$ℙ$ -value hypothesis test

The $ℙ$ -value test involves finding the probability, under our assumed ( $𝐻 0$ ) model, of getting a test statistic at least as extreme as observed. If it is less than a designated level of significance $𝛼$ ¹, the result is said to be statistically significant and $𝐻 0$ is rejected in favour of $𝐻 1$ .

Steps

Identify the appropriate distribution of the underlying random variable $𝑋$
Formulate a null hypothesis $𝐻 0$ of our assumed parameterisation of the distribution; and an alternate hypothesis $𝐻 1$ of its negation, which may be either one-sided or two-sided.
Construct the distribution of the test statistic being used $𝑍$ under the assumptions of $𝐻 0$ .
Find the probability of a test statistic at least as extreme as observed $𝑧$ under $𝐻 0$ .
State the conclusion: if the $ℙ$ -value is less than the selected level of significance $𝛼$ , it is highly unlikely $𝐻 0$ is true and we therefore reject it in favour of $𝐻 1$ ; otherwise we maintain $𝐻 0$ .
Interpret these results in the context of the problem.

#state/tidy | #SemBr

Typically $𝛼 = 0.05$ or $𝛼 = 0.01$ . ↩

ℙ-value hypothesis test

Steps

Footnotes

$ℙ$ -value hypothesis test