Acta Geodaetica, Geophysica et Montanistica Hungarica 24. (1989)

3-4. szám - Hajagos B.–Steiner F.: Measure of the linear dependence

418 В HAJAGOS and F STEINER strongly simplifying assumptions. Concerning these simplifications it is normally avoided to emphasize (especially in practical applications) that the mea­sure computed from the set of data (x^, y^), containing n elements from the distributions and ^ , is an adequate measure only if certain conditions are fulfilled, e.g. if the dependence is a linear one (x and ÿ are the corresponding algebraic averages). The classics of mathematical statistics (Cramér 1946, Rényi 1971) do not forget to tell this (and Rényi even proposes a generalization which, unfortunately, did not prove useful in practice). The general use of Eq. (1) is connected with the comfortable property that its value lies between +1 and -1 and this property remains in case of gross errors, too. A value near zero means independence. The possiblity that the value determined from Eq. (1) and lying between +1 and -1 can be very far from a realistic value is presented by a simple example in Fig. 1. The measured values x^ and y^ have both an expected value of +100 and unit scatter, both are distributed according to the Gaussian law and they are independent. From the 100 sample of these values one has a gross error, resulting in a pair of values (0, 0) (let us say due to an error in the power supply). For this sample Eq. (1) does not yield a value near zero as sign of the independence - what should be expected as the values of x and y are indepen­dent - but the resulting coefficient is +0.989, indicating a very close connection. The expression in Eq. (1) is therefore far from being resistant (i.e. it is very sensitive for gross errors), that is why the reliability of coefficients computed according to Eq. (1) may be questioned even in cases much less accentuated than in the example mentioned. Some further remarks follow about the restricted

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