Efficiency in Experimental Design

Efficient experimental design is intended to provide the maximum amount of information in the fewest number of trials. Suppose we have three different unknown solutions of acid, designated A, B, and C. If we titrate each one once with base, we find its concentration, but have no estimate of uncertainty. If we titrate each solution three times, for a total of nine measurements, we would find each concentration and its standard deviation. 

For each experiment, mmol of base consumed equals mmol of acid in the mixture  

Excel finds the least-squares slopes in row 12 and their uncertainties in row 13. These slopes are the molarites [C], [B], and [A], in reverse order. So. for example, cells C12 and C13 tell us that the molarity of acid C is 0.8099 0.0062 M. 

We require at least n equations to solve for n unknowns. In this example, we have five equations (7-20), but just three unknowns ([A], [B], [C]). The two extra equations allow us to estimate uncertainty in the unknowns. If you do more experiments, you will generally decrease the uncertainty in concentration. An efficient experimental design with five experiments leaves us with more uncertainty than if we had done nine experiments. However, we have cut our effort nearly in half with the efficient design. 

Acids could be delivered by transfer pipets whose tolerances are given in Table 2-4. So 2 mL means 2.000 0.006 mL 

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Human umbilical cord tissue is relatively readily available in most locations, and the ability to fragment it into multiple similar carriers allows for replicates and statistical efficiency in experimental design. Ethical clearance and informed consent for its use in experimentation are required. 

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