Definition:Linear Hypothesis
Definition
A linear hypothesis is a hypothesis which concerns linear functions of parameters in the context of regression analysis and analysis of variance.
Examples
Arbitrary Example
An example of a linear hypothesis:
- Let $H_0$ be the hypothesis that the difference between two treatment means $\tau_1$ and $\tau_2$ is zero, or takes a specific constant value.
Thus $H_0$ is a linear hypothesis about $\tau_1 - \tau_2$.
Also see
- Results about linear hypotheses can be found here.
Linguistic Note
The word hypothesis is pronounced hy-po-the-sis, the stress going on the second syllable.
Its plural is hypotheses, which is pronounced hy-po-the-seez.
The word hypothesis comes from the Greek for supposition, literally to put under, that is sub-position.
The idea is that one puts an idea under scrutiny.
The verb hypothesize (British English: hypothesise) means to make a hypothesis, that is, to suppose.
The adjective hypothetical means having the nature of a hypothesis.
A hypothetical question is a question which relates to a situation that is supposed (or pretended) to be imaginary. One would, for example, announce that a question about to be posed is hypothetical if the questioner wishes to be believed to be at some distance from the possibility of actually being the subject of the question.
- As a purely hypothetical question, what would the fate be of a student who had been found to have cheated in his examinations?
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): linear hypothesis
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): linear hypothesis