**Abstract**

In geodesy, statistical testing aids in determining the extent to which the criteria and requirements needed in the measurement and calculation proceedings have been fulfilled. A “rule of thumb” method that compares test statistics to constants Tcrit = 3 or Tcrit = 5 has been established. The test statistic T is the ratio between the displacement and its precision. Since it is not distributed through any of the known distribution functions, (statistical) simulations are used to assess the empirical distribution in 2D and 3D geodetic networks. The proposed alternative procedure leads to a more precise detection of significant displacements at a given test significance level α. Regardless of the network's dimensionality, Tcrit obtains the value of 3 at a risk level below 1%. When 5% is considered to be an acceptable risk level, the critical value can be lower than 3 or 5. Thus, significant displacements should be considered with regard to the acceptable risk level and not according to the usual “rule of thumb”.

**Key words**: statistical hypothesis testing, significance level, simulated distribution function, critical value, actual risk, point displacement