The Belief-Bias Effect refers to the results that happen when an individual’s own values, beliefs, prior knowledge, etc. affects, or distorts, the reasoning process through the acceptance of invalid arguments or data. This can happen when an observer assumes ahead of time that they know what the results of an experiment will be and uses that belief to distort the results.
An example of this could be an researcher studying the affect of prayer on illness. A completely open-minded researcher will gather data and then come to a conclusion based purely on the data collected, while a highly religious person may interpret the data in favor of prayer as a factor in healing, while an atheist may discount pro-prayer data.