What is the correct way to use parentheses?

to set off structurally independent elements

Examples:

• The patterns were significant (see Figure 5).
• (When a complete sentence is enclosed in parentheses, place punctuation in the sentence inside the parentheses, like this.)
• If only part of a sentence is enclosed in parentheses (like this), place punctuation outside the parentheses (like this).

to set off letters that identify items in a series within a sentence or paragraph (see also section 3.04 on seriation)

• Example:
  The subject areas included (a) synonyms associated with cultural interactions, (b) descriptors for ethnic group membership, and (c) psychological symptoms and outcomes associated with bicultural adaptation.

to group mathematical expressions (see also sections 4.09 and 4.48 in the Publication Manual)

• Example:
  (k – 1)/(g – 2)

to enclose numbers that identify displayed formulas and equations

• Example:
  Mj = αMj–1 + fj + gj * gj' (1)

to enclose statistical values

• Example:
  was statistically significant (p = .031)

(adapted from the sixth edition of the APA Publication Manual, © 2010)