The Thorpe analysis is a recognized method allowing to identify and characterize turbulent regions within stably stratified fluids. By comparing an observed profile of potential temperature or potential density to a reference profile obtained by sorting the data, overturns resulting in statically unstable regions mainly due to turbulent patches and Kelvin-Helmholtz billows can be identified. However, measurement noise may induce artificial inversions of potential temperature or density, which can be very difficult to distinguish from real (physical) overturns. A method for selecting real overturns is proposed. The method is based on the data range statistics, the range being defined as the difference between the maximum and the minimum of the values in a sample. A statistical hypothesis test on the range is derived and evaluated through Monte-Carlo simulations. Basically, the test relies on a comparison of the range of a data sample with the range of a normally distributed population of same size as the data sample. The power of the test, i.e. the probability of detecting the existing overturns, is found to be an increasing function of both trend to noise ratio (tnr) and overturns size. A threshold for the detectable size of the overturns as a function of tnr is derived. For very low tnr data, the test is shown to be unreliable whatever the size of the overturns. In such a case, a procedure aimed to increase the tnr, mainly based on subsampling, is described. The selection procedure is applied to atmospheric data collected during a balloon flight with low and high vertical resolutions. The fraction of the vertical profile selected as being unstable (turbulent) is 47% (27%) from the high (respectively low) resolution data-set. Furthermore, relatively small tnr measurements are found to give rise to a poor estimation of the vertical extent of the overturns.