# What is “Discriminant hotelling”?

Recently I have encountered the term Discriminant hotelling. And I have no idea what this term means. All I know is that this is in context with multivariable data analysis. I tried googling but in vain. So can someone explain to me what this term means?

• Hotelling is the name of a statistician and goes with capital latter. Discriminant must be referring to "discriminant function analysis" and goes with lower-case. But what does Discriminant hotelling mean - I don't know, sorry. Do you mean hotelling as derivative from "hotel": short-term provision of office space to a temporary worker?, and speaking really of abuses of discriminatory hoteling? – ttnphns Oct 11 '16 at 8:34
• OK then. Linear discriminant function analysis (LDA) is based on eigendecomposition of $\bf{W^{-1}B}$ where W and B are the within and the between scatter matrices. The sum of the eigenvalues = trace of the above matrix is known as Hotelling's trace. It is the multivariate analogue of "B/W" idea of ANOVA. – ttnphns Oct 11 '16 at 8:43
• Hotelling's T test is a multivariate test analoguos to univariate Student's t-test and based on the above eigenvalues. – ttnphns Oct 11 '16 at 9:39
• The phrase does appear in Google searches with a slash, as in Discriminant/Hotelling--and in a few instances even without the slash. A pattern emerges upon examining these instances: they tend to be in obscure badly-formatted journals (meaning editing was poor or nonexistent), written in English by non-English speakers. A reasonable hypothesis is that "Hotelling's Discriminant" test was intended. – whuber Feb 28 '17 at 20:00
• Without a precise reference the value of this question is limited. – Nick Cox Mar 1 '17 at 10:29

Discriminant analysis and Hotelling's T$^2$: Beware: The combination of discriminant analysis and Hotelling's T$^2$ test is sometimes misused. One should not be surprised to find a statistically significant difference between two samples which have been chosen with the objective of maximizing distance in the first place! The division into two groups should ideally be based on independent evidence. Indeed, in the cited paper above, the classification was properly taken a priori.