By Rao C.R., Krishnaiah P.R.
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Some examples of characteristics amenable to this approach are: (i) age; the phenomenon of stating one's age in round numbers (30 or 35 rather than 33), called 'age heaping', should be discussed; (ii) education; the phenomenon of exaggerating one's education should be mentioned; (iii) having smoked marijuana; the respondent may not want to give a true answer; other examples of 'sensitive' topics may be discussed as well; and (iv) size of farm; again, rounding may occur. For many other characteristics, the approach involving a 'true value' is less suitable, or not suitable at all, as a basis for defining measurement error.
I , ~ _ 1 in I N . ~ . S l ~ i , il, s 2 ~ i l , i2 . . , S m ~ i,,_ ~, j. This 'connectedness' is an 'equivalence relation' which splits Iu into 'equivalence classes' U~ . . . U k, say, called the 'components' of I u under a design p (say). If k = 1, than p is a 'connected design' implying that every pair of labels in I u is 'connected'. j), called C-matrix with such that (i) C is symmetric, (ii) C~j <~ O, Vi ¢ j . (if) Zj Co = 0, Vi. Suppose for a design p, 5e is partitioned into ~ (r = 1, .
ArM; (ii) the clusters are of equal sizes: N l . . . Nz . . . N M = N o. Many textbooks begin the presentation of the theory by considering clusters of equal size, and then proceed to the case of clusters of unequal sizes. My suggestion is to reverse this order: having presented theory for the case of clusters of unequal sizes, the theory for the case of clusters of equal size follows directly/simply by substituting N O for the N t in the formulas for the general theory. In Section 3, some general theory will be presented for simple random sampling, when the clusters are of unequal sizes.