statistical hypothesis testing A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis. Hypothesis testing allows us to make probabilistic statements about population parameters. ...

, a two-sample test is a test performed on the data of two

random sample In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attem ...

s, each

independent Independent or Independents may refer to: Arts, entertainment, and media Artist groups * Independents (artist group), a group of modernist painters based in the New Hope, Pennsylvania, area of the United States during the early 1930s * Independe ...

ly obtained from a different given

population Population typically refers to the number of people in a single area, whether it be a city or town, region, country, continent, or the world. Governments typically quantify the size of the resident population within their jurisdiction using ...

. The purpose of the test is to determine whether the difference between these two populations is

statistically significant In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis (simply by chance alone). More precisely, a study's defined significance level, denoted by \alpha, is the p ...

. There are a large number of statistical tests that can be used in a two-sample test. Which one(s) are appropriate depend on a variety of factors, such as: * Which assumptions (if any) may be made ''a priori'' about the

distribution Distribution may refer to: Mathematics *Distribution (mathematics), generalized functions used to formulate solutions of partial differential equations *Probability distribution, the probability of a particular value or value range of a varia ...

s from which the data have been sampled? For example, in many situations it may be assumed that the underlying distributions are

normal distribution In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu i ...

s. In other cases the data are categorical, coming from a

discrete distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon ...

over a

nominal scale Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scale ...

, such as which entry was selected from a menu. * Does the hypothesis being tested apply to the distributions as a whole, or just some

population parameter In statistics, as opposed to its general use in mathematics, a parameter is any measured quantity of a statistical population that summarises or describes an aspect of the population, such as a mean or a standard deviation. If a population e ...

, for example the

mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ari ...

or the

variance In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of number ...

? * Is the

hypothesis A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a hypothesis to be a scientific hypothesis, the scientific method requires that one can testable, test it. Scientists generally base scientific hypotheses on prev ...

being tested merely that there is a difference in the relevant population characteristics (in which case a

two-sided test 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. A two-tailed test is appropriate if ...

may be indicated), or does it involve a specific bias ("A is better than B"), so that a

one-sided test 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. A two-tailed test is appropriate if ...

can be used?

Relevant tests

Statistical tests that may apply for two-sample testing include: * Hotelling's T-squared distribution#Two-sample statistic * Kernel embedding of distributions#Kernel two-sample test *

Kolmogorov–Smirnov test In statistics, the Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions that can be used to compare a sample wi ...

Kuiper's test Kuiper's test is used in statistics to test that whether a given distribution, or family of distributions, is contradicted by evidence from a sample of data. It is named after Dutch mathematician Nicolaas Kuiper. Kuiper's test is closely related t ...

Median test In statistics, Mood's median test is a special case of Pearson's chi-squared test. It is a nonparametric test that tests the null hypothesis that the medians of the populations from which two or more samples are drawn are identical. The data in ...

Pearson's chi-squared test Pearson's chi-squared test (\chi^2) 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 ...

Student's t-test A ''t''-test is any statistical hypothesis test in which the test statistic follows a Student's ''t''-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of ...

Tukey–Duckworth test In statistics, the Tukey–Duckworth test is a two-sample location test – a statistical test of whether one of two samples was significantly greater than the other. It was introduced by John Tukey John Wilder Tukey (; June 16, 1915 – July ...

Welch's t-test In statistics, Welch's ''t''-test, or unequal variances ''t''-test, is a two-sample location test which is used to test the hypothesis that two populations have equal means. It is named for its creator, Bernard Lewis Welch, is an adaptation of ...

Relevant tests

See also