how to write a standard of review

Under the abuse of discretion standard, the reviewing court must have a definite and firm conviction that the lower court committed a clear error of judgment in the conclusion it reached upon a weighing of relevant factors. And, the lower court must have the discretion to make the judgment it did. (Check the court rules.) The abuse of discretion standard affords virtually the same amount of deference to the decisions of lower tribunals as the clearly erroneous standard though the clearly erroneous standard affords lower courts slightly more deference.
Under the arbitrary and capricious standard, the court considers whether the agency’s decision was based on a consideration of the relevant factors and whether there has been a clear error of judgment. The standard is highly deferential to the agency.

Because a statement of the standard of review often appears early in an appellate brief, put the issue in context first.

See also American Telephone and Telegraph Company v. United Computer Systems, 98 F.3d 1206, 1209 (9th Cir. 1996) (treating the interpretation of 28 U.S.C. § 1961 as a pure issue of law subject to de novo review on appeal).

Whether you are an advanced law student looking to review the basics, or an aspiring law student looking for head start, this course will help you build the foundation you will need to succeed in law school and beyond.
Enjoying the lectures? Come join Prof. Ayres’ on Coursera! Enrolling in his course will allow you to join in discussions with fellow learners, take assessments on the material, and earn a certificate! Link – https://www.coursera.org/learn/law-st.

Bona Law also advises litigators and trial attorneys when an appeal is anticipated to ensure that all issues are preserved and the record is sufficiently developed.
Example: a trial court’s legal conclusion that the defendant is entitled to judgment as a matter of law is subject to de novo review.

A district court’s findings of fact are reviewed under the clearly erroneous standard. See Fed. R. Civ. P. 52(a)(6) ; United States v. Cazares , 121 F.3d 1241, 1245 (9th Cir. 1997) (standard applied in both civil and criminal proceedings). “Findings of fact are made on the basis of evidentiary hearings and usually involve credibility determinations, which explains why they are reviewed deferentially under the clearly erroneous standard.” Rand v. Rowland , 154 F.3d 952, 957 n.4 (9th Cir. 1998) (en banc) . Special deference is paid to a trial court’s credibility findings. See Anderson v. City of Bessemer , 470 U.S. 564, 573 (1985) ; McClure v. Thompson , 323 F.3d 1233, 1241 (9th Cir. 2003) .
In a civil case, the court of appeals reviews a jury verdict to determine whether it is supported by substantial evidence. See Hangarter v. Provident Life and Accident Ins. Co ., 373 F.3d 998, 1008 (9th Cir. 2004) ; see also Engquist v. Oregon Dep’t of Agric. , 478 F.3d 985, 993 (9th Cir. 2007) . Substantial evidence is such relevant evidence as reasonable minds might accept as adequate to support a conclusion even if it is possible to draw a contrary conclusion from the evidence. See Pavao v. Pagay , 307 F.3d 915, 918 (9th Cir. 2002) ; see also McCollough v. Johnson, Rodenburg & Lauinger, LLC , 637 F.3d 939, 955 (9th Cir. 2011) ; Harper v. City of Los Angeles , 533 F.3d 1010, 1021 (9th Cir. 2008) . Neither the trial court nor the appellate court may weigh the evidence or assess the credibility of witnesses in determining whether substantial evidence exists. See Gilbrook v. City of Westminster , 177 F.3d 839, 856 (9th Cir. 1999) ; see also McCollough , 637 F.3d at 957 ; Three Boys Music Corp. v. Bolton , 212 F.3d 477, 482 (9th Cir. 2000) (“The credibility of witnesses is an issue for the jury and is generally not subject to appellate review.”).

References:

http://lawprofessors.typepad.com/legal_skills/2011/04/a-helpful-formula-for-writing-that-pesky-standard-of-review-paragraph.html
http://m.youtube.com/watch?v=nLcFskaXPbc
http://www.businessjustice.com/what-is-the-standard-of-review-on-appeal.html
http://cdn.ca9.uscourts.gov/datastore/uploads/guides/stand_of_review/I_Definitions.html
http://www.emeraldgrouppublishing.com/archived/learning/study_skills/structured_writing.htm