Robert Hirsch - Statistical Hypothesis Testing with Microsoft ® Office Excel ® (Synthesis Lectures on Mathematics & Statistics)

This series includes titles in applied mathematics and statistics for cross-disciplinary STEM professionals, educators, researchers, and students. The series focuses on new and traditional techniques to develop mathematical knowledge and skills, an understanding of core mathematical reasoning, and the ability to utilize data in specific applications.

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If you need to interpret the results of statistical tests, want to be able to analyze your own data, or plan a study without having to consult with a statistician, this text is for you. It is written for the researcher who does not want to take a statistics course but needs to understand what the statistician does. It is largely nonmathematical except where absolutely necessary. It does not assume the reader knows much about statistics except what a mean and proportion are. To get the most out of the text, you should have access to Microsoft Office Excel but you need not be an expert on its use.

In Chap. you will learn what a P-value is, where it comes from, and how to interpret its value. You will also learn about the type of errors that can be made when drawing conclusions based on the P-value. You will become familiar with two approaches: testing hypotheses and their advantages and disadvantages. You will learn how to use these approaches to interpret a collection of several statistical tests in the same study.

Chapter explains how samples can be taken from the population in a way that creates an unbiased and analyzable dataset. The steps in the sampling process are examined. Then, the methods of drawing the sample are explained with their advantages and disadvantages.

In Chap. you will learn how to choose a statistical test that is appropriate for a given set of data. Then, you will learn about the most common statistical tests, how to use Excel to perform them, and how to interpret the results by using them.

Chapter discusses what you can do if you dont want to wait until a study gets to its planned end before you start looking at the data and draw conclusions about what will happen if the study is allowed to go to completion. It discusses two approaches, both of which can be used to decide to stop a study early if the results look promising. One can also stop a study early if the results do not look promising.

Chapter tells you how to determine the size of a planned sample that allows it to be big enough to see important relationships without being bigger than required. Methods are given for nominal and continuous variables and for datasets with and without independent variables.

The examples in this book are based on fictitious data and should not be taken as a reflection of real relationships. Those data have been created only to illustrate statistical principles.

The classical or frequentist approach to hypothesis is the one used most often and is taught in most introductory statistics texts. We will begin by understanding the logic behind this approach to statistical hypothesis testing.

Suppose researchers are comparing a new antiviral treatment to the standard treatment as to how well they keep infected persons from hospitalization. Those researchers hypothesize that the new treatment is better than the standard treatment and they want a statistical analysis of their data to support that hypothesis. The way statistics can do that is by eliminating chance as a likely reason for an observed difference between the two treatments. To do that, statistics calculates the probability of observing the observed difference if a hypothesis about the difference is true. Unfortunately, this probability cannot be calculated using the researchers hypothesis. To calculate the probability, the hypothesis must make a specific statement about the difference between the treatments. The researchers hypothesis just states that the new treatment is better but does not specify how much better. To make a specific statement about the difference between the treatments, statistics uses a hypothesis that the researchers believe is not true. That hypothesis is that there is no difference between the treatments. That is a specific statement that the difference is equal to zero in the population. This statistical hypothesis is still useful to the researchers, because if it can be eliminated as a likely explanation for the observed difference, they can, through the process of elimination, conclude that there is a difference not due to chance.