Hirsch - Workbook to Accompany Introduction to Biostatistical Applications in Health Research

Copyright 2016 by John Wiley & Sons, Inc. All rights reserved

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Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Name: Hirsch, Robert P., author.

Title: Introduction to biostatistical applications in health research with Microsoft Office Excel / Robert P. Hirsch.

Description: New York, NY : John Wiley & Sons Inc., 2016.

Identifiers: LCCN 2015039977 | ISBN: 9781119089650 (cloth) | ISBN: 9781119089865

(workbook)

Subjects: | MESH: Microsoft Excel (Computer file) | Biostatisticsmethods. | Data Interpretation, Statistical. | Mathematical Computing.

Classification: LCC R858 | NLM WA 950 | DDC 610.285dc23 LC record availableat http://lccn.loc.gov/2015039977

For many students of statistics, working out problems helps their understanding. For those students, I have written this workbook. For each chapter of the textbook there are several Examples with detailed answers. In addition, I have provided a summary of each chapter, a glossary, and a list of equations. These are intended to provide readers with a quick reference and as a means of review. Also for each chapter there are problems (Exercises with answers for only the odd exercises. The even exercises are problems that might be assigned for grading by your instructor.

The workbook has 13 chapters, but the text has only 12 chapters. The 13th chapter in the workbook addresses using the flowchart to select statistical methods for a given set of data. This chapter provides an overview of the textbook and its flowcharts.

Robert P. Hirsch

I gratefully acknowledge the role my students play in challenging me to help them to really understand statistical methods using more than just mathematical explanations.

The examples in this text are not intended to be a reflection of good clinical practice nor are they intended to provide information on use of medications. Some of the examples use data that have been created or modified to illustrate statistical methods.

In we learn that probabilities are useful in thinking about events (things that occur or characteristics that exist) relative to observations (opportunities for things to occur or characteristics to exist). When thinking about probabilities, we use literary, graphic, or mathematic language. In literary language, a probability is the frequency of events relative to the number of observations. In graphic language, we use Venn diagrams to think about probabilities. In Venn diagrams, a circular area usually represents occurrences of the event and a rectangle represents the observations. Then, the probability of the event is reflected by the area of the circle relative to the area of the rectangle. Mathematically, probabilities are proportions, because the number of events is part of the number of observations.

Regardless of which language we use to think about probabilities, we notice that probabilities have certain properties. One of these is that a probability must have a value within the range of zero to one. A probability of zero tells us that the event never occurs. A probability of one tells us that the event always occurs. Probabilities between zero and one tell us that the event sometimes occurs.

In addition to thinking about single events, we can use probabilities to think about collections of events. The first collection of events considered in includes the event and its complement. The complement of an event includes everything that could happen in an observation except the event. Events and their complements always have two characteristics. One is that they are always collectively exhaustive. Events are collectively exhaustive when at least one of the events must occur in every observation. Another characteristic of events and their complements is that they are mutually exclusive. Being mutually exclusive means that, at most, only one of the events can occur in a particular observation.

We can have collections of events other than just a particular event and its complement. Other collections of events might be collectively exhaustive and/or mutually exclusive. An event and its complement, however, are always collectively exhaustive and mutually exclusive.

With other collections of events, we can be interested in two types relationships of the events. These are the intersection and the union of those events. In an intersection of events, we are interested in those observations in which all of the events occur. In a union of events, we are interested in those observations in which at least one of the events occurs.

When we are interested in the intersection of events, we can use the multiplication rule to calculate the probability of the intersection. There are two versions of the multiplication rule. The simplified version involves multiplying the probabilities of each event together. This simplified version is appropriate if the events are statistically independent (from each other). That is, if the probability of each event is the same regardless of whether the other event(s) occur(s). The full version of the multiplication rule uses conditional probabilities.

Many of the probabilities we encounter in health research and practice are conditional probabilities. What distinguishes conditional probabilities from other probabilities is the fact that conditional probabilities address a subset of the observations, rather than all of the observations. That subset of observations is specified by the conditioning event(s). The event(s) addressed by the conditional probability is specified by the conditional event(s). If events are statistically independent, then the probability of the conditional event occurring is the same regardless of whether the conditioning event occurs.