Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected or encouraged over others in sampling or testing. Bias can occur during any research phase, including study design, data collection, analysis, and publication.
In statistics, a sampling bias is created when a sample is collected from a population, and some members of the population are not as likely to be chosen as others (remember, each member of the population should have an equally likely chance of being chosen). When a sampling bias happens, there can be incorrect conclusions drawn about the population that is being studied. In addition to selection bias, several types of biases are commonly observed in experiment design and data analysis - Observer bias, measurement bias, publication bias, etc.
It is important to realize that in many situations, the outcomes are not equally likely. A coin or die may be unfair or biased. Two math professors in Europe had their statistics students test the Belgian one Euro coin and discovered that in 250 trials, a head was obtained 56% of the time, and a tail was obtained 44% of the time. The data seem to show that the coin is not a fair coin; more repetitions would be helpful to draw a more accurate conclusion about such bias. Some dice may be biased. Look at the dice in a game you have at home; the spots on each face are usually small holes carved out and then painted to make the spots visible. Your dice may or may not be biased; it is possible that the outcomes may be affected by the slight weight differences due to the different numbers of holes in the faces. Gambling casinos make a lot of money depending on outcomes from rolling dice, so casino dice are made differently to eliminate bias. Casino dice have flat faces; the holes are completely filled with paint having the same density as the material that the dice are made out of so that each face is equally likely to occur.
This text is adapted from Openstax, Introductory Statistics, Section 3, Probability.