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tokens: the SPEX package 1 ( Kaastra et al. 1996 ). To help the user to see if a -value corresponds to an acceptable fit, SPEX gives, after spectral fitting, the expected value of and its rms spread, based on the best-fit model. Both quantities are simply determined by adding the expected contributions and their variances over all bins. 3. Simple approximations for the expected value and variance of <italic>C</italic> We obtained simple approximations to the infinite series involved in ( 4 ) and ( 6 ), with relative errors better than for and better than for , as follows: With the help of the above equations, the goodness of fit for the model can be easily assessed. Given the other properties of cstat , such as unbiased parameter estimates, in almost all circumstances cstat is the preferred statistic to be used and the use of -statistics in X-ray spectral analysis should be avoided. 4. Two practical examples Fig. 2 Simplified spectra of the Perseus cluster ( top ) with Hitomi and of Capella ( bottom ) with RGS. We tested our method to assess the goodness of fit with two examples. In the first example, we simulated a spectrum that has approximately the shape of the Perseus cluster as measured with the Hitomi SXS instrument ( Hitomi Collaboration et al. 2016 ). For this demonstration purpose we simplified the model by adopting an isothermal spectrum in collisional ionisation equilibrium with a temperature of 4 keV, proto-solar abundances, and an emission measure matching the flux of Perseus as measured by Hitomi. In our spectral fits, we used the temperature and emission measure of the source as free parameters. The spectrum has 5804 bins and is shown in Fig. 2 , without noise, but with instrumental features included. We scaled this spectrum in flux by factors of with ranging from 0–10, i.e. higher values of corresponding to lower fluxes. For each flux value, we simulated 1000 spectra, performed a best fit, and determined . We then produced a histogram of -values and calculated the 90%, 95%, and 99% percentile points , , and of this distribution. In an actual analysis of an observed spectrum, a model would be rejected at the 90% confidence level if , and this is similar for the other confidence levels. We compare these percentile points, scaled with the expected mean and variance , as delivered by SPEX and described in Sect. 2 , in Fig. 3 . Our second example is a simulation of the spectrum of Capella with the Reflection Grating Spectrometer (RGS) of XMM-Newton. This spectrum is approximated by a single isothermal component with temperature 0.5 keV and appropriate flux for Capella. All further steps are the same as for the Perseus example. The main difference between both spectra is that while Perseus is dominated by continuum emission, owing to its high temperature, Capella is dominated by line emission, owing to its low temperature. The Capella spectrum has 1433 bins and is also shown in Fig. 2 . Fig. 3 Percentile points 90%, 95%, and 99% for the