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ELEMENTARY STATISTICAL METHODS

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The purpose of this book is to acquaint the reader with the increasing number of applications of statistics in engineering and the applied sciences. It can be used as a textbook for a first course in statistical methods in Universities and Polytechnics. The book can also be used by decision makers and researchers to either gain basic understanding or to extend their knowledge of some of the most commonly used statistical methods. Our goal is to introduce the basic theory without getting too involved in mathematical detail, and thus to enable a larger proportion of the book to be devoted to practical applications. Because of this, some results are stated without proof, where this is unlikely to affect the reader’s comprehension. However, we have tried to avoid the cook-book approach to statistics by carefully explaining the basic concepts of the subject, such as probability and sampling distributions; these the reader must understand. The worst abuses of statistics occur when scientists try to analyze their data by substituting measurements into statistical formulae which they do not understand.
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... If p is the proportion of observations in a random sample of size n that belongs to a class of interest, then an approximate 100(1 -)% confidence interval of the proportion p of the population that belongs to this class is (see Ofosu & Hesse, 2011) Exercise 2(b) 1. A researcher found that 66% of a sample of 14 infants had completed the hepatitis B vaccine series. ...
... In many situations we want to know whether we can conclude that a set of observations constitute a random sample from an infinite population. Test for randomness is of major importance because the assumption of randomness underlies statistical inference (see Ofosu & Hesse, 2011 ...
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A statistical method is called non-parametric if it makes no assumption on the population distribution or sample size. This is in contrast with most parametric methods in elementary statistics that assume that the data set used is quantitative, the population has a normal distribution and the sample size is sufficiently large. In general, conclusions drawn from non-parametric methods are not as powerful as the parametric ones. However, as non-parametric methods make fewer assumptions, they are more flexible, more robust, and applicable to non-quantitative data. This book is designed for students to acquire basic skills needed for solving real life problems where data meet minimal assumption and secondly to beef up their reading list as well as provide them with a “one shop stop” textbook on Nonparametric.
... They also take charge of quality control issues in manufacturing and ensuring quality and dependability of product. In the health sector, they are responsible for studying and improving the efficiency of delivery systems and practices (Ofosu and Hesse, 2011). Statistical knowledge is required in many areas of life to enable one to understand the world around and also to make accurate decisions in life (Cimpoeru and Roman, 2018). ...
... The test statistic is given by (see Cramér (1946) and Birch (1964) It can also be shown that, for large n, the statistic H has an approximate chi-square distribution with (r -1)(c -1) degrees of freedom if 0 H is true (see Ofosu and Hesse (2011)). Therefore, we would reject the hypothesis of independence if the observed value of the test statistic H is greater than the critical value 2 ...
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In this paper, data on road traffic casualties by age groups, from 2009 to 2013, will be used. Using published road traffic casualty statistics from the National Road Safety Commission of Ghana, a 2  8 contingency table is used to determine whether road traffic casualty and age group are independent. A one factor analysis of variance tests shall be used to conduct a comparative analysis of the rate of road traffic fatalities per 100 casualties across the various age groups in Ghana. A multiple comparison test, using the Fisher least significance difference (LSD) method, shall be conducted to determine which pairs of age groups are significantly different. The study will show that road traffic casualty is not independent of age group. The analysis of variance will show that there are significant differences in road traffic fatality indices (fatality per 100 casualties) among various age groups in Ghana. The risks of dying in a road traffic accident among children under 6 years and older population who are over 65 years are both significantly higher than those of other age groups. This points to the fact that, although smaller number of children under 6 years and older population who are over 65 years die in road traffic accidents each year, more and more people as a proportion of the recorded number of casualties, are being killed through road traffic accidents among these two categories of age groups. Thus, the probability of being killed in a fatal road traffic accident is significantly high in each of these two age groups.
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This book began many years ago as lecture notes for students at King Saud University in Saudi Arabia and later at the Methodist University College Ghana. Students in the third and fourth years of their undergraduate study, as well as those taking MSc courses, have used draft versions of the chapters, which have been subsequently revised and enriched. Although some previous knowledge of basic statistical methods is assumed, yet, the coverage in this book has been made very comprehensive to provide quick revision to the necessary basic concepts wherever required. The book contains twelve chapters. Chapter 1 provides useful means of revising the normal, χ² and F distributions, which are used frequently in the subsequent chapters. Chapters 2, 3, 4 and 5 present the basic ideas of point estimation. Readers are advised to approach these topics gradually, and allow them time to digest before attempting complicated exercises. Chapter 6 covers interval estimation while Chapters 7 and 8 cover hypothesis testing and the likelihood ratio test, respectively. Chapters 9 and 10 deal with single-factor and multifactor experiments, respectively. The notions of randomization, blocking, factorial designs, and interactions are emphasized. Chapter 11 presents the concept of correlation between variables and introduces the principles of regression in the form of simple linear regression. Chapter 12 then presents multiple linear regression, with extensive coverage on applications of matrix algebra in multiple regression.
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Moment tests, combinations of moment tests, and three other simple tests of normality are compared to the Shapiro-Wilk W statistic. Monte Carlo trials indicate that some of the tests give adequate control of Type I error rates for sample sizes as low as 4. Over a variety of distributions the W statistic is generally the most powerful. However, moment tests are sometimes more powerful and, additionally, may help in identifying the actual shape of the nonnormal population distribution.
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The concept of degrees of freedom, considered of central importance to interpretation of psychological and educational data, is presented and the computational procedure outlined. A section is devoted to the importance of the concept and illustrations are given to show how the number of degrees of freedom may be determined for various situations. Bibliography of 13 references. (PsycINFO Database Record (c) 2012 APA, all rights reserved)