Atheists are much fairer to Christians than Christians are to atheists, according to a new study that has analysed interactions between the two groups.

But if you're an atheist, don't get too excited about your moral superiority yet. The study suggests that atheists are nicer in an attempt to compensate for the stereotype that atheists are immoral.

Researchers at Ohio University were seeking to study in-group bias and prosocial behaviour, or the tendency groups have to favour their own members.

"We often see that negative stereotypes about a group can lead members of that group to behave in compensatory ways that ostensibly seek to disconfirm that stereotype, such as when American immigrants strive to emphasise their American identity when it is threatened," researcher Colleen Cowgill told Psypost.

"This was the rationale behind my hypotheses stating that atheists' behaviour toward Christians in economic games might be different from Christians' behaviour toward atheists in economic games."

The study was divided into three parts. The first part was conducted using 297 subjects, 150 Christians and 147 atheists. These participants were tasked to play a game based on the Dictator Game, in which one player gives the other player an amount of money.

It was designed to test how self-interested people are, with the general prediction that very few people will choose to give their partner money when there are no consequences involved.

The researchers modified the game, however, so that participants were led to believe that several rounds of the game would be played, and that the other player would give them a reputation score that other people could see.

They were told that the other person knew that they were Christian or atheist. They were then told whether they were paired with a fictional Christian or atheist. Each of them was then told they had the task of dividing up the money they had been given.

The second part of the study, involving 233 different participants, 151 Christians and 82 atheists, was almost exactly the same, except for some key differences. The second group didn't know that they weren't partnered with real people, and they had to complete a survey afterwards that evaluated the morality of their partner.

What these parts both found was that Christians gave more money to Christians than they gave to atheists, but that atheists gave the same amount to everyone, regardless of religious status.

However, the third part of the study, involving 524 participants, 140 atheists and 384 Christians, showed that this discrepancy isn't purely motivated by altruism. These participants were divided into two groups. The first was told that the other person would not be informed of their religious status. The second was told that they would.

When atheists thought that Christians would not know of their atheism, they showed as much in-group bias as Christians did, giving more money to fellow atheists than Christians.

"Our results show that atheists are uniquely concerned about outgroup members seeing them as immoral by virtue of their lack of religiosity, and that these concerns are at least partially responsible for atheists' behaviour toward their Christian partners in economic games," the researchers wrote in the study.

Interplay between the two groups is of ongoing interest to the research team. Researchers Ain Simpson and Kimberly Rios published a study last year that found that they don't understand each other - and that atheists speak more negatively about Christians than the other way round.

"I think it is quite telling that atheists are perhaps so acutely aware of negative stereotypes about themselves that there are observable differences in their behaviour as compared with Christians in even this small, low-stakes type of interaction," Cowgill said.

"Research like this in the aggregate begins to build a case that there may be these kinds of hidden costs to the prevalent, unchallenged negative stereotyping in our society."

The team's paper has been published in the Journal of Experimental Social Psychology.