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Using brackets
to enclose parenthetical material that is already within parentheses.
For example:
(The results for the control group [n = 8] are also presented in Figure 2.)
Exception 1: Do not use brackets if the material can be set off easily with commas without confounding meaning:
Unnecessary: (as Imai [1990] later concluded) Better: (as Imai, 1990, later concluded)
Exception 2: In mathematical material, the placement of brackets and parentheses is reversed; that is, parentheses appear within brackets.
to enclose material inserted in a quotation by some person other than the original writer.
For example: "when [his own and others'] behaviors were studied" (Hanisch, 1992, p. 24)
(adapted from the fifth edition of APA's Publication Manual, © 2001)


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