The backfire effect is the tendency of some people to resist accepting evidence that conflicts with their beliefs. The effect is demonstrated when people presented with that conflicting information become even more convinced of their original beliefs rather than questioning them.
Common sense tells us that if we are presented with new information that clearly suggests we've been wrong about something, we will consider that information and adjust our thinking on the matter. That may happen most of the time. However, some people in some cases will react illogically.
The backfire effect is one manifestation of confirmation bias, the tendency of people to give more credence to evidence that supports their preexisting beliefs. In this case, the bias is so strong that people refuse to consider the possibility that they were mistaken. Data that does not support their beliefs is dismissed and, perhaps because they know on some level that they were wrong, they profess even greater confidence that they have been correct all along. They may dismiss data as statistical noise and take even more extreme positions on issues than was initially the case.
Cognitive errors such as the backfire effect can be problematic for data analysis. Despite all the technology, the human factor is inevitably involved in selection of inputs and criteria as well as interpretation of results. Cognitive bias is unavoidable, however. The best protection from it is awareness of its presence and applying critical thinking skills to overcome it.