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Glossary of Statistical Terms

affine transformation
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...
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...
alternative hypothesis
    In hypothesis testing, a null hypothesis (typically that there is no effect) is compared with an alternative hypothesis (typically that there is an effect, or that there is an effect of a particul...
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 ...
    An applet is a small program that is automatically downloaded from a website to your computer when you visit a particular web page; it allows a page to be interactive—to respond to your input. the...
axioms of probability
    There are three axioms of probability: (1) chances are always at least zero. (2) the chance that something happens is 100%. (3) if two events cannot both occur at the same time (if they are disjoi...
base rate fallacy
    The base rate fallacy consists of failing to take into account prior probabilities (base rates) when computing conditional probabilities from other conditional probabilities. it is related to the ...
bayes` rule
    Bayes` rule expresses the conditional probability of the event a given the event b in terms of the conditional probability of the event b given the event a and the unconditional probability of a:<...
bernoulli`s inequality
    The bernoulli inequality says that if x ≥ −1 then (1+x)n ≥ 1 + nx for every integer n ≥ 0. if n is even, the inequality holds for all x.
binomial coefficient
binomial theorem
    The binomial theorem says that (x+y)n = xn + nxn−1y + … + nckxn−kyk + … + yn.
bootstrap estimate of standard error
    The name for this idea comes from the idiom "to pull oneself up by one`s bootstraps," which connotes getting out of a hole without anything to stand on. the idea of the bootstrap is to assume, for...
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...
breakdown point
    The breakdown point of an estimator is the smallest fraction of observations one must corrupt to make the estimator take any value one wants.
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...
central limit theorem
    The central limit theorem states that the probability histograms of the sample mean and sample sum of n draws with replacement from a box of labeled tickets converge to a normal curve as the sampl...
certain event
    An event is certain if its probability is 100%. even if an event is certain, it might not occur. however, by the complement rule, the chance that it does not occur is 0%.
change of units or variables
    Also transformation
chebychev`s inequality
    For lists: for every number k>0, the fraction of elements in a list that are k sd`s or further from the arithmetic mean of the list is at most 1/k2.
chi-square curve
    The chi-square curve is a family of curves that depend on a parameter called degrees of freedom (d.f.). the chi-square curve is an approximation to the probability histogram of the chi-square stat...
chi-square statistic
    The chi-square statistic is used to measure the agreement between categorical data and a multinomial model that predicts the relative frequency of outcomes in each possible category. suppose there...
class boundary
    A point that is the left endpoint of one class interval, and the right endpoint of another class interval.
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;
cluster sample
  1. In a cluster sample, the sampling unit is a collection of population units, not single population units. for example, techniques for adjusting the u.s. census start with a sample of geographic... выборка;
    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;
complement rule
    The probability of the complement of an event is 100% minus the probability of the event: p(ac) = 100% − p(a).
compound proposition
    A logical proposition formed from other propositions using logical operations such as !, |, xor, &, → and ↔.
conditional probability
    Suppose we are interested in the probability that some event a occurs, and we learn that the event b occurred. how should we update the probability of a to reflect this new knowledge? this is what... вероятность условная;
  1. In a conditional p → q, the consequent is q.

  2. N второй член услов- ного предложения, следствие
continuity correction
    In using the normal approximation to the binomial probability histogram, one can get more accurate answers by finding the area under the normal curve corresponding to half-integers, transformed to...
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 ...
    If p and q are two logical propositions, then the contrapositive of the proposition (p → q) is the proposition ((! q) → (!p) ). the contrapositive is logically equivalent to the origin...
control for a variable
    To control for a variable is to try to separate its effect from the treatment effect, so it will not confound with the treatment. there are many methods that try to control for variables. some are...
control group
  1. The subjects in a controlled experiment who do not receive the treatment.

  2. A group of people who are not being treated but whose test data are used as a comparison in a study

    ... cg; контрольная группа;
controlled experiment
    An experiment that uses the method of comparison to evaluate the effect of a treatment by comparing treated subjects with a control group, who do not receive the treatment.
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;
convergence in probability
    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
correlation coefficient
    The correlation coefficient r is a measure of how nearly a scatterplot falls on a straight line. the correlation coefficient is always between −1 and +1. to compute the correlation coefficie... корреляции коэффициент;
countable set
    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, 0, 1...
coverage probability
    The coverage probability of a procedure for making confidence intervals is the chance that the procedure produces an interval that covers the truth.
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...
cumulative probability distribution function (cdf)
    The cumulative distribution function of a random variable is the chance that the random variable is less than or equal to x, as a function of x. in symbols, if f is the cdf of the random variable ...
de morgan`s laws
    De morgan`s laws are identities involving logical operations: the negation of a conjunction is logically equivalent to the disjunction of the negations, and the negation of a disjunction is logica...