Preventing, or redressing such confounding is called "controlling," and requires balancing out factors other than the exposure of interest between study groups- either when enrolling participants (i.e., randomization; stratification; etc)., or through statistical and analytical manipulations.
More manageable notation should allow and encourage analytical manipulation and investigation of models - and even formulation of models - where calculational difficulty has previously got in the way.
A geographic information system (GIS) provides an integrated set of tools that allow both the analytical manipulation and the visual representation of spatial data.
Now, advances in bioreactor technology, metabolic engineering, and analytical instrumentation are improving the production, manipulation, and scientific understanding of such remedies.
For the purposes of the present study, we were most interested in the depressive rumination sub- scale of this questionnaire because the items used in the manipulations of analytical and experiential thinking (e.g. Watkins & Teasdale, 2004) are based on the content of this sub-scale.
In Table 1, demographic, clinical and analytical characteristics of patients, as well as their therapeutic manipulations, have been summarized.
VAS happiness and despondency ratings were taken immediately pre and post the analytical and experiential manipulations (happiness: analytical pre: M=5.55, SD=1.73, post: M=5.48, SD=2.01; experiential pre: M=5.11, SD=1.84, post: M=5.41, SD=1.23; despondency: analytical pre: M=2.75, SD=1.77, post: M=2.92, SD=2.11; experiential pre: M=2.67, SD=1.83, post: M=2.97, SD=1.87).
The response of particles to acoustic forcing at gigahertz frequencies was studied by observation of manipulation and removal of individual particles, and by analytical and computational modeling of the mean acoustic removal forces.
Advanced Algebra and Analytical Geometry.
He's very thoughtful and analytical.
