We survey combinatorial interpretations of some dozen identities for the double factorial such as, for instance, (2n− 2)!! + ∑n k=2 (2n−1)!!(2k−4)!! (2k−1)!! = (2n − 1)!!.

Factorial experiments are widely used to assess the marginal, joint, and interactive effects of multiple concurrent factors. While a robust literature covers design analysis these experiments, there is less work on how handle treatment noncompliance in this setting. To fill gap, we introduce new methodology that uses potential outcomes framework for analyzing 2K factorial with any number This b...

Because of complex interactions among the components of PCR and the wide and increasing variety of applications in which this technique is used, optimization is necessary for every reaction. Here we describe the use of experimental design techniques (2k fractional factorial design and central composite design) to attain easier, quicker and cheaper PCR optimization of DNA from blood spots. By de...