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TLDR; The 40% number is wrong and plain old bad science. In attempt to recreate the numbers, by the same researchers, they received a rate of 24% while including violence as shouting. Further researchers found rates of 7%, 7.8%, 10%, and 13% with stricter definitions and better research methodology.

The 40% claim is intentionally misleading and unequivocally inaccurate. Numerous studies over the years report domestic violence rates in police families as low as 7%, with the highest at 40% defining violence to include shouting or a loss of temper. The referenced study where the 40% claim originates is Neidig, P.H.., Russell, H.E. & Seng, A.F. (1992). Interspousal aggression in law enforcement families: A preliminary investigation. It states:

Survey results revealed that approximately 40% of the participating officers reported marital conflicts involving physical aggression in the previous year.

There are a number of flaws with the aforementioned study:

The study includes as 'violent incidents' a one time push, shove, shout, loss of temper, or an incidents where a spouse acted out in anger. These do not meet the legal standard for domestic violence. This same study reports that the victims reported a 10% rate of physical domestic violence from their partner. The statement doesn't indicate who the aggressor is; the officer or the spouse. The study is a survey and not an empirical scientific study. The “domestic violence” acts are not confirmed as actually being violent. The study occurred nearly 30 years ago. This study shows minority and female officers were more likely to commit the DV, and white males were least likely. Additional reference from a Congressional hearing on the study: https://babel.hathitrust.org/cgi/pt?id=umn.31951003089863c

An additional study conducted by the same researcher, which reported rates of 24%, suffer from additional flaws:

The study is a survey and not an empirical scientific study. The study was not a random sample, and was isolated to high ranking officers at a police conference. This study also occurred nearly 30 years ago.

More current research, including a larger empirical study with thousands of responses from 2009 notes, 'Over 87 percent of officers reported never having engaged in physical domestic violence in their lifetime.' Blumenstein, Lindsey, Domestic violence within law enforcement families: The link between traditional police subculture and domestic violence among police (2009). Graduate Theses and Dissertations. http://scholarcommons.usf.edu/etd/1862

Yet another study "indicated that 10 percent of respondents (148 candidates) admitted to having ever slapped, punched, or otherwise injured a spouse or romantic partner, with 7.2 percent (110 candidates) stating that this had happened once, and 2.1 percent (33 candidates) indicating that this had happened two or three times. Repeated abuse (four or more occurrences) was reported by only five respondents (0.3 percent)." A.H. Ryan JR, Department of Defense, Polygraph Institute “The Prevalence of Domestic Violence in Police Families.” https://www.researchgate.net/publication/308603826_The_prevalence_of_domestic_violence_in_police_families

Another: In a 1999 study, 7% of Baltimore City police officers admitted to 'getting physical' (pushing, shoving, grabbing and/or hitting) with a partner. A 2000 study of seven law enforcement agencies in the Southeast and Midwest United States found 10% of officers reporting that they had slapped, punched, or otherwise injured their partners. L. Goodmark, 2016, BRIGHAM YOUNG UNIVERSITY LAW REVIEW “Hands up at Home: Militarized Masculinity and Police Officers Who Commit Intimate Partner Abuse “. https://digitalcommons.law.umaryland.edu/cgi/viewcontent.cgi?article=2519&context=fac_pubs