In statistics, the<unk>  is the<unk>  of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples.
Ronald<unk>  in 1935 introduced fiducial inference in order to apply it to this<unk> . He referred to an earlier paper by W. V.<unk>  from 1929.<unk>  and<unk>  proposed to find the probability distribution of
where 
x
¯
1
{\displaystyle {\bar {x}}_{1}}
 and 
x
¯
2
{\displaystyle {\bar {x}}_{2}}
 are the two sample means, and 
s
1
{\displaystyle s_{1}}
 and 
s
2
{\displaystyle s_{2}}
 are their standard deviations.<unk>  approximated the distribution of this by ignoring the random variation of the relative sizes of the standard deviations, 
s
1
/
n
1
s
1
2
/
n
1
+
s
2
2
/
n
2
{\displaystyle {s_{1}/{\sqrt {n_{1}}} \over {\sqrt {s_{1}^{2}/n_{1}+s_{2}^{2}/n_{2}}}}}
.<unk> 's solution provoked controversy because it did not have the property that the hypothesis of equal means would be rejected with probability α if the means were in fact equal. Many other methods of treating the<unk>  have been proposed since.
Behrens-Fisher problem
Naegele's rule
Weber–Fechner law
Hund's rule of maximum multiplicity
Pauli exclusion principle
Van der Waals strain
Gibbs' phase rule
Chichibabin reaction