## Basic Statistical Methods and Models for the SciencesThe use of statistics in biology, medicine, engineering, and the sciences has grown dramatically in recent years and having a basic background in the subject has become a near necessity for students and researchers in these fields. Although many introductory statistics books already exist, too often their focus leans towards theory and few help readers gain effective experience in using a standard statistical software package. Designed to be used in a first course for graduate or upper-level undergraduate students, Basic Statistical Methods and Models builds a practical foundation in the use of statistical tools and imparts a clear understanding of their underlying assumptions and limitations. Without getting bogged down in proofs and derivations, thorough discussions help readers understand why the stated methods and results are reasonable. The use of the statistical software Minitab is integrated throughout the book, giving readers valuable experience with computer simulation and problem-solving techniques. The author focuses on applications and the models appropriate to each problem while emphasizing Monte Carlo methods, the Central Limit Theorem, confidence intervals, and power functions. The text assumes that readers have some degree of maturity in mathematics, but it does not require the use of calculus. This, along with its very clear explanations, generous number of exercises, and demonstrations of the extensive uses of statistics in diverse areas applications make Basic Statistical Methods and Models highly accessible to students in a wide range of disciplines. |

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### Contents

Introduction | 1 |

Classes of Models and Statistical Inference | 19 |

Topic Exponential distributions | 32 |

Sampling and Descriptive Statistics | 47 |

2 Descriptive Statistics of Location | 61 |

3 Descriptive Statistics of Variability | 67 |

Topic Scatter plots | 74 |

Topic The empirical cumulative distribution function | 80 |

Theorem Distribution of independent normal sums | 141 |

2 Distribution of Sample Percentiles | 147 |

Topic Elementary confidence interval construction | 155 |

5 Confidence Limits and Interval for Binomial? | 162 |

6 Comparing Estimators | 169 |

Testing Hypotheses | 181 |

2 Some Commonly Used Statistical Tests | 187 |

Topic Independent twosample Z tests | 193 |

Survey of Basic Probability | 89 |

Topic Formation of events from other events | 95 |

Theorem Bonferroni Inequalities | 102 |

Theorem Corollary to Theorem 4 I ordered sampling | 108 |

Definition Conditional probability of A given B | 114 |

5 Statistical Independence | 121 |

6 Systematic Approach to Probability Problems | 123 |

Definition Variance and standard deviation | 131 |

### Common terms and phrases

95 level confidence ahout ANOVA answer approximately assumed assumptions binomial coefficient binomial distribution blood pressure box plots Calc Cauchy Central Limit Theorem choose chosen cl c2 column cl command compute confidence limit Definition denoted descriptive statistics determine distribution function distribution with mean elements equation error estimate event Example expect experiment Figure formula frequency interpretation given graph histogram independent two-sample integer level confidence interval macro measurements median mice Minitab Monte Carlo normal random variables null hypothesis observations order statistics P-Value pair of dice parameters percentile plot Poisson Poisson distribution population mean Practice Exercises predictions Prob probability density probability distribution problems proportion quantity random sample reasonable regression replacement rows S0BO sample correlation coefficient sample mean sample space sample standard deviation session window simulation specified standard normal distribution statistically independent success Suppose Topic tosses treatment trials variance Wilcoxon