• It directly tells you how confident you can be (how close the probability is to 100%) that the conclusion is correct. By 'conclusion' I mean the demonstration of some proposed effect that can be measured and analyzed. For example, if p=.05, then you have a 95% confidence level in your conclusion. If p=.01 the level is 99%. p is defined as the probability that the null hypothesis is correct, in which case the conclusion is incorrect.
  • In statistical hypothesis testing, the p-value is the probability of obtaining a result at least as extreme as a given data point, under the null hypothesis. The fact that p-values are based on this assumption is crucial to their correct interpretation. More technically, a p-value of an experiment is a random variable defined over the sample space of the experiment such that its distribution under the null hypothesis is uniform on the interval [0,1]. Many p-values can be defined for the same experiment.

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