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This online calculator calculates the p-value for one-sided and two-sided tests given the z-score. For a quick recap of what p-value is, you can find citations from Wikipedia just below the calculator.
The p-value or probability value or asymptotic significance1
The p-value is defined as the probability, under the null hypothesis, here simply denoted by (but is often denoted , as opposed to , which is sometimes used to represent the alternative hypothesis), of obtaining a result equal to or more extreme than what was actually observed. Depending on how it is looked at, the "more extreme than what was actually observed" can mean (right-tail event) or (left-tail event) or the "smaller" of and (double-tailed event). Thus, the p-value is given by
for right tail event,
for left tail event,
for double tail event.
The smaller the p-value, the higher the significance because it tells the investigator that the hypothesis under consideration may not adequately explain the observation. The null hypothesis is rejected if any of these probabilities is less than or equal to a small, fixed but arbitrarily pre-defined threshold value , which is referred to as the level of significance. Unlike the p-value, the level is not derived from any observational data and does not depend on the underlying hypothesis; the value of is instead set by the researcher before examining the data.