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The paper makes a few comments on the characterizations of the log-change index numbers, and then builds up a link between the log-change indexes and the factorial indexes (Stuvel's indexes). It is also suggestedinter alia that log-change index numbers tend to ignore the effect of interaction between price and quantity (consumption) on the expenditure, in contrast to what is admitted by the factorial model.

White and Hultquist (1965) developed a method of combining finite fields mapped into a finite commutative ring to provide confounding plans for mixed factorial experiments where the numbers of the levels of factors have to be prime or the power of a prime. This paper extends their procedure to cover mixed factorials where the numbers of levels of factors need to be relatively prime, and not necessarily all prime, thus covering a wider range of mixed factorial experiments amenable to the traditional way of analysis of variance suggested by White and Hultquist.

This paper examines what of the Eichhorn-Voeller axioms are satisfied by the multilateral index numbers based on the factorial approach. Finally, concerning the overall performance of the system, a pertinent observation is made strengthening its dependability as a practical guide.

It has been shown in this note how “index numbers” could be constructed and used for expressions for the main effects in case of 2 n -factorial experiments. Such indexes satisfy the tests basic in the theory of index numbers and are easy to calculate. The factorial combinations which get involved in these indexes constitute a special kind of meaningful fractional replicates. As the fractions are small, such replicates may be conveniently used for experimental purposes, and index numbers readily constructed to indicate the trend of main effects. These index formulae may also be taken over to econometric fields for use as multi-dimensional indexes.

Let v objects be weighed in combinations of k at a time (k

In [1] the problem of singular weighing designs was cast in the framework of a reflexive generalized inverse, and it was shown how a singular design could be augmented to secure maximized efficiency. This note proves, in the same context, a theorem which may be called an analog of Price's Theorem, R. 16, in respect of the generalized inverse used in [1].

In [1], the problem of singular weighing designs was cast in the framework of a reflexive generalized inverse, and it was shown how a singular design could be augmented to secure maximized efficiency. The procedure of augmentation, as given in [1], was based on inspection and trial. Here, an attempt has been made to treat the augmentation procedure on an analytical basis.