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In [[statistical hypothesis testing]], a '''two-sample test''' is a test performed on the data of two [[random sample]]s, each [[Paired data|independent]]ly obtained from a different given [[population (statistics)|population]]. The purpose of the test is to determine whether the difference between these two populations is [[statistically significant]].
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 (statistics)|distribution]]s from which the data have been sampled? For example, in many situations it may be assumed that the underlying distributions are [[normal distribution]]s. In other cases the data are [[Categorical data|categorical]], coming from a [[discrete distribution]] over a [[nominal 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]], for example the [[Mean#Mean of a probability distribution|mean]] or the [[variance]]?
* Is the [[Alternative hypothesis|hypothesis]] being tested merely that there is a difference in the relevant population characteristics (in which case a [[two-sided test]] may be indicated), or does it involve a specific bias ("A is better than B"), so that a [[one-sided]] test 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]]
* [[Kuiper's test]]
* [[Median test]]
* [[Pearson's chi-squared test]]
* [[Student's t-test]]
* [[Tukey–Duckworth test]]
* [[Welch's t-test]]
==See also==
* [[A/B testing]]
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 (statistics)|distribution]]s from which the data have been sampled? For example, in many situations it may be assumed that the underlying distributions are [[normal distribution]]s. In other cases the data are [[Categorical data|categorical]], coming from a [[discrete distribution]] over a [[nominal 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]], for example the [[Mean#Mean of a probability distribution|mean]] or the [[variance]]?
* Is the [[Alternative hypothesis|hypothesis]] being tested merely that there is a difference in the relevant population characteristics (in which case a [[two-sided test]] may be indicated), or does it involve a specific bias ("A is better than B"), so that a [[one-sided]] test 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]]
* [[Kuiper's test]]
* [[Median test]]
* [[Pearson's chi-squared test]]
* [[Student's t-test]]
* [[Tukey–Duckworth test]]
* [[Welch's t-test]]
==See also==
* [[A/B testing]]
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