This online calculator calculates p-value for one sided and two sided tests given the z-score

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.



Digits after the decimal point: 2
p-value (one-sided test)
p-value (two sided test)
Probability Density Function
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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 H (but is often denoted H_{0}, as opposed to H_{a}, 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 \{X\geq x\} (right-tail event) or \{X\leq x\} (left-tail event) or the "smaller" of \{X\leq x\} and \{X\geq x\} (double-tailed event). Thus, the p-value is given by

Pr(X\geq x|H) for right tail event,
Pr(X\leq x|H) for left tail event,
2\min\{\Pr(X\leq x|H),\Pr(X\geq x|H)\} 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 H is rejected if any of these probabilities is less than or equal to a small, fixed but arbitrarily pre-defined threshold value \alpha, which is referred to as the level of significance. Unlike the p-value, the \alpha level is not derived from any observational data and does not depend on the underlying hypothesis; the value of \alpha is instead set by the researcher before examining the data.

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