My Math Forum easy explanation about definition of p-value

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 December 22nd, 2015, 02:12 AM #1 Senior Member   Joined: Jan 2013 From: Italy Posts: 154 Thanks: 7 easy explanation about definition of p-value Hi, please, I would want to know an easy and linear explanation of the following statement about the definition of the p-value: So let $\displaystyle H_0$ be the null hypothesis, "the p-value of the test is the probability that a value of the test statistic in the direction of the alternative hypothesis and as extreme as the one that actually did occur would have occurred if $\displaystyle H_0$ where true." So, I know that the "test statistic" is a procedure or function whose value ("test value") can be computed from the sample results. The "direction of the alternative hypothesis", depends from the fact that an alternative hypothesis can be one-sided or two-sided. A one sided alternative hypothesis says that the parameter has changed in a specified direction, while a two-sided alternative hypothesis is bi-directional. I encounter major problems in comprehend this part of the statement: "...and as extreme as the one that actually did occur would have occurred if $\displaystyle H_0$ where true." can you help me to understand? many thanks!

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