Yes, ANALYSIS is a Scrabble word!

Letter values in Scrabble US: A 1, N 1, A 1, L 1, Y 4, S 1, I 1, S 1.

Is it a valid word?

ANALYSIS is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

an investigation of the component parts of a whole and their relations in making up the whole
the abstract separation of a whole into its constituent parts in order to study the parts and their relations
a form of literary criticism in which the structure of a piece of writing is analyzed
the use of closed-class words instead of inflections: e.g., `the father of the bride' instead of `the bride's father'
a branch of mathematics involving calculus and the theory of limits; sequences and series and integration and differentiation
a set of techniques for exploring underlying motives and a method of treating various mental disorders; based on the theories of Sigmund Freud

Also: analytic thinking, depth psychology.