## A Handbook of Numerical and Statistical Techniques: With Examples Mainly from the Life SciencesThis handbook is designed for experimental scientists, particularly those in the life sciences. It is for the non-specialist, and although it assumes only a little knowledge of statistics and mathematics, those with a deeper understanding will also find it useful. The book is directed at the scientist who wishes to solve his numerical and statistical problems on a programmable calculator, mini-computer or interactive terminal. The volume is also useful for the user of full-scale computer systems in that it describes how the large computer solves numerical and statistical problems. The book is divided into three parts. Part I deals with numerical techniques and Part II with statistical techniques. Part III is devoted to the method of least squares which can be regarded as both a statistical and numerical method. The handbook shows clearly how each calculation is performed. Each technique is illustrated by at least one example and there are worked examples and exercises throughout the volume. |

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### Contents

STATISTICAL TABLES | 4 |

Errors mistakes and the arrangement of work | 14 |

Simple methods for smoothing crude data | 26 |

The area under a curve | 37 |

Finite differences interpolation and numerical differentiation | 44 |

Some other numerical techniques | 60 |

Probability statistical distributions and moments | 75 |

The normal and related distributions | 90 |

Fishers ztransformation table 12 31 1 | 200 |

Point and interval estimation | 210 |

Some special statistical techniques | 236 |

1S Simple linear regression and the method of least squares | 255 |

Curvilinear regression | 275 |

Multiple linear regression | 300 |

Nonlinear regression | 313 |

Appendix | 321 |

The common discrete distributions | 100 |

The Pearson system of probabilitydensity functions | 122 |

Hypothesis testing | 133 |

The upper 100a per cent points of the KolmogorovSmirnov distribution | 153 |

The upper 100a per cent points of the KruskalWallis distribution table | 180 |

A3 Students distribution | 327 |

334 | |

337 | |

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100a per cent 2-j per cent 95 per cent analysis of variance Balaam bivariate Brownlee calculate cent confidence limits cent point cent region chi-square distribution column Computation of test confidence interval correlation coefficient critical region curve degrees of freedom denote difference Draper and Smith equal example expected number F-distribution fitted values form of data formula Further reading Hoel 45 independent integer Johnson and Kotz Kendall and Stuart Kotz 47 lack-of-fit least squares lower 2-j matrix maximum likelihood estimate mean and variance median method of section negative binomial distribution Notation and statistical null hypothesis obtain 95 orthogonal polynomials parameter Point estimator Poisson distribution probability probability-density function quadratic random observation random variable reject the null residual mean square residual sum sample mean sample variance Simpson's rule Smith 19 smooth statistical model sum of squares test statistic test the null Total unit normal distribution variance a2 variance table vector zero

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Page xi - The expected value of the dependent variable for a given value of the. independent variable is, 3) For any given value of X, the observed y values are distributed independently and normally.