Do you use brackets the same way you use parentheses?
to enclose the values that are the limits of a confidence interval.
95% CIs [-7.2, 4.3], [9.2, 12.4], and [-1.2, -0.5]
to enclose parenthetical material that is already within parentheses.
(The results for the control group [n = 8] are also presented in Figure 2.)
to enclose material inserted in a quotation by some person other than the original writer.
"when [his own and others'] behaviors were studied" (Hanisch, 1992, p. 24)
to include nonroutine information in a reference
Van Nuys, D. (Producer). (2007, December 19). Shrink rap radio [Audio podcast].
Retrieved from http://www.shrinkrapradio.com
Exception 1: Do not use brackets if the material can be set off easily with commas without confounding meaning:
- Correct: (as Imai, 1990, later concluded)
- Incorrect: (as Imai  later concluded)
Exception 2: In mathematical material, the placement of brackets and parentheses is reversed; that is, parentheses appear within brackets.
(adapted from the sixth edition of the APA Publication Manual, © 2010)