# Test statistic

Common test statisticst''-test of test statistics
A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.wikipedia
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### Statistic

sample statisticempiricalmeasure
A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.
When a statistic (a function) is being used for a specific purpose, it may be referred to by a name indicating its purpose: in descriptive statistics, a descriptive statistic is used to describe the data; in estimation theory, an estimator is used to estimate a parameter of the distribution (population); in statistical hypothesis testing, a test statistic is used to test a hypothesis.

### Statistical hypothesis testing

hypothesis testingstatistical teststatistical tests
A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.
Sometime around 1940, in an apparent effort to provide researchers with a "non-controversial" way to have their cake and eat it too, the authors of statistical text books began anonymously combining these two strategies by using the p-value in place of the test statistic (or data) to test against the Neyman–Pearson "significance level".

### F-test

F''-testF testF-statistic
Two widely used test statistics are the t-statistic and the F-test.
An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis.

### Null hypothesis

nullnull hypotheseshypothesis
In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis.
This class of data-sets is usually specified via a test statistic which is designed to measure the extent of apparent departure from the null hypothesis.

### P-value

p''-valuepp''-values
An important property of a test statistic is that its sampling distribution under the null hypothesis must be calculable, either exactly or approximately, which allows p-values to be calculated.
Usually, X is a test statistic, rather than any of the actual observations.

### One- and two-tailed tests

one-tailed testtwo-tailed testone-sided
Using one of these sampling distributions, it is possible to compute either a one-tailed or two-tailed p-value for the null hypothesis that the coin is fair.
In statistical significance testing, a one-tailed test and a two-tailed test are alternative ways of computing the statistical significance of a parameter inferred from a data set, in terms of a test statistic.

### Student's t-test

t-testt''-testStudent's ''t''-test
A t-test is appropriate for comparing means under relaxed conditions (less is assumed).
The t-test is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis.

### Z-test

Z''-teststandardized testingStouffer Z
Z-tests are appropriate for comparing means under stringent conditions regarding normality and a known standard deviation.
A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution.

### Normal distribution

normally distributedGaussian distributionnormal
Many test statistics, scores, and estimators encountered in practice contain sums of certain random variables in them, and even more estimators can be represented as sums of random variables through the use of influence functions.

### Chi-squared test

chi-square testchi-squared statisticChi-squared
One test statistic that follows a chi-squared distribution exactly is the test that the variance of a normally distributed population has a given value based on a sample variance.

### Sample (statistics)

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

### Alternative hypothesis

alternative hypothesesalternativealternatives
In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis.

### Sampling distribution

finite sample distributiondistributionsampling
An important property of a test statistic is that its sampling distribution under the null hypothesis must be calculable, either exactly or approximately, which allows p-values to be calculated.

### Descriptive statistics

descriptivedescriptive statisticstatistics
A test statistic shares some of the same qualities of a descriptive statistic, and many statistics can be used as both test statistics and descriptive statistics.

### Range (statistics)

rangerangingsample range
Some informative descriptive statistics, such as the sample range, do not make good test statistics since it is difficult to determine their sampling distribution.

### T-statistic

Student's t-statistict''-statisticStudent's ''t''-statistic
Two widely used test statistics are the t-statistic and the F-test.

### Marginal distribution

marginal probabilitymarginalmarginals

### Binomial distribution

binomialbinomial modelBinomial probability

### Paired difference test

matching methodpaired samples
The common example scenario for when a paired difference test is appropriate is when a single set of test subjects has something applied to them and the test is intended to check for an effect.

### Chebyshev's inequality

Bienaymé–Chebyshev inequalityChebyshev inequalityAn inequality on location and scale parameters

### Welch's t-test

Welch's ''t''-testWelch's t testunequal variances

### Regression analysis

regressionmultiple regressionregression model

### Handedness

right-handedleft-handedsouthpaw

### Libertarianism

libertarianlibertarianslibertarian state