P-Value

P-value

Definition:

The p-value of a test is the probability of observing a test statistic at least as extreme

(compared to the critical limit) as the one computed given that the null-hypothesis is true.

p-value = P(a least as extreme test statistic as the one computed | H0 is true)

The p-value is something we calculate when conducting hypothesis tests. We do it in order to say

something about the amount of statistical evidence that supports the alternative hypothesis (H1). The

smaller the p-value, the more statistical evidence exists to support the alternative hypothesis. That

is, the smaller the p-value, the more certain we can be that the alternative hypothesis is true.

In order to reject the null-hypothesis, the p-value must be lower than the chosen/given significance

level (_). If the significance level is 5 %, then the p-value must be lower than 5 % in order to reject

the null hypothesis.

Decision rules

If p-value > significance level (_) then H0 cannot be rejected, i.e. maintain H0.

If p-value < significance level (_) then H1 is plausible, i.e. reject H0.

The way the p-value is calculated depends on the hypothesis that is tested, i.e. it depends on

whether it is a one- or two-sided test.

Two-sided test1

A two-sided test is applied when there is a “” in the H1 hypothesis

The way we depict a two-sided hypothesis test is as follows:

1 All examples in this paper are illustrated by use of the normal distribution and a 5 % significance level.

In this case the sample results have led to the calculation of a value of the test statistic of 2.24.

At the 5 % significance level (resulting in critical limits of -1.96 and 1.96) we reject the null

hypothesis.

We always calculate the p-value as the probability of obtaining a value of the test statistic that is at

least as extreme (compared to the critical limit) as the calculated test statistic. When conducting a

two-sided test, we just have to remember to multiply by 2 because...