# Definition

In a statistical test, the p-value is the probability under the null hypothesis of reaching a more extreme value than the one observed.

It generally allows the null hypothesis condition to be tested by the absurd.

# The case of a normal distribution with reduced centre

In a normal distribution, the p-value corresponds to the area under the curve above the extreme value tested. The table below gives the correspondence between the Z-score (which corresponds to the number of standard deviations separating the mean from the tested value) and the p-value. The greater the deviation from the mean, the more unlikely the result and thus the lower the p-value.

# Application

A test has a probability distribution that follows a normal distribution, it can be centred and reduced, by subtracting the mean and dividing by the standard deviation.

The probability distribution is thus equivalent to a normal distribution.

To find out the probability of a result equal to 2 times the standard deviation, simply look up the value 2 in the table above.

The value 2 is between 1.960 and 2.054, i.e. a p-value between 2 % (0.0+0.020) and 2.5 % (0.0+0.025).

The threshold value for assessing whether a result is unlikely is 5%, so by this criterion the result of this test is unlikely.