View source for Up and Down Identification (analysis)

==== Student<nowiki>'</nowiki>s test ====

This criterion is assigned to test mean values homogeneity (''a''<sub>''x''</sub> = ''a''<sub>''y''</sub>) of two normal-distributed samples with equal (but unknown) dispersion σ<sup>2</sup>. (Note, that to apply this test both samples should have three or more values). As a critical statistic in this method we use:

:: [[File:Statistics-Up-and-Down-Identification-s1.png]]

where:

:: [[File:Statistics-Up-and-Down-Identification-s2.png]]

Corresponding sample means are:

:: [[File:Statistics-Up-and-Down-Identification-s3.png]]

Corresponding sample dispersions are:

:: [[File:Statistics-Up-and-Down-Identification-s4.png]]

If the hypothesis ''H''<sub>0</sub> is true, this statistic should obey ''t''-distribution with ''m''+''n''-2 degrees of freedom.

Using double-sided criterion, we estimate ''P-value'' as:

:: [[File:Statistics-Up-and-Down-Identification-s6.png]]