Two-sample hypothesis testing

• Which assumptions may be made a priori about the distributions from which the data have been sampled? For example, in many situations it may be assumed that the underlying distributions are normal distributions. In other cases the data are 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 or the variance?
• Is the hypothesis being tested merely that there is a difference in the relevant population characteristics, or does it involve a specific bias, so that a one-sided test can be used?

  Relevant tests

• 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