Before the inherent variability of the test-animals was appreciated, assays
were sometimes carried out on as few as three rabbits: as one pharmacologist
put it, those were the happy days.-- E. C. Fieller, Suppl., J. Royal Stat. Soc.,
vol. vii, 1940-41: p. 3.

Some definitions: universe, frame, ideal bowl, random sampling.
This chapter will contain some basic theory for simple designs and for
further development in later chapters. There will be a frame, which is
to be thought of as a list of the N sampling units which constitute the
universe. A list is one kind of frame, but the frame is often a file of
cards, a map or set of maps, or verbal descriptions--any device by which
the N sampling units are definitely identifiable one by one. In sampling
a file of cards, the cards themselves constitute the frame.

For ease in classroom demonstrations, and for simplicity in discourse,
the identification (e.g., name and address) of every sampling unit will
be written on a poker chip, and the N physically similar poker chips
will be placed in a bowl, the ideal bowl. One or more of the chips is to
be drawn out of the bowl at random; the corresponding sampling units
constitute the sample. The identifying information is necessary so that
if a particular chip is drawn into the sample, an interviewer may be
sent to the corresponding sampling unit to determine its population. In
industrial sampling, the unit (manufactured article) is usually brought
to the inspector who determines its quality, which in this text will be
called the population of the unit (see Table 1 on p. 84 ).

Associated with each sampling unit (each chip) is a certain P-value
or probability of being drawn into the sample. The P-values will corre-
spond to some specific procedure of sampling. In the theory to be
developed in this book, the P-values will all be equal within any bowl. ¹
It is not to be inferred, however, that P-values must always be equal:
some of the recent advances made by Neyman ² and Hansen and Hurwitz
³, ⁴ have involved unequal probabilities (e.g., sampling with proba-

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