The aim of the reduction process is to minimize the influence of data acquisition imperfections on the estimation of the desired astronomical quantity (see Gilliland 1992 for a short review on noise sources and reduction processes of CCD data). For this purpose, one must perform appropriate manipulations with the data and calibration frames. The arithmetic work involved in this process must be taken into account in order to get reliable estimates of line-strength errors.
In order to trace in full detail the error propagation, error frames must be created at the beginning of the reduction procedure. After this point, error and data frames should be processed in parallel, translating the basic arithmetic manipulations performed over the data images into the error frames by following the law of combination of errors.
The starting point is the creation of initial error images with
the expected rms variances from photon statistics and read-out noise. For a
single spectrum:
where 
is the variance in the pixel [j] (
in
number of counts, ADU, --analogic to digital number--), g the gain of the
A/D converter (in 
/ADU), 
the number of counts in the
pixel [j] (after the bias-level subtraction), and 
is
the read-out noise (in ADU)
.
Some of the reduction steps that may have a non negligible effect in the index errors are flatfielding, geometrical distortion corrections, wavelength calibration, sky subtraction and rebinning of the spectra. Note that if error spectra were computed from the final number of counts in the reduced data frame, index errors would tend to be underestimated. The extra benefit of a parallel processing of data and error frames is the possibility of obtaining, at any time of the reduction, the variation in the mean S/N ratio produced by a particular reduction step. Under these conditions, it is possible to determine which parts of the reduction process are more sensitive to errors and even to decide whether some manipulations of the data images can be avoided, either because the resulting S/N ratio is seriously reduced and the benefit of the product insignificant, or because such manipulations become a waste of time.
A full error propagation in the reduction of spectroscopic data has been
previously implemented by González (1993), and it is also included in the
reduction package R-0.35exED0.85exuc-.35exmE
(Cardiel & Gorgas 1997).
To obtain errors on line-strength indices from the reduced data and error spectra, two different approaches can be followed. On one hand, analytical formulae to evaluate index errors as a function of the data and variance values in each pixel can be applied (González 1993). Another method is to simulate numerically the effect of the computed pixel variances in the index measurements (e.g. Cardiel et al. 1995). Both techniques are examined in the next sections.