The significance test is used to test whether a given *null-hypothesis*
is to be abandoned; in favor of the alternative hypothesis.
In this case, the null-hypothesis is that the *input u*
of this block is a realization of a random number distributed with
a given *cumulative density function H*. The alternative
hypothesis is then that the input u is NOT such a realization,
i.e. it has a different probability distribution.

The test is carried out by comparing the size of the input u with the probability (given the null-hypothesis H) that this can input occur. The further the input is away from the expected mean value (of H), the more improbable it becomes that the null-hypothesis is true. This can be carried out on both ends, i.e. very high and very low values. The low values are tested against using the parameter setting leftTail = true, i.e. a test is carried out that the input is lower than the assumed distribution. The high values are tested against using the parameter setting rightTail = true, i.e. a test is carried that the input is higher than the assumed distribution. If you set both values to true, a test is carried out that the input is simply not from the assumed distribution.

If the input is very high (or very low), the null-hypothesis is to be abandoned. However, the assumed distributions are typically not bounded, such that abandoning the null-hypothesis may always be a wrong decision. The output of this block is the probability of committing this error.

The output of this block is known as the *p-value*. If the p-value is low,
the null-hypothesis should be abandoned. It is therefore usually comapred
against a threshold, e.g. p < 0.05 or p < 0.01.
In order to be more accurate, the p-value is usually also given along with
the decision to keep or abandon the null-hypothesis.

More information about significance testing can be found e.g. on Wikipedia: https://en.wikipedia.org/wiki/Statistical_significance.

Name | Description |
---|---|

H | Cumulative density function of the null hypothesis |

Developed 2014 at the DLR Institute of System Dynamics and Control |

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