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# P-value

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

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This online calculator calculates p-value for one sided and two sided tests given the z-score. For quick recap of what p-value is, you can find citation from wikipedia just below the calculator.

### P-value

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.