Panel b) the N_p statistical distribution as a function of K for the random field case. The blue solid circles represent the median and the gray shaded area represents the 1-σ confidence level region around the median for each value of K. The dashed black line represents the N_p = K + 1 law. Panel e) same as in panel b) for the sky test field 1 case. Panel a) number of detected clusters for the random test field case (blue solid points) as a function of K, and best fit by means of a Poissonian survival function (red empty bars). Panel c) number of detected cluster for the sky test field 1 case (black solid points), for the fake clusters as a function of K, and best fit by means of a Poissonian survival function (red empty bars). Panel d) number of detected cluster for the sky test field 1 case (red solid boxes) for the true clusters as a function of K, and best fit by means of a Poissonian survival function (black empty boxes).