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Configural Frequency Analysis
Configural frequency analysis (CFA) is a method of exploratory data analysis, introduced by Gustav A. Lienert in 1969. The goal of a configural frequency analysis is to detect patterns in the data that occur significantly more (such patterns are called ''Types'') or significantly less often (such patterns are called ''Antitypes'') than expected by chance. Thus, the idea of a CFA is to provide the identified types and antitypes some insight into the structure of the data. Types are interpreted as concepts which are constituted by a pattern of variable values. Antitypes are interpreted as patterns of variable values that do not in general occur together. Basic idea of the CFA algorithm We explain the basic idea of CFA by a simple example. Assume that we have a data set that describes for each of ''n'' patients if they show certain symptoms ''s''1, ..., ''s''''m''. We assume for simplicity that a symptom is shown or not, i.e. we have a dichotomous data set. Each record in the data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exploratory Data Analysis
In statistics, exploratory data analysis (EDA) is an approach of data analysis, analyzing data sets to summarize their main characteristics, often using statistical graphics and other data visualization methods. A statistical model can be used or not, but primarily EDA is for seeing what the data can tell beyond the formal modeling and thereby contrasts with traditional hypothesis testing, in which a model is supposed to be selected before the data is seen. Exploratory data analysis has been promoted by John Tukey since 1970 to encourage statisticians to explore the data, and possibly formulate hypotheses that could lead to new data collection and experiments. EDA is different from Data analysis#Initial data analysis, initial data analysis (IDA), which focuses more narrowly on checking assumptions required for model fitting and hypothesis testing, and handling missing values and making transformations of variables as needed. EDA encompasses IDA. Overview Tukey defined data analysi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gustav A
Gustav, Gustaf or Gustave may refer to: *Gustav (name), a male given name of Old Swedish origin Art, entertainment, and media * ''Primeval'' (film), a 2007 American horror film * ''Gustav'' (film series), a Hungarian series of animated short cartoons * Gustav (''Zoids''), a transportation mecha in the ''Zoids'' fictional universe *Gustav, a character in '' Sesamstraße'' *Monsieur Gustav H., a leading character in '' The Grand Budapest Hotel'' * Gustaf, an American art punk band from Brooklyn, New York. Weapons * Carl Gustav recoilless rifle, dubbed "the Gustav" by US soldiers * Schwerer Gustav, 800-mm German siege cannon used during World War II Other uses * Gustav (pigeon), a pigeon of the RAF pigeon service in WWII *Gustave (crocodile), a large male Nile crocodile in Burundi *Gustave, South Dakota *Hurricane Gustav (other), a name used for several tropical cyclones and storms *Gustav, a streetwear clothing brand See also *Gustav of Sweden (other) *Gustav A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Significance
In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by \alpha, is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the p-value, ''p''-value of a result, ''p'', is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is said to be ''statistically significant'', by the standards of the study, when p \le \alpha. The significance level for a study is chosen before data collection, and is typically set to 5% or much lower—depending on the field of study. In any experiment or Observational study, observation that involves drawing a Sampling (statistics), sample from a Statistical population, population, there is always the possibility that an observed effect would have occurred due to sampling error al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Set
A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more table (database), database tables, where every column (database), column of a table represents a particular Variable (computer science), variable, and each row (database), row corresponds to a given Record (computer science), record of the data set in question. The data set lists values for each of the variables, such as for example height and weight of an object, for each member of the data set. Data sets can also consist of a collection of documents or files. In the open data discipline, a dataset is a unit used to measure the amount of information released in a public open data repository. The European data.europa.eu portal aggregates more than a million data sets. Properties Several characteristics define a data set's structure and properties. These include the number and types of the attributes or variables, and various statistical measures applicable to the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dichotomy
A dichotomy () is a partition of a set, partition of a whole (or a set) into two parts (subsets). In other words, this couple of parts must be * jointly exhaustive: everything must belong to one part or the other, and * mutually exclusive: nothing can belong simultaneously to both parts. If there is a concept A, and it is split into parts B and not-B, then the parts form a dichotomy: they are mutually exclusive, since no part of B is contained in not-B and vice versa, and they are jointly exhaustive, since they cover all of A, and together again give A. Such a partition is also frequently called a bipartition. The two parts thus formed are Complement (set theory), complements. In logic, the partitions are dual (category theory), opposites if there exists a proposition such that it holds over one and not the other. Treating continuous variables or multicategorical variables as binary variables is called discretization, dichotomization. The discretization error inherent in dichoto ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistically Independent
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes. Two event (probability theory), events are independent, statistically independent, or stochastically independent if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds. Similarly, two random variables are independent if the realization of one does not affect the probability distribution of the other. When dealing with collections of more than two events, two notions of independence need to be distinguished. The events are called Pairwise independence, pairwise independent if any two events in the collection are independent of each other, while mutual independence (or collective independence) of events means, informally speaking, that each event is independent of any combination of other events in the collection. A similar notion exists for collections of random variables. M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pearson's Chi-squared Test
Pearson's chi-squared test or Pearson's \chi^2 test is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates, likelihood ratio, portmanteau test in time series, etc.) – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900. In contexts where it is important to improve a distinction between the test statistic and its distribution, names similar to ''Pearson χ-squared'' test or statistic are used. It is a p-value test. The setup is as follows: * Before the experiment, the experimenter fixes a certain number N of samples to take. * The observed data is (O_1, O_2, ..., O_n), the count number of samples from a finite set of given categories. They satisfy \sum_i O_i = N. * The null hypothesis is that the count numbers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Test
Binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories using sample data. Usage A binomial test is a statistical hypothesis test used to determine whether the proportion of successes in a sample differs from an expected proportion in a binomial distribution. It is useful for situations when there are two possible outcomes (e.g., success/failure, yes/no, heads/tails), i.e., where repeated experiments produce binary data. If one assumes an underlying probability \pi_0 between 0 and 1, the null hypothesis is : H_0\colon\pi=\pi_0 For a sample of size n, we would expect n\pi_0 successes. The formula of the binomial distribution gives the probability of those n samples instead producing k successes: : \Pr(X=k)=\binom\pi_0^k(1-\pi_0)^ Suppose that we want to test the alternative hypothesis : H_\colon\pi\pi_0 using the summation of the range from k to n instead. Calculating a p-val ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type I And Type II Errors
Type I error, or a false positive, is the erroneous rejection of a true null hypothesis in statistical hypothesis testing. A type II error, or a false negative, is the erroneous failure in bringing about appropriate rejection of a false null hypothesis. Type I errors can be thought of as errors of commission, in which the status quo is erroneously rejected in favour of new, misleading information. Type II errors can be thought of as errors of omission, in which a misleading status quo is allowed to remain due to failures in identifying it as such. For example, if the assumption that people are ''innocent until proven guilty'' were taken as a null hypothesis, then proving an innocent person as guilty would constitute a Type I error, while failing to prove a guilty person as guilty would constitute a Type II error. If the null hypothesis were inverted, such that people were by default presumed to be ''guilty until proven innocent'', then proving a guilty person's innocence would ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Null Hypothesis
The null hypothesis (often denoted ''H''0) is the claim in scientific research that the effect being studied does not exist. The null hypothesis can also be described as the hypothesis in which no relationship exists between two sets of data or variables being analyzed. If the null hypothesis is true, any experimentally observed effect is due to chance alone, hence the term "null". In contrast with the null hypothesis, an alternative hypothesis (often denoted ''H''A or ''H''1) is developed, which claims that a relationship does exist between two variables. Basic definitions The null hypothesis and the ''alternative hypothesis'' are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise. The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bonferroni Correction
In statistics, the Bonferroni correction is a method to counteract the multiple comparisons problem. Background The method is named for its use of the Bonferroni inequalities. Application of the method to confidence intervals was described by Olive Jean Dunn. Statistical hypothesis testing is based on rejecting the null hypothesis when the likelihood of the observed data would be low if the null hypothesis were true. If multiple hypotheses are tested, the probability of observing a rare event increases, and therefore, the likelihood of incorrectly rejecting a null hypothesis (i.e., making a Type I error) increases. The Bonferroni correction compensates for that increase by testing each individual hypothesis at a significance level of \alpha/m, where \alpha is the desired overall alpha level and m is the number of hypotheses. For example, if a trial is testing m = 20 hypotheses with a desired overall \alpha = 0.05, then the Bonferroni correction would test each individual hypot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Holm–Bonferroni Method
In statistics, the Holm–Bonferroni method, also called the Holm method or Bonferroni–Holm method, is used to counteract the problem of multiple comparisons. It is intended to control the family-wise error rate (FWER) and offers a simple test uniformly more powerful than the Bonferroni correction. It is named after Sture Holm, who codified the method, and Carlo Emilio Bonferroni. Motivation When considering several hypotheses, the problem of multiplicity arises: the more hypotheses are tested, the higher the probability of obtaining Type I errors (false positives). The Holm–Bonferroni method is one of many approaches for controlling the FWER, i.e., the probability that one or more Type I errors will occur, by adjusting the rejection criterion for each of the individual hypotheses. Formulation The method is as follows: * Suppose you have m p-values, sorted into order lowest-to-highest P_1,\ldots,P_m, and their corresponding hypotheses H_1,\ldots,H_m(null hypotheses). Y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
