational study rather than an experiment), it is unwise to conclu...
      deck of cards
        A standard deck of playing cards contains 52 cards, 13 each of four suits: spades, hearts, diamonds, and clubs. the thirteen cards of each suit are {ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, k...
        A subset of a given set is a collection of things that belong to the original set. every element of the subset must belong to the original set, but not every element of the original set need be in...
      systematic sample
        A systematic sample from a frame of units is one drawn by listing the units and selecting every kth element of the list. for example, if there are n units in the frame, and we want a sample of siz... выборка;
      systematic random sample
        A systematic sample starting at a random point in the listing of units in the of frame, instead of starting at the first unit. systematic random sampling is better than systematic sampling, but ty...
      selection bias
        A systematic tendency for a sampling procedure to include and/or exclude units of a certain type. for example, in a quota sample, unconscious prejudices or predilections on the part of the intervi... систематическая ошибка отбора;
      valid (logical) argument
        A valid logical argument is one in which the truth of the premises indeed guarantees the truth of the conclusion. for example, the following logical argument is valid: if the forecast calls for ra...
      denying the consequent
        A valid logical argument that concludes from the premise a → b and the premise !b that therefore, !a. the name comes from the fact that the operation denies (i.e., asserts the logical negati...
      affirming the antecedent
        A valid logical argument that concludes from the premise a → b and the premise a that therefore, b is true. the name comes from the fact that the argument affirms (i.e., asserts as true) the...
      standard units
        A variable (a set of data) is said to be in standard units if its mean is zero and its standard deviation is one. you transform a set of data into standard units by subtracting the mean from each ...
      quantitative variable
        A variable that takes numerical values for which arithmetic makes sense, for example, counts, temperatures, weights, amounts of money, etc. for some variables that take numerical values, arithmeti...
      ordinal variable
        A variable whose possible values have a natural order, such as {short, medium, long}, {cold, warm, hot}, or {0, 1, 2, 3, …}. in contrast, a variable whose possible values are {straight, curly} or ...
      categorical variable
        A variable whose value ranges over categories, such as {red, green, blue}, {male, female}, {arizona, california, montana, new york}, {short, tall}, {asian, african-american, caucasian, hispanic, n...
      payoff matrix
      1. A way of representing what each player in a game wins or loses, as a function of his and his opponent`s strategies.

      2. Платежная матрица
      box model
        An analogy between an experiment and drawing numbered tickets "at random" from a box with replacement. for example, suppose we are trying to evaluate a cold remedy by giving it or a placebo to a g...