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Glossary of Statistical Terms

random variable1) 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 random var...
compound propositionA logical proposition formed from other propositions using logical operations such as !, |, XOR, &, → and ↔.
appeal to ignoranceA 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 is f...
affirming the consequentA 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 consequent (B...
denying the antecedentA 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 antecedent ...
sound argumentA 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.
logical argumentA 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 logic) ...
secular trendA linear association (trend) with time.
game theoryA 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" during ...
fair betA 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 ante...
quota sampleA 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 that th...
discrete variableA 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 numb...
continuous variableA 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 meas...
qualitative variableA qualitative variable is one whose values are adjectives, such as colors, genders, nationalities, etc. C.f. quantitative variable and categorical variable.
probability histogramA 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 inte...
nearly normal distributionA 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 that th...
class boundaryA point that is the left endpoint of one class interval, and the right endpoint of another class interval.
venn diagramA 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 cor...
multimodal distributionA distribution with more than one mode. The histogram of a multimodal distribution has more than one "bump."
skewed distributionA distribution that is not symmetrical.
cross-sectional studyA 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 effec...
normal curveThe 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 cir...
standard normal curve;
standard normal curvenormal curve
normal curve;
element of a setmember
disjoint events or disjoint sets mutually exclusive;
mutually exclusivedisjoint events or disjoint sets
disjoint events or disjoint sets;
combinationsThe 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 of t...
binomial coefficient;
binomial coefficientcombinations
class intervalIn 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 interval....
change of units or variablesalso transformation
frequency theory of probabilityProbability, Theories of
probability, theories of;
lower quartile (lq)quartiles
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.
placebo1) A "dummy" treatment that has no pharmacological effect; e.g., a sugar pill.
2) placebo

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!
affine transformationtransformation
sample survey1) 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, sample inqui...

random experimentAn 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" is...
random event;
random eventrandom experiment
random experiment;
upper quartile (uq)quartiles
quartilesThere 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, and at...
lower quartile (lq); upper quartile (uq);