## Statistical Models for Proportions and ProbabilitiesMethods for making inferences from data about one or more probabilities and proportions are a fundamental part of a statistician’s toolbox and statistics courses. Unfortunately many of the quick, approximate methods currently taught have recently been found to be inappropriate. This monograph gives an up-to-date review of recent research on the topic and presents both exact methods and helpful approximations. Detailed theory is also presented for the different distributions involved, and can be used in a classroom setting. It will be useful for those teaching statistics at university level and for those involved in statistical consulting. |

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### Contents

1 | |

2 Single Probability | 9 |

3 Several Proportions or Probabilities | 19 |

4 Multivariate Hypothesis Tests | 41 |

5 Logarithmic Models | 58 |

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### Common terms and phrases

American Statistician animals asymptotically Normal Bernoulli trials capture-recapture Chap Chi-square confidence interval contingency table deviance discrete distributions discussed exact test example F-distribution G. A. F. Seber given H0 is true Hypergeometric distribution hypothesis H0 hypothesis testing independent Binomial distributions inference inverse sampling large sample likelihood function likelihood-ratio test linear models lists log likelihood log-linear model logistic models matrix maximum likelihood estimates method Models for Proportions Multi-hypergeometric distribution Multinomial distribution multiple-recapture Multivariate npij obtain odds ratio p-value parameters Pearson’s Poisson population pr(X probability function probability of getting Proportions and Probabilities random variable regression model residuals sampling fraction sampling without replacement score statistic score test Sect simple random sample Simultaneous confidence intervals so-called SpringerBriefs in Statistics test H0 test statistic trials two-sided unbiased estimator var(Y vector Wald interval Wald test