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# Chi-squared test

A chi-squared test, also written as test, is any statistical hypothesis test where the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true. [1]

## Autocorrelation

Autocorrelation, also known as serial correlation, is the correlation of a signal with a delayed copy of itself as a function of delay.

## Binomial distribution

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own boolean-valued outcome: a random variable containing a single bit of information: success/yes/true/one (with probability p) or failure/no/false/zero (with probability q.

## Bioinformatics

Bioinformatics is an interdisciplinary field that develops methods and software tools for understanding biological data.

## Central limit theorem

In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.

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## Ciphertext

In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher.

## Cochran–Mantel–Haenszel statistics

In statistics, the Cochran–Mantel–Haenszel test (CMH) is a test used in the analysis of stratified or matched categorical data.

## Contingency table

In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables.

## Cryptanalysis

Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to loosen" or "to untie") is the study of analyzing information systems in order to study the hidden aspects of the systems.

## Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

## Designation of workers by collar color

Groups of working individuals are typically classified based on the colors of their collars worn at work; these can commonly reflect one's occupation or sometimes gender.

## Fisher's exact test

Fisher's exact test is a statistical significance test used in the analysis of contingency tables.

## Frank Yates

Frank Yates FRS (12 May 1902 &ndash; 17 June 1994) was one of the pioneers of 20th century statistics.

## G-test

In statistics, G-tests are likelihood-ratio or maximum likelihood statistical significance tests that are increasingly being used in situations where chi-squared tests were previously recommended.

## George Biddell Airy

Sir George Biddell Airy (27 July 18012 January 1892) was an English mathematician and astronomer, Astronomer Royal from 1835 to 1881.

## Journal of the Royal Statistical Society

The Journal of the Royal Statistical Society is a peer-reviewed scientific journal of statistics.

## Karl Pearson

Karl Pearson HFRSE LLD (originally named Carl; 27 March 1857 – 27 April 1936) was an English mathematician and biostatistician. He has been credited with establishing the discipline of mathematical statistics. He founded the world's first university statistics department at University College London in 1911, and contributed significantly to the field of biometrics, meteorology, theories of social Darwinism and eugenics. Pearson was also a protégé and biographer of Sir Francis Galton.

## Likelihood-ratio test

In statistics, a likelihood ratio test (LR test) is a statistical test used for comparing the goodness of fit of two statistical models — a null model against an alternative model.

## Mansfield Merriman

Mansfield Merriman (March 27, 1848 – June 7, 1925) was an American civil engineer, born at Southington, Conn. He graduated at Yale's Sheffield Scientific School in 1871, was assistant in the United States Corps of Engineers in 1872-73, and instructor in civil engineering at Sheffield from 1875 to 1878.

## McNemar's test

In statistics, McNemar's test is a statistical test used on paired nominal data.

## Minimum chi-square estimation

In statistics, minimum chi-square estimation is a method of estimation of unobserved quantities based on observed data.

## Nonparametric statistics

Nonparametric statistics is the branch of statistics that is not based solely on parameterized families of probability distributions (common examples of parameters are the mean and variance).

## Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

## Null hypothesis

In inferential statistics, the term "null hypothesis" is a general statement or default position that there is no relationship between two measured phenomena, or no association among groups.

## P-value

In statistical hypothesis testing, the p-value or probability value or asymptotic significance is the probability for a given statistical model that, when the null hypothesis is true, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or of greater magnitude than the actual observed results.

## Pearson distribution

The Pearson distribution is a family of continuous probability distributions.

## Pearson's chi-squared test

Pearson's chi-squared test (χ) 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.

## Plaintext

In cryptography, plaintext or cleartext is unencrypted information, as opposed to information encrypted for storage or transmission.

## Portmanteau test

A portmanteau test is a type of statistical hypothesis test in which the null hypothesis is well specified, but the alternative hypothesis is more loosely specified.

## Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

## Sampling distribution

In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.

## Skewness

In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.

## Statistical hypothesis testing

A statistical hypothesis, sometimes called confirmatory data analysis, is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.

## Statistical model

A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of some sample data and similar data from a larger population.

## Statistical significance

In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis.

## Test statistic

A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.

## Time series

A time series is a series of data points indexed (or listed or graphed) in time order.

In statistics, Tukey's test of additivity, named for John Tukey, is an approach used in two-way ANOVA (regression analysis involving two qualitative factors) to assess whether the factor variables are additively related to the expected value of the response variable.

## Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

## Wald test

The Wald test is a parametric statistical test named after the statistician Abraham Wald.

## References

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