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# Compute from the observations the observed value <var>t</var><sub>obs</sub></var> of the test statistic <var>T</var>.
# Calculate the [[p-value|''p''-value]]. This is the probability, under the null hypothesis, of sampling a test statistic at least as extreme as that which was observed (the maximal probability of that event, if the hypothesis is composite).
# Reject the null hypothesis, in favor of the alternative hypothesis, if and only if the ''p''-value is less than (or equal to) the significance level (the selected probability) threshold (
The former process was advantageous in the past when only tables of test statistics at common probability thresholds were available. It allowed a decision to be made without the calculation of a probability. It was adequate for classwork and for operational use, but it was deficient for reporting results. The latter process relied on extensive tables or on computational support not always available. The explicit calculation of a probability is useful for reporting. The calculations are now trivially performed with appropriate software.
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The former report is adequate, the latter gives a more detailed explanation of the data and the reason why the suitcase is being checked.
Not rejecting the null hypothesis does not mean the null hypothesis is "accepted
The processes described here are perfectly adequate for computation. They seriously neglect the [[design of experiments]] considerations.<ref>{{cite book|author=Hinkelmann, Klaus and [[Oscar Kempthorne|Kempthorne, Oscar]]|year=2008|title=Design and Analysis of Experiments|volume=I and II|edition=Second|publisher=Wiley|isbn=978-0-470-38551-7}}</ref><ref>{{cite book|last=Montgomery|first=Douglas|title=Design and analysis of experiments|publisher=Wiley|___location=Hoboken, N.J.|year=2009|isbn=978-0-470-12866-4}}</ref>
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