Although we rely on them, probability and statistics have more than the inherent vice of being only probably accurate. The intervention of human intentionality can turn them into weapons with which people can be manipulated into believing something that isn’t probable to be so. Also, they can lead to biased studies for the same reasons.
Grey Shades of Statistics and Probability That Might Lead to Biased Studies
It is used to manipulate the trends in different groups by combining their data. It’s a paradox used to prove something to be beneficial when it isn’t—an item, such as a medical treatment. By mixing the results in a specific group – for which the item proved to be beneficial – with the results of the same item in all the groups, a study can transform the item into a solution for everybody.
Base rate fallacy
This one is a standard statistical error made when the base rate is neglected. It refers to the judgment we might make on something based on how likely it would be to and living aside important information.
We’d think it’s more likely for someone that enjoys opera to be a musician and not an accountant. Since opera isn’t something that most people enjoy, it would seem right to believe it. But the base rate of accountants is way higher than the base rate of musicians. So, someone who enjoys opera is, in fact, more likely to be an accountant.
Will Rogers paradox
This probability and statistics paradox was named after the famous American comedian’s joke saying, “when the Okies left Oklahoma and moved to California, they raised the average intelligence in both states.” It is used to manipulate the odds of distinct groups to respond to a trial. Either by age, gender, or cognitive skills, the goal is to create comparable average trends.
It is the strange appearance that one independent variable can create over a second one without the two variables being in any way connected. This happens when we generate conclusions by looking at only one subset of the whole population that isn’t unbiased.
Two different diseases that share no common ground will negatively associate when patients suffering from either one of them will get together in a clinic where there are patients that suffer from both of the diseases.
Multiple comparisons fallacy
This one occurs when multiple random variables appear to be connected by chance when they are to be expected, given the high number of variables. The higher the number of variables, the higher the chances of existing trends. It means you might overlook trends while looking for patterns. The Birthday paradox is a classic multiple comparison fallacy. Moreover, it’s one of the probability and statistics paradoxes that can be used in biased studies.