The degree of correlation between two parameters can visually be estimated by plotting them. This expression assumes that the quantities have normal distribution. If non-linear relations are expected, the variables are transformed into a linear domain by means of standard mathematical functions. Since the angle is obtained from the axial ratio, a cosine transformation is used to achieve a homogenous variance. Unfortunately, it is not always possible to obtain both a linear relation and homogeneity of variance with the same transformation.
All methods assume that the single data points are unbiased and uncorrelated.
Great care must be taken to assure that this is fulfilled. If this is not the case, significant systematic errors may be introduced in the estimates. A standard example is magnitude limited samples which may be affected by the Malmquist bias.