# The Precise Meaning of the Probability Value (1 of 3)

There is often confusion about the precise meaning of the

probability computed in a

significance test. As stated in

Step 4 of the steps in hypothesis testing,
the

null hypothesis (H

_{0}) is
assumed to be true. The difference between the statistic computed in
the sample and the parameter specified by H

_{0} is computed
and the probability of obtaining a difference this large or large is
calculated. This probability value is the probability of obtaining
data as extreme or more extreme than the current data (assuming
H

_{0} is true). It is not the probability of the null
hypothesis itself. Thus, if the probability value is 0.005, this does
not mean that the probability that the null hypothesis is true is
.005. It means that the probability of obtaining data as different or
more different from the null hypothesis as those obtained in the
experiment is 0.005.

The inferential step to conclude that the null
hypothesis is false goes as follows: The data (or data more extreme)
are very unlikely given that the null hypothesis is true. This means
that: (1) a very unlikely event occurred or (2) the null hypothesis
is false.
The inference usually made is that the null hypothesis is false.