Quantitative real-time PCR represents a highly sensitive and powerful technique for the quantitation of nucleic acids. It has a tremendous potential for the high-throughput analysis of gene expression in research and routine diagnostics. However, the major hurdle is not the practical performance of the experiments themselves but rather the efficient evaluation and the mathematical and statistical analysis of the enormous amount of data gained by this technology, as these functions are not included in the software provided by the manufacturers of the detection systems. In this work, we focus on the mathematical evaluation and analysis of the data generated by quantitative real-time PCR, the calculation of the final results, the propagation of experimental variation of the measured values to the final results, and the statistical analysis. We developed a Microsoft Excel-based software application coded in Visual Basic for Applications, called Q-Gene, which addresses these points. Q-Gene manages and expedites the planning, performance, and evaluation of quantitative real-time PCR experiments, as well as the mathematical and statistical analysis, storage, and graphical presentation of the data. The Q-Gene software application is a tool to cope with complex quantitative real-time PCR experiments at a high-throughput scale and considerably expedites and rationalizes the experimental setup, data analysis, and data management while ensuring highest reproducibility.

Processing of gene expression data generated by quantitative real-time RT-PCR.

A Numerical Study

Wheaton, J. M., Brasington, J., Darby, S. E., Sear, D. A. (2010). Accounting for uncertainty in DEMs from repeat topographic surveys: improved sediment budgets. Earth Surface Processes and Landforms, 35, (2), 136-156.

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Accounting for uncertainty in DEMs from repeat topographic surveys: improved sediment budgets

The National Institute of Standards and Technology (NIST) and the Pacific Northwest National Laboratory (PNNL) are each creating quantitative databases containing the vapor-phase infrared spectra of pure chemicals. The digital databases have been created with both laboratory and remote-sensing applications in mind. A spectral resolution of approximate, equals 0.1 cm(-1) was selected to avoid degrading sharp spectral features, while also realizing that atmospheric broadening typically limits line widths to 0.1 cm(-1). Calculated positional (wave- number, cm(-1)) uncertainty is /=9) path length-concentration burdens and fitting a weighted Beer's law plot to each wavenumber channel. The two databases include different classes of compounds and were compared using 12 samples. Though these 12 samples span a range of polarities, absorption strengths, and vapor pressures, the data agree to within experimental uncertainties with only one exception.

Gas-Phase Databases for Quantitative Infrared Spectroscopy

Correlation and regression are different, but not mutually exclusive, techniques. Roughly, regression is used for prediction (which does not extrapolate beyond the data used in the analysis) whereas correlation is used to determine the degree of association. There situations in which the x variable is not fixed or readily chosen by the experimenter, but instead is a random covariate to the y variable. This paper shows the relationships between the coefficient of determination, the multiple correlation coefficient, the covariance, the correlation coefficient and the coefficient of alienation, for the case of two related variables x and y. It discusses the uses of the correlation coefficient r, either as a way to infer correlation, or to test linearity. A number of graphical examples are provided as well as examples of actual chemical applications. The paper recommends the use of z Fisher transformation instead of r values because r is not normally distributed but z is (at least in approximation). For eithe...

The Correlation Coefficient: An Overview

Students in a science or engineering curriculum ought to be introduced early to the requirement that a meaningful measurement result should always be accompanied by a statement of its uncertainty. This book has been written specifically with this objective in mind. That the first edition has been successful in doing this is attested to by its popularity with both faculty and students, and its translation into six languages. This book is not a statistics text - nor was it intended to be - but an introdution to the mathematics required for the analysis of measurements at the level of a first-year laboratory course. Part 1 begins with uncertainty as a qualitative concept and builds slowly, using many numerical examples and exercises for the student, to develop methods for quantifying uncertainty, and ultimately relating it to the standard deviation of a statistical distribution. Along the way, Taylor develops the rules for expressing and combining (`propagating') uncertainties, and introduces the student to the gaussian (normal) distribution and some of its properties. Part 2 covers, with somewhat more mathematical rigor, specific topics such as data rejection criteria, the binomial and Poisson distributions, covariance and correlation, least-squares fitting, and the chi-squared test. I was not familiar with the first edition, and from a quick scan of the Preface I looked forward to reading this book and learning something about the state of statistical analysis in first-year university texts today. I was disappointed (in part with what the level of the book implies about the sad state of preparation of today's students). Although there are now two ISO publications ( International Vocabulary of Basic and General Terms in Metrology (VIM) and Guide to the Expression of Uncertainty in Measurement (GUM), Geneva, 1993), Taylor makes no mention of either, and never gives a formal definition of `uncertainty' (although he ultimately associates `random uncertainty' with the standard deviation of a gaussian distribution). The book also does not clearly define `error', or the distinction between error and uncertainty. The important point, that the `propagation of uncertainty' is additive in terms of variances is valid for any distributions with finite variance, is not emphasized; instead Taylor restricts the discussion solely to the normal distribution and or those that can be approximated by it. I also find it unfortunate that the book does not clearly distinguish between the variance of a sample , the variance of a distribution , and the sample estimate of the variance of the distribution ( or ). Instead, he accepts the fact that formulas for the variance with either N or N - 1 dividing the sum of the squares of the deviations from the mean exist in the literature and concludes simply: `Nevertheless, you need to be aware of both definitions. In the physics laboratory, using the more conservative... def- inition... is almost always best.' In spite of these shortcomings, the book is a significant contribution to a student laboratory reading list, and it is written at a level that facilitates a self-study program. It has an important message to deliver and it appears to be delivering it well.

E Richard Cohen

Papers

An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements