Two ways of calculating the P-value were derived from this procedure. P-value1 was estimated assuming that the corrected chi-square is proportional to a chi-square with one degree of freedom, the coefficient of over-(or under-) dispersion (ĉ) being defined by the mean of the bootstrapped corrected chi-square. P-value2 was given by the proportion of bootstrapped corrected chisquares which were smaller than the observed value. In principle, P-value2 is better (no assumption on the distribution of the Likelihood Ratio Test, LRT, is made), but requires running enough simulations, which may be long in some cases. P-value1 allows working with smaller numbers of simulations when simulation times are too long.