Assessing the contributions of individual components in multi-component interventions poses complex challenges for prevention researchers. We review the strengths and weaknesses of designs and analyses that may be useful in answering three questions: (1) Is each of the individual components contributing to the outcome? (2) Is the program optimal? and (3), Through what processes are the componen...

Box and Hunter (1961) made an important observation that any fractional factorial design of resolutionR has the property that when projected onto anyR 1 factors it becomes a full factorial design. This has a signi cant implication for statistical analysis. We observe that the Plackett-Burman and related designs have a hidden projection property with an analogous implication for the analysis. Be...

In k 2 experimental design, the classical fractional factorial designs, the Plackett-Burman designs and the Taguchi orthogonal-array designs all require, with few exceptions, n 2 test conditions, for some k n ≤ . Tsao and Wibowo (2005) pointed out that when only m of the k 2 effects/interactions are non-zero, only m test conditions are required for their estimation. Given the identities of m pr...

Fractional factorial designs are widely used for designing screening experiments. Nonregular fractional can have better properties than regular designs, but their construction is challenging. Current research on the of nonregular focuses two-level designs. We provide a novel class multilevel by permuting levels develop theory illustrating how be permuted without computer search and accordingly ...

Tests for dispersion effects in replicated two-level factorial experiments assuming a location-dispersion model are presented. The tests use individual measures of dispersion which remove the location effects and also provide an estimate of pure error. Empirical critical values for two such tests are given for two-level full or regular fractional factorial designs with 8, 16, 32 and 64 runs. Th...

Every fraction is a union of points, which are trivial regular fractions. To characterize non trivial decomposition, we derive a condition for the inclusion of a regular fraction as follows. Let F =