The word "that" has a few different functions in English, which can lead to confusion because some instances of "that" are more optional than others in academic writing.
One important use of "that" is for embedding (inserting) a certain type of dependent clause called a noun clause into an independent clause. Frequently, such clauses serve as the direct object of a reporting verb (e.g., found, reported, posited, argued, claimed, maintained, and hypothesized) to introduce a paraphrase, summary, or quotation.
Also see our webpage for other Uses of "That."
Key: Yellow, bold = subject; green, underline = verb; blue, italics = object
For example,
In formal written English, for clarity, most academic writers choose to keep "that" when it introduces a noun clause (Caplan, 2012). Leaving out "that" can cause the reader to misread (at first anyway) the subject of the dependent clause as being the object of the reporting verb (Jamieson, 2012).
References
Caplan, N. (2012). Grammar choices for graduate and professional writers. University of Michigan Press.
Jamieson, P. (2012). Use of that. http://www.proofreadnow.com/blog/bid/89915/Use-of-That