Experiments that might require a handful of real-number measurements (variables data) could need hundreds or more attribute data for comparable power, i.e., the ability to determine whether an experiment improves performance over that of a control. Sample sizes needed for ANSI/ASQ Z1.4 (for inspection by attributes) are similarly much larger than sample sizes for ANSI/ASQ Z1.9 (for inspection by variables).

One application of attribute data is the estimation of the nonconforming fraction (p) from a process. The binomial distribution is the standard model in which p is the probability that each of n items will or will not have a certain attribute (such as meeting or not meeting specifications). The probability p is assumed to be identical for every item in the population; that is, every item has the same chance of being nonconforming. In addition, the sample n is assumed to come from an infinite population. That is, removal and inspection of an item does not change the probability that the next one will have the attribute in question.

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