By Ian Birnbaum

ISBN-10: 0333261127

ISBN-13: 9780333261125

ISBN-10: 1349164666

ISBN-13: 9781349164660

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**Example text**

The standard deviation does not change its value with a change of origin, but this is because it is a second order measure concerned with the distances between variables, which, of course, are independent of origin. ) The mean is not invariant to the transformations preserving the relationships on ordinal variables. As a very simple example, a variable with values 0, I, 3 has a mean lying between I and 3. The same variable with new values 0, 6, 7 has a mean lying between 0 and 6. Thus order, which must remain invariant, is not preserved for the mean.

L8 the normal equations for the standardised path regression coefficients (or path coefficients). l6 similarly only the covariations are required. l8 from its standardised equivalent, by treating the sample covariance (or correlation) between Uk and the explicit variables as zero. This can be used as a rule of thumb to obtain the normal equations.

Further, x2 and XJ affect the variance of X 1 in a different way from the variance of X4. It follows that the ratio a 1 2 ja4 2 is population-specific. Hence, comparing p 41 2 in two populations depends in part on the variance of implicit causes in each of the two populations. Similarly, the ratio P41 2 IP42 2 depends on a 1 2 /a 2 2 , and the same objection arises. a2 2 depends in part on the variance of U2, whereas a 1 2 does not. Furthermore, X 3 and X4 have differential 'effects' on the variance of X1 and X2.

### An Introduction to Causal Analysis in Sociology by Ian Birnbaum

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