The cases also were investigated by the districts themselves, subject to cost constraints, image concerns, and individual interpretations of the anti-bullying regulation implemented in September 2011.
Among educators and others, there is a perception that some schools were more zealous than others in reporting incidents.
Joel Haber, a clinical psychologist and bullying authority based in White Plains, N.Y., thinks New Jersey's report is laudable in its intent, but lacking.
"There's a lot more that's not being reported here," he said. "There are gaps, clearly."
The analysis, released this month, is aimed at supporting programs to prevent and root out bullying. It is an overview that informs the public about "areas where programs and policies are having a positive impact, or where more support may be needed," according to state Education Commissioner Chris Cerf.
According to the data, a third of the 35,552 alleged HIB cases investigated statewide last year were verified.
The report provides no details of incidents. The Inquirer asked to review individual case reports but state and local education officials said the records are confidential.
New Jersey's anti-bullying law, considered one of the nation's strictest, has a specific list of what educators call "protected classes."
Pennsylvania has an anti-bullying law, but it does not have protected classes nor does it require districts to report to the state. State Rep. Dan Truitt (R., Chester) has introduced legislation that would establish a uniform anti-bullying policy and an online reporting system for superintendents to report incidents of violence and bullying.
New Jersey's protected classes are based on the victim's origin; ancestry; religion; gender identity and expression; color; race; mental, physical, or sensory disability; gender; sexual orientation; or other "distinguishing characteristic."
The last category, which could include body size, dress, or hair color, accounted for nearly two-thirds of the verified cases.
"Some are really easy to define, some are not," said Rafe Vecere, anti-bullying coordinator for the Burlington Township School District. The law "leaves a lot open to interpretation."
Vecere offered a clear-cut example of bullying and one that was more ambiguous.
In the clear-cut situation, a boy might tell a girl of Asian descent, "You're Indian and you should go back to your own country."
In the other case, an overweight girl boards a bus and one student says to another, "The seats aren't big enough for her, she's so fat." The girl does not hear it, but another girl does and reports it.
By law, an act qualifies as bullying if it creates a hostile educational environment or causes the target physical or emotional harm. But it also is bullying if it interferes with "the rights of other students."
Though the overweight girl received no spared direct abuse, the child who did the reporting may be a victim if she felt she was in a hostile environment or suffered emotional harm due to the unkind words.
"It's a judgment call on your part who was the victim," Vecere said. "You have to do a full investigation whether or not you think it's bullying."
With about 1.4 million students in the state's public and charter schools, the number of verified HIB cases last year translated to eight cases per 1,000 students, or a rate of 0.08 percent.
That is far below the estimated 10 percent of U.S. schoolchildren that experts, including the American Academy of Child and Adolescent Psychiatry, say feel the sting of bullying on a regular basis.
State education officials said New Jersey's report should not be compared with national studies because of the state law's specific definition of bullying.
Schools are expected to rely on their codes of conduct to deal with meanness and other inappropriate behavior - such as hazing - that do not fall under the law.
Hank J. Nuwer, another bullying expert, said whatever flaws this initial report has in measuring the scope of bullying, "it is a start, especially if the state perceives there is a real problem."
"It's creating awareness and it sends a clear message that New Jersey public schools are against all kinds of abuse," said Nuwer, of Franklin (Ind.) College, who has written extensively on the subject.
With 603 New Jersey school districts and 75 charter schools, application of the law is uneven for a variety reasons, including economics, educators say.
The state awarded $1 million in implementation grants in the 2011-12 school year after the state Council on Local Mandates ruled the law was an unfunded mandate. Districts requested $5 million.
This school year brought no new state anti-bullying funds.
"It would be very helpful if there was state support in this," said Lynne Strickland, director of the Garden State Coalition of Schools.
The state's statistics reveal jarring disparities in the number of HIB incidents reported by districts.
For example, the Lenape School District in Burlington County, with more than 7,000 high school students, reported three cases last year. Yet one of its sending districts, Medford Lakes, with a kindergarten through eighth-grade population of 535 students and a well-established anti-bullying program, reported 19. Moorestown, with 4,067 students, reported none.
Lenape's antibullying coordinator, Christopher Heilig, said in an e-mail that the district had implemented an anti-bullying program "well ahead" of the 2010 law and noted that high school students "learn the importance of appropriate behavior and good citizenship at a faster rate as they are becoming mature functioning members of society."
"As a result, districts with elementary- and middle-grade students are seeing more HIB," he said, adding substance abuse was a bigger problem in high schools.
Moorestown district officials did not respond to requests for comment.
State officials acknowledge differences exist in how districts handle and report bullying.
"We are committed to supporting our districts if they need assistance in the process of identification so we ensure that the information provided to the public is as accurate as possible," said Barbara Morgan, an Education Department spokeswoman.
Another obstacle in getting a true picture is that victims seldom report their abuse. From 70 percent to 90 percent of them keep it to themselves, according to authorities.
Much of the anti-bullying education in the state is aimed at getting victims and witnesses to step forward.
The report does offer some interesting details. At a time when so much attention is being given to cyberbullying, only 12 percent of the state's verified HIB incidents last year involved electronic communications.
An overwhelming three-quarters of the cases had a verbal element and one in five had a physical aspect. A bullying incident can involve more than one element.
Of the 2,229 cases involving physical contact, 655 resulted in injury, including nine where victims suffered major or serious injury.
While students from grades five through eight make up about a third of the state's student population, they accounted for just over half of the 13,101 perpetrators of bullying, according to the study.
The offenders faced 49,200 disciplinary actions, including four expulsions and 3,730 out-of-school suspensions.
At the same time, the report found that in only about a third of the cases did the offenders understand that their actions would cause physical or emotional harm or damage property.
Under state law, all school employees must report bullying they observe or of which they have been informed by a victim or offender.
Haber noted that a disproportionate one-third of the verified incidents occurred in a classroom, indicating teachers were aware of the problem and willing to report it.
He said most bullying occurred in less-supervised areas, such a cafeterias, hallways, locker rooms, and buses, and that the proportion of classroom incidents probably would have been less if victims had come forward.
Contact Joseph Gambardello at email@example.com or 856-779-3844.
Inquirer staff writer Rita Giordano contributed to this article.