Statistical inference confidence levels

The experiments described here are principally diagnostic in nature where cellular biomass was significantly enhanced in bottles after resource (iron or light) amendment, relative to control (or other) treatments, we infer that algal growth rates in the control (or other) treatments were limited by a deficiency in that resource. The statistical significance of differences between mean values of parameters measured in different treatments were assessed using a two-tailed r-test for comparisons between two treatments, or a one-way analysis of variance (ANOVA) for comparisons between three or more treatments, at a confidence level of 95% (P = 0.05). 

By definition, the experimental unit is the smallest unit randomly allocated to a distinct level of a treatment factor. Note that if there is no randomization, there is no experimental unit and (in nearly all cases) no experiment. Although it is possible to perform experiments without randomization, it is difficult to do well, and risky unless the experimental system is very well understood (7). Randomization is important for several reasons. Randomization changes the sources of bias into sources of variation in general, a noisy assay is better than a biased assay. Further, randomization allows estimates of variation to represent variation in the population this in turn justifies statistical inference (standard errors, confidence intervals, etc.). A common practice in cell-culture bioassay is to rotate among a small collection of layouts rather than use random allocation. Whereas rotation among a collection of layouts is certainly better than a fixed layout, it is both possible and practical to use carefully structured randomization on a routine basis, particularly when using a robot. 

Ultimately, an attorney will seek technical opinions of the expert on issues in the case. Often sought are opinions with a reasonable degree of scientific and engineering certainty. In a legal sense, this infers a certainty of 51 % or greater. The question is whether the expert is more sure than not sure on an issue. It is not certainty in a statistical sense, where one uses a 95% or similar statistical confidence level in drawing inferences or conclusions from data. 

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