A model-independent approach to the theory of experimental designs and a special discussion of bib. i general definition and designs with one or two block factors

Experimental designs are definded by introducing an assignment matrix Z. It is shown by block designs and double block designs that using Z or an operator on Z otherwise defined, well known designs can be got as special cases. Till now we didn' find an experimental design which could not be defined by our matrix Z. The definitions of properties of experimental designs can be given independently of the model of the statistical analysis. This is shown for the property of balance of block designs.     

Factorial and time course designs for cDNA microarray experiments

Microarrays are powerful tools for surveying the expression levels of many thousands of genes simultaneously. They belong to the new genomics technologies which have important applications in the biological, agricultural and pharmaceutical sciences. There are myriad sources of uncertainty in microarray experiments, and rigorous experimental design is essential for fully realizing the potential of these valuable resources. Two questions frequently asked by biologists on the brink of conducting cDNA or two-colour, spotted microarray experiments are 'Which mRNA samples should be competitively hybridized together on the same slide?' and 'How many times should each slide be replicated?' Early experience has shown that whilst the field of classical experimental design has much to offer this emerging multi-disciplinary area, new approaches which accommodate features specific to the microarray context are needed. In this paper, we propose optimal designs for factorial and time course experiments, which are special designs arising quite frequently in microarray experimentation. Our criterion for optimality is statistical efficiency based on a new notion of admissible designs; our approach enables efficient designs to be selected subject to the information available on the effects of most interest to biologists, the number of arrays available for the experiment, and other resource or practical constraints, including limitations on the amount of mRNA probe. We show that our designs are superior to both the popular reference designs, which are highly inefficient, and to designs incorporating all possible direct pairwise comparisons. Moreover, our proposed designs represent a substantial practical improvement over classical experimental designs which work in terms of standard interactions and main effects. The latter do not provide a basis for meaningful inference on the effects of most interest to biologists, nor make the most efficient use of valuable and limited resources.     

Augmented cellulase production by Bacillus subtilis strain MU S1 using different statistical experimental designs

The production of cellulase by Bacillus subtilis MU S1, a strain isolated from Eravikulam National Park, was optimized using one-factor-at-a-time (OFAT) and statistical methods. Physical parameters like incubation temperature and agitation speed were optimized using OFAT and found to be 40?°C and 150?rpm, respectively, whereas, medium was optimized by statistical tools. Plackett-Burman design (PBD) was employed to screen the significant variables that highly influence cellulase production. The design showed carboxymethyl cellulose (CMC), yeast extract, NaCl, pH, MgSO₄ and NaNO₃ as the most significant components that affect cellulase production. Among these CMC, yeast extract, NaCl and pH showed positive effect whereas MgSO₄ and NaNO₃ were found to be significant at their lower levels. The optimum levels of the components that positively affect enzyme production were determined using response surface methodology (RSM) based on central composite design (CCD). Three factors namely CMC, yeast extract and NaCl were studied at five levels whilst pH of the medium was kept constant at 7. The optimal levels of the components were CMC (13.46?g/l), yeast extract (8.38?g/l) and NaCl (6.31?g/l) at pH 7. The maximum cellulase activity in optimized medium was 566.66?U/ml which was close to the predicted activity of 541.05?U/ml. Optimization of physical parameters and medium components showed an overall 3.2-fold increase in activity compared to unoptimized condition (179.06?U/ml).