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Is statistics hard?

October 30, 2010

Statistics is backwards! You might think that given a particular set of data, you are able to say how likely it is that a particular theory is true. Unfortunately, you would be wrong!

One thing most people (even statisticians!) would like to do is describe how likely a theory or hypothesis might be in light of a particular set of data. This is not possible in the commonly used classical/frequentist approach to statistics, which is the approach taken in these notes. Instead, statistics talks about the probability of observing particular sets of data, assuming a theory holds.

We are NOT allowed to say, “Because of these data, there is only a small probability that this theory is true.” Instead, we say things like, “If this theory is true, the probability of seeing data like these is small.”

The first statement is relatively clear. If we could say that based on a particular set of data a theory has a 10% chance of being true, then the theory has a 10% chance of being true. The second statement is murky. If the result is that there is only a 10% chance of seeing data like these if a theory is true, is that small enough to make us doubt the theory? How likely are the data under some other theory? Perhaps there’s no theory under which data like these are more likely! This means we need methods for translating this latter type of statement into a declaration that a theory is true or false. As a result…

Statistical methods are convoluted! In order to show an effect exists, […]

via Is statistics hard?.

There are many more important points made on this site that need to be read by all those new (and not so new) to statistics.

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