Statistical analysis sample size

The book is aimed at those who have to use statistics, but have no ambition to become statisticians per se. It avoids getting bogged down in calculation methods and focuses instead on crucial issues that surround data generation and analysis (sample size estimation, interpretation of statistical results, the hazards of multiple testing, potential abuses, etc.). In this day of statistical packages, it is the latter that cause the real problems, not the number-crunching. 

Vitha, M. F. Carr, P. W. A Laboratory Exercise in Statistical Analysis of Data, /. Chem. Educ. 1997, 74, 998-1000. Students determine the average weight of vitamin E pills using several different methods (one at a time, in sets of ten pills, and in sets of 100 pills). The data collected by the class are pooled together, plotted as histograms, and compared with results predicted by a normal distribution. The histograms and standard deviations for the pooled data also show the effect of sample size on the standard error of the mean. 

The role of quality in reliability would seem obvious, and yet at times has been rather elusive. While it seems intuitively correct, it is difficult to measure. Since much of the equipment discussed in this book is built as a custom engineered product, the classic statistical methods do not readily apply. Even for the smaller, more standardized rotary units discussed in Chapter 4, the production runs are not high, keeping the sample size too small for a classical statistical analysis. Run adjustments are difficult if the run is complete before the data can be analyzed. However, modified methods have been developed that do provide useful statistical information. These data can be used to determine a machine tool s capability, which must be known for proper machine selection to match the required precision of a part. The information can also be used to test for continuous improvement in the work process. 

However, since the data used in this study are subject to the limitations and uncertainties cited above, the results of this analysis represent only a very rough approximation of the national frequency distribution of indoor radon levels. EPA s national survey will seek to more accurately characterize this distribution through use of a larger sample size, a statistically based survey design, and consistent, quality assured sample collection and measurement procedures. 

Particle shape plays an important role in particle size determination. The simplest definition of particle size diameter is based on a sphere, which has a unique diameter. In reality, however, many particles are not well represented by this model. Figure 1 illustrates the variety of shapes that may be found in particle samples [1]. As the size of a particle increases, so does its tendency to have an irregular shape [2], complicating statistical analysis. Particle shape coefficients have been derived for different geometries [3], and various equivalent diame-... 

Sampling procedures are extremely important in the analysis of soils, sediments and sludges. It is essential to ensure that the composition of the portion of the sample being analysed is representative of the material being analysed. This fact is even more evident when it is conceded that the size of the portion of sample being analysed is in many modern methods of analysis extremely small. It is therefore essential to ensure before the analysis is commenced that correct statistically validated sampling procedures are used to ensure as far as is possible that the portion of the sample being analysed is representative of the bulk of material from which the sample was taken. 

Discussion This was the first study involving volunteers - four members of the laboratory staff who, with minimal baselines, were observed for 48 hours, or until effects appeared to have subsided. No statistical analysis was done with the data, due to the small sample size and the fact that this was essentially a range-finding study, designed to indicate the approximate doses required to produce moderate to severe incapacitation. 

Results on the refinement of protocols for sampling analysis are forthcoming in the report on the EPA/NBS workshop on monitoring. Additional work on statistical design is also in progress to find practical ways to reduce required sample size which in turn leads to reductions in cost and more efficiency in dealing with contractor release after abatement. 

Timing of any interim analysis Reason for sample size Power of clinical study Level of significance Criteria for termination of study Procedure for missing and imused data Reporting procedures for deviations from statistical plan... 

It is generally the case that when more complex statistical analysis strategies and designs are under consideration, standard sample size calculations are inadequate to cover them. In such circumstances simulation is often used to determine the t)rpe-I and type-II errors of the proposed studies for a given sample size. 

---