## Designing Quantitative Experiments: Prediction AnalysisEarly in my career I was given the task of designing a sub-critical nuclear reactor facility that was to be used to perform basic research in the area of reactor physics. We planned to run a series of experiments to determine fundamental parameters related to the distribution of neutrons in such s- tems. I felt that it was extremely important to understand how the design would impact upon the accuracy of our results and as a result of this - quirement I developed a design methodology that I subsequently called prediction analysis. After working with this method for several years and applying it to a variety of different experiments, I wrote a book on the subject. Not surprisingly, it was entitled Prediction Analysis and was p- lished by Van Nostrand in 1967. Since the book was published over 40 years ago science and technology have undergone massive changes due to the computer revolution. Not - ly has available computing power increased by many orders of magnitude, easily available and easy to use software has become almost ubiquitous. In the 1960's my emphasis was on the development of equations, tables and graphs to help researchers design experiments based upon some we- known mathematical models. When I reconsider this work in the light of today's world, the emphasis should shift towards applying current techn- ogy to facilitate the design process. |

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### Contents

1 | |

Chapter 2 STATISTICAL BACKGROUND | 19 |

Chapter 3 THE METHOD OF LEAST SQUARES | 47 |

Chapter 4 PREDICTION ANALYSIS | 90 |

Chapter 5 SEPARATION EXPERIMENTS | 128 |

Chapter 6 INITIAL VALUE EXPERIMENTS | 157 |

Chapter 7 RANDOM DISTRIBUTIONS | 186 |

205 | |

209 | |

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### Common terms and phrases

a1 and a2 ak's amplitude analyzed approaches approximately assume assumption average value Ceres chemostat coefficient computed value consider correlation count rate data points decreases defined degrees of freedom dependent design an experiment determine dimensionless groups effect Equa equal example experiments based exponential fractional uncertainty Gamma Distributions increases independent variable initial value inverse matrix kurtosis least squares analysis linear regression mathematical model matrix mean value method of least nonlinear nonlinear regression number of counts number of data observed obtained orbit orthogonal Poisson distribution Poisson statistics predicted value prediction analysis prior estimates probability proposed experiment range REGRESS program shown in Figure simulation solution standard deviation standard normal distribution straight line systematic errors tion true value uncertainties associated uncorrelated unit weighting unknown parameters values of a1 vector x1 and x2 xmax xmin zero σ σ