In the aftermath of November's election, many have expressed distress at an apparent wave of reported bias incidents. There were 867 reported incidents of language or behavior in which bias or prejudice played a role in the 10 days following the election, according to the Southern Poverty Law Center, an antibigotry advocacy group. One of the most visible such events occurred on December 6, when a man screamed “terrorist” at a hijab-wearing New York City transit worker and pushed her down the stairs in Grand Central Station. An unidentified “good Samaritan” stepped in and took the woman to the hospital.

Was that the right thing to do? Did the helpful bystander risk danger? Was the action typical of most bystanders? Over the past few decades researchers have studied the behavior of bystanders at violent incidents. They have discovered factors that motivate these people to act or do nothing. They have also studied the result of various forms of intervention, both for the bystanders and for the victims.

Early research found that the more witnesses there were to an incident, the less individual responsibility to act each person felt. Subsequent study has discovered, however, that witness response is far more complicated. In fact, experts say, whether and how to act in such a situation involves a complex calculus in almost all circumstances. But learning the best possible approaches can help prepare you, should you ever witness an aggressor threatening or harming someone.

—Prepare yourself by thinking ahead or getting training. If you see a news story about a bias incident, suggests Sherry Hamby, an expert on the psychology of violence at Sewanee: The University of the South, “Role-play in your head what you would do and say. That may help you be more ready.”

—Stay alert to potential incidents. That’s one of the things taught by Elena Waldman, executive director and instructor of Artemis, a self-defense training organization located in New York and other east coast cities. “If I see an agitated or menacing person stalking another person,” she says, “maybe I’ll strike up a conversation with the vulnerable person. I might even say, ‘That guy over there is giving me a bad vibe. Is it okay if I stand here?’ I might ask another person to stand near us, just to create a safer space.”

—Call 911 immediately if there’s violence. This sounds obvious, but in the heat of the moment not everyone thinks to do it first, experts say. Then try to apply first aid if you have had training. Offer comfort and a sense of safety.

—Consider what feels safe before you attempt any intervention. Research by Hamby and her colleagues shows that a significant number of people are harmed when intervening. That's bad enough—but in addition, she says, “It was more traumatizing to the victim if the bystander made it worse or got harmed. It’s trickier than it’s treated to be a helpful bystander.”

—Don’t confront the aggressor with angry talk or violence. If you talk to the aggressor at all, do it in a mild and unchallenging way. “We all think we are going to be Harrison Ford in a movie,” Hamby says. It’s important, she says, not to escalate the situation. Instead, defuse the tension by changing the subject or even using humor. If the attacks are just verbal, she suggests you move closer to the victim and talk to him or her about something unrelated such as the weather or a popular television show, or pay them a compliment such as, “Love your outfit!” “You can act like you didn't even notice the person harassing the victim,” she says.

—Aid the victim. Ask whether he or she needs help; whether it is a ride or calling a friend.

—Enlist other bystanders. Often they will join you if you ask.

—Record the incident. If it feels safe, photograph or video the scene and the person. Or memorize everything about the attacker and the incident, including the actual words used. “The words used in the commission of the act,” says Los Angeles criminal defense attorney Kacey McBroom, “can be the difference between a regular crime and a hate crime.”

Remember that intervening is a personal decision. In such a threatening situation many people feel frightened and freeze. Decisions often have to be made within seconds. A former Navy Seal may decide to act in a way you wouldn’t—and depending on the situation, that might make things better or worse. At a minimum, you can call 911.

If you want to be better prepared, Waldman says, there are free or low-cost bystander classes at empowerment self-defense organizations around the country. For additional resources, she recommends the National Women’s Martial Arts Federation Web site. At Artemis, “We have lots of people of all genders in our classes,” she adds.

The fact that so many people are distressed by these bias incidents can be seen as a good thing. “The sky is not falling,” says David Lehrer, president of the human rights organization Community Advocates and a former executive of the Anti-Defamation League. “We believe Americans are more tolerant than ever before. The trends are in the right direction.”