Statistical Methods in Medical Research 4ed

336 Modelling continuous data
the investigator is clearly interested in differences between groups in the mean
value of y, after correction for x, and not in the reverse problem. Occasionally,
when x and y have a symmetric type of relation to each other, as in §11.2, both of
the analyses of covariance (of y on x, and of x on y) will be misleading. Lines
representing the general trend of a functional relationship may well be coincident
(as in Fig. 11.8), and yet both sets of regression lines are non-coincident. Here the
difficulties of §11.2 apply, and lines drawn by eye, or the other methods discussed
on p. 319, may provide the most satisfactory description of the data. For a fuller
discussion, see Ehrenberg (1968).
The analysis of covariance described in this section is appropriate for data
forming a one-way classification into groups. The method is essentially a combination
of linear regression (§7.2) and a one-way analysis of variance (§8.1).
Similar problems arise in the analysis of more complex data. For example, in the
analysis of a variable y in a Latin square one may wish to adjust the apparent
treatment effects to correct for variation in another variable x. In particular, x
may be some pretreatment characteristic known to be associated with y; the
covariance adjustment would then be expected to increase the precision with
which the treatments can be compared. The general procedure is an extension of
that considered above and the details will not be given.
The methods presented in this and the previous section were developed
before the use of computers became widespread, and were designed to simplify
y
Fig. 11.8 Scatter diagram showing a common trend for two groups of observations but with noncoincident
regression lines. (Ð Ð) Regression of y on x; (± ± ±) regression of x on y.
x