Summary

• Hypothesis tests are typically conducted to arrive at a decision. That decision is to reject the null hypothesis or to not reject the null hypothesis.
• However, if we only pay attention to this decision we may miss out on the extent to which the sample provided evidence against the null hypothesis.
• There is an alternative method for conducting a hypothesis test, which involves calculating the P-value for the test.
• The P-value gives an indication as to how likely or unlikely the observed sample is if the null hypothesis is true. The more unlikely, the stronger the evidence against the null hypothesis.
• We calculate the likelihood of a sample by calculating the likelihood of the test statistic for that sample. In particular, the test statistic belongs in a probability distribution, and we calculate the chance of that probability distribution assuming a value as extreme as the test statistic.
• Calculating the P-value will depend on whether the test is one-sided or two-sided.
• Under the P-value method of hypothesis testing, a level of significance α is still chosen at the beginning of the test.
• If the P-value is below α, we reject the null hypothesis. Otherwise, we do not reject the null hypothesis.
• However, using the P-value approach to hypothesis testing, we also have a number along with our conclusion of the test. This number is the P-value: the likelihood of the observed sample if the null hypothesis is true.
• Therefore we can judge for ourselves the extent of the evidence against the null hypothesis, regardless of the specific outcome of the test.