Distribution of p-values obtained in LR- and F-tests in a Monte Carlo simulation of true null hypotheses. The expectation for the p-value distribution is uniform in the interval 0 ≤ p ≤ 0.5 where 50% of the p-values are predicted. The other half of the p-values are expected at p = 1, which is due to the constraint on positive energy cutoffs (see also Appendix A). Upper panel: resulting p-value distribution in the range 0 ≤ p ≤ 0.5 when the simulated spectral points disperse around the true data according to a Student t-distribution with 5 degrees of freedom. It is clear that the LR-test (red) deviates from the uniform expectation for small p-values. This means that the LR-test severely overestimates the significance in this case. The distribution of p-values for the F-test (blue) is compatible with the uniform expectation. The distribution of p-values in the lower panel is generated when the simulated spectral points are normally distributed around their true value. In this case, the p-value distribution for both tests is compatible with the uniform expectation. The parameters of the Monte Carlo simulation are discussed in Sect. 4.2.