In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems. It can be visualized as a Turing machine with a black box, called an oracle, which is able to solve certain problems in a single operation. The problem can be of any complexity class. Even undecidable problems, such as the halting problem, can be used.
In mathematics, Pascal's triangle is an infinite triangular array of the binomial coefficients which play a crucial role in probability theory, combinatorics, and algebra. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in Persia, India, China, Germany, and Italy.
In the theory of probability and statistics, a Bernoulli trial is a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted. It is named after Jacob Bernoulli, a 17th-century Swiss mathematician, who analyzed them in his Ars Conjectandi (1713).
In population genetics, the Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences. These influences include genetic drift, mate choice, assortative mating, natural selection, sexual selection, mutation, gene flow, meiotic drive, genetic hitchhiking, population bottleneck, founder effect,inbreeding and outbreeding depression.
Questionnaire construction refers to the design of a questionnaire to gather statistically useful information about a given topic. When properly constructed and responsibly administered, questionnaires can provide valuable data about any given subject.
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability distribution, or by a random process which generates them. The theory of random graphs lies at the intersection between graph theory and probability theory. From a mathematical perspective, random graphs are used to answer questions about the properties of typical graphs. Its practical applications are found in all areas in which complex networks need to be modeled – many random graph models are thus known, mirroring the diverse types of complex networks encountered in different areas. In a mathematical context, random graph refers almost exclusively to the Erdős–Rényi random graph model. In other contexts, any graph model may be referred to as a random graph.
Multiple choice (MC), objective response or MCQ is a form of an objective assessment in which respondents are asked to select only correct answers from the choices offered as a list. The multiple choice format is most frequently used in educational testing, in market research, and in elections, when a person chooses between multiple candidates, parties, or policies.
A questionnaire is a research instrument that consists of a set of questions for the purpose of gathering information from respondents through survey or statistical study. A research questionnaire is typically a mix of close-ended questions and open-ended questions. Open-ended, long-term questions offer the respondent the ability to elaborate on their thoughts. The Research questionnaire was developed by the Statistical Society of London in 1838.
Response bias is a general term for a wide range of tendencies for participants to respond inaccurately or falsely to questions. These biases are prevalent in research involving participant self-report, such as structured interviews or surveys. Response biases can have a large impact on the validity of questionnaires or surveys.
The Boy or Girl paradox surrounds a set of questions in probability theory, which are also known as The Two Child Problem, Mr. Smith's Children and the Mrs. Smith Problem. The initial formulation of the question dates back to at least 1959, when Martin Gardner featured it in his October 1959 "Mathematical Games column" in Scientific American. He titled it The Two Children Problem, and phrased the paradox as follows:
In social science research, social-desirability bias is a type of response bias that is the tendency of survey respondents to answer questions in a manner that will be viewed favorably by others. It can take the form of over-reporting "good behavior" or under-reporting "bad", or undesirable behavior. The tendency poses a serious problem with conducting research with self-reports. This bias interferes with the interpretation of average tendencies as well as individual differences.
A self-report study is a type of survey, questionnaire, or poll in which respondents read the question and select a response by themselves without any outside interference. A self-report is any method which involves asking a participant about their feelings, attitudes, beliefs and so on. Examples of self-reports are questionnaires and interviews; self-reports are often used as a way of gaining participants' responses in observational studies and experiments.
The three prisoners problem appeared in Martin Gardner's "Mathematical Games" column in Scientific American in 1959. It is mathematically equivalent to the Monty Hall problem with car and goat replaced respectively with freedom and execution.
In mathematics, Paley graphs are undirected graphs constructed from the members of a suitable finite field by connecting pairs of elements that differ by a quadratic residue. The Paley graphs form an infinite family of conference graphs, which yield an infinite family of symmetric conference matrices. Paley graphs allow graph-theoretic tools to be applied to the number theory of quadratic residues, and have interesting properties that make them useful in graph theory more generally.
The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975. It became famous as a question from reader Craig F. Whitaker's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Discrimination testing is a technique employed in sensory analysis to determine whether there is a detectable difference among two or more products. The test uses a group of assessors (panellists) with a degree of training appropriate to the complexity of the test to discriminate from one product to another through one of a variety of experimental designs. Though useful, these tests typically do not quantify or describe any differences, requiring a more specifically trained panel under different study design to describe differences and assess significance of the difference.
The Hardest Logic Puzzle Ever is a logic puzzle so called by American philosopher and logician George Boolos and published in The Harvard Review of Philosophy in 1996. Boolos' article includes multiple ways of solving the problem. A translation in Italian was published earlier in the newspaper La Repubblica, under the title L'indovinello più difficile del mondo.
Cochran's test is a non-parametric statistical test to verify whether k treatments have identical effects in the analysis of two-way randomized block designs where the response variable is binary. It is named after William Gemmell Cochran. Cochran's Q test should not be confused with Cochran's C test, which is a variance outlier test. Put in simple technical terms, Cochran's Q test requires that there only be a binary response and that there be more than 2 groups of the same size. The test assesses whether the proportion of successes is the same between groups. Often it is used to assess if different observers of the same phenomenon have consistent results.
In theoretical computer science, the Aanderaa–Karp–Rosenberg conjecture is a group of related conjectures about the number of questions of the form "Is there an edge between vertex and vertex ?" that have to be answered to determine whether or not an undirected graph has a particular property such as planarity or bipartiteness. They are named after Stål Aanderaa, Richard M. Karp, and Arnold L. Rosenberg. According to the conjecture, for a wide class of properties, no algorithm can guarantee that it will be able to skip any questions: any algorithm for determining whether the graph has the property, no matter how clever, might need to examine every pair of vertices before it can give its answer. A property satisfying this conjecture is called evasive.
In psychology and social research, unmatched count, or item count, is a technique to improve, through anonymity, the number of true answers to possibly embarrassing or self-incriminating questions. It is very simple to use but yields only the number of people bearing the property of interest and leads to a larger sampling error than direct questions. It was introduced by Raghavarao and Federer in 1979.
