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### COMMON MISTEAKS
MISTAKES IN
USING STATISTICS: Spotting and Avoiding Them

Introduction
Types
of Mistakes
Suggestions
Resources
Table
of Contents
About

# Misunderstandings arising from
different perspectives on probability

There are four perspectives
on probability that are commonly used:
Classical,
Empirical
(or Frequentist), Subjective,
and Axiomatic.
Using one
perspective when another is intended can lead to misunderstandings and
errors.

Various authors^{1 }have
pointed out that students' first
formal introduction to probability, whether in middle grades, high
school, or an introductory college statistics course, is often from the
classical perspective, where we talk about outcomes (such as the
numbers that can come up when tossing a fair die) that have equal
probabilities. However, many applications of probability (including
statistical inference) involve situations where outcomes may not have
equal probabilities. This can lead
to misunderstandings such as the following:

Common misunderstanding:
If there
are only two possible outcomes, and you don't know which is true, the
probability of each of these outcomes is 1/2.

In fact, probabilities in
such "binary outcome" situations could
be
anything from 0 to 1. For example, if the outcomes of interest are "has
cancer" and "does not have cancer," the probabilities of having cancer
are (in most cases) much less than 1/2. The empirical
(frequentist) perspective allows
us to estimate such probabilities.

Notes:

1. See Albert, James H. (2003), "College Students' Conceptions of
Probability", The American
Statistician, vol. 57 No. 1,
pp. 37 - 45, and references therein.