1 Introduction

One of the most important constraints on the structure of quasars is variability. Short term variations set limits on the size of the emitting region, and differences in the nature of the variation in the X-ray, optical and radio domains give clues to the underlying structure. Variations on longer timescales of a few years are not so easily accounted for by the current black hole paradigm, and microlensing has been put forward as an alternative explanation for the observations. Although the most extensive monitoring of quasar variability has been done in optical wavebands, there is still little consensus even over the broad picture. One of the first problems is to parametrise the variation in such a way that it can be compared with models, or even more general expectations. The timescale of variation and the amplitude are the two parameters which have been mostly studied, although some authors have succeeded in confusing the two. This typically involves claiming that in a short run of data, objects varying on a short timescale will achieve a larger amplitude than those varying on a longer timescale, and so amplitude can be taken as an (inverse) measure of timescale (Hook et al. [1994]).

In this paper we shall confine our attention to the correlation of amplitude with other parameters. Amplitude is an easy parameter to measure, and involves none of the difficulties inherent in estimating timescale of variation. There are modes of variability in which some uncertainty will be introduced by the length of the run of observations, but this is a problem which can arise in any time series analysis. Most attention has so far been given to possible correlations of amplitude with redshift or luminosity (e.g. Trevese et al. [1989]; Giallongo et al. [1991]; Hook et al. [1994]; Cristiani et al. [1996]), but even in such straightforward situations there has been little agreement.

The reasons for the lack of consensus are not easy to understand, but it is clear that any effect which is present is not large compared with the cosmic scatter in the data, which in the case of amplitude appears to be about one magnitude, much larger than any photometric errors. Perhaps the most likely cause of disagreement is in the selection of samples for analysis. In order to obtain a meaningful measure of correlation it is essential that unbiassed samples are used, and that they cover a large range of redshift and luminosity. In this paper particular attention is paid to the sample selection process, and by extending the analysis to high redshifts the baseline for the measurement of correlations is greatly extended over earlier samples.