Mathematical statistics and probability is hard. It often involves what, at a first glance, involves complicated calculations and the sheer volume of data coming out of some studies can often be hard to interpret, even if you know all of the mathematics behind it. Although it is important to understand the math, it is equally important (or perhaps even more important) to understand what the results mean and don’t mean. It is easy to get dazzled by fancy mathematics or over-interpret results to mean something they really do not. Therefore, a basic understanding of statistical fallacies should be a part of every scientific skeptics toolbox or baloney detection kit.

Here is a list of the most common statistical fallacies, what they are and how to combat them.

**1. Confusing correlation with causation**

A correlation is when two variables vary together, whereas causation occurs when one factor causes the other. It may be tempting to think that the former implies the latter, but that is hardly ever the case. For instance, ice cream sales may increase in the summer and decrease in the winter. The same may be true for drowning accidents. Does this mean we can draw the conclusion that drowning accidents causing ice cream sales? Does this mean that people have become so selfish and morally vile that they prefer to buy ice cream and watching people drown than trying to save them!? Fortunately, not really. Just because two variables vary together does not mean that one caused the other. It might be that the other caused the first, that they both cause each other or that a third factor causes both. In the case of ice cream sales and drowning accidents, a third factor that probably explain the correlation is season. In the summer, more people eat ice cream and go bathing, but fewer to these things in the winter. Confusing correlation with causation is widespread in many areas of pseudoscience, such as the anti-vaccination movement; one of their claims is that as the number of vaccines given have increased, so has the rates of cancer. This shows that the two factors correlate, not that vaccines caused cancer (in fact, the vaccine against HPV and Hepatitis B can prevent cancers) is a correlation, not a causation. A more likely factor is better healthcare as a third factor; better healthcare has meant more vaccines, but also increased lifespan, which is associated with an increase in the risk of cancer.

**2. Post hoc**

Post hoc and denotes the fallacy of thinking that A causes B just because B follows A in time. This fallacy, like the fallacy of confusing correlation with causation, is understandable from an evolutionary perspective. Those that where too skeptical of attributing an upset stomach to poisonous berries where less likely to reproduce. However, this kind of instinct-based reasoning can no longer be thought of as justified in our modern society Read more of this post

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