# Alternate Sampling Designs

In the case above, we might decide that the number of random numbers that was going to be discarded was too large. We might select an alternate sampling scheme, in which we ignored the separate shelves. If we estimated that there were no more than 7,000 books, then we would select random numbers in the range 1 to 7,000 and draw the sample by counting our way along the shelves. This would be more effort in finding the books, but by discarding fewer numbers might make the study easier. If we did not expect the order of the books to have any biasing effect, we might dispense with random sampling and take a fractional sample. If we wanted a sample size of 200 we would simply select every thirty-fifth book. (because 7,000 divided by 200 is 35.) To be slightly more secure in the randomness of the sample, we might draw one random number between 1 and 35 and use this as our first book rather than starting with the 35th book from the beginning.
The selection of books in the example above could offer a temptation to the inattentive researcher. One might argue that counting books was tedious and suggest instead that the books be selected by measurement. One could draw a random shelf number, a number of inches between zero and thirty five (assuming 36 inch shelves) and then a number of sixteenths of an inch between zero and fifteen. Such a sampling technique would be unbiased only if all the books were the same thickness; otherwise, fat books would have a greater chance of being selected and this would bias the sample.

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