Hello Antonio,

I do not fully understand the Familywise error rate option within the definition of the test statistic properties.

Usually, a global or overall test is used to evaluate the stochastic and functional models. If such a test is rejected, several individual tests are applied in parallel e.g. to scan the data for outliers, cf. Teunissen: Testing Theory. ISBN 9789040719752.

However, if several hypothesis tests are applied in parallel, the likelihood increases to reject a true H0 (type I error) in one of the tests. To overcome this drawback, the e.g. Bonferroni model can be used to adjust the global (familywise) α and the individual α' used in the individual tests, cf. Multiple comparisons problem. Specifying α' yields α and wise versa.

In what situations would it be preferable to turn on this option, and in what not? What do you recommend while adjusting a classical levelling network?

There is no such a situation. The choice is independent of the application itself. The choice depends on your preferences. If you like to take such a statistic property into account, enable the option - if not, disable the option.

regards
Micha