Intuitive Biostatistics: A Nonmathematical Guide to Statistical Thinking, 3rd edition

What makes the book unique?
Intuitive Biostatistics is both an introduction and review of statistics. Compared to other books, it has:

• Breadth rather than depth. It is a guidebook, not a cookbook.
• Words rather than math. It has very few equations.
• Explanations rather than recipes. This book presents few details of statistical methods and only a few tables required to complete the calculations.

• How common sense can mislead. Chapter 1 is a fun chapter that explains how common sense can lead you astray and why we therefore need to understand statistical principles.
• Multiple comparisons. It is simply impossible to understand statistical results without a deep understanding of how to think about multiple comparisons. This isn't just a practical issue, but almost a philosophical issue in analyzing data. Chapters 22, 23, and 40 are devoted to this topic. I explain several approaches used to deal with multiple comparisons, including the false discovery rate (FDR).
• Nonlinear regression. In many fields of science, nonlinear regression is used more often than linear regression, but most introductory statistics books ignore nonlinear regression completely. This book gives them equal weight. Chapters 34 and 35 set the stage by explaining the concept of fitting models to data and comparing alternative models. Chapter 36 then discusses nonlinear regression.
• Bayesian logic. Bayesian thinking is briefly mentioned in Chapter 2 and is then explored in Chapter 18 as a way to interpret a finding that a comparison is statistically significant. This topic returns in Chapter 42, which compares interpreting statistical significance to interpreting the results of clinical laboratory tests. These are only brief introductions to Bayesian thinking. This book is about conventional (Frequentist) statistics, and only briefly introduces Bayesian approaches to data analysis.
• Lognormal distributions. These are commonly found in scientific data, but not in statistics books. They are explained in Chapter 11 and are touched upon again in several examples that appear in later chapters. Logarithms and antilogarithms are reviewed in Appendix E.
• Testing for equivalence. Sometimes the goal is not to prove that two groups differ, but rather to prove that they are the same. This requires a different mindset, as explained in Chapter 21.
• Normality tests. Many statistical tests assume data are sampled from a Gaussian (also called normal) distribution, and normality tests are used to test this assumption. Chapter 24 explains why these tests are less useful than many hope.
• Outliers. Values far from the other values in a set are called outliers. Chapter 25 explains how to think about outliers.
• Comparing the fit of alternative models. Statistical hypothesis testing is usually viewed as a way to test a null hypothesis. Chapter 35 explains an alternative way to view statistical hypothesis testing as a way to compare the fits of alternative models.
• Meta-analysis as a way to reach conclusions by combining data from several studies. This topic is the subject of new chapter (Chapter 43).
• Detailed review of assumptions. All analyses are based on a set of assumptions, and many chapters discuss these assumptions in depth. 
• Lengthy discussion of common mistakes in data analysis. Most chapters include lists (with explanations) of common mistakes and misunderstandings.

• Probability. I assume that you have at least a vague familiarity with the ideas of probability, and this book does not explain these principles in much depth. I have added a new chapter (Chapter 2) to this edition that explains why probability can seem confusing. But you can still understand the rest of the book even if you skip this chapter.
• Equations needed to compute statistical tests. I assume that you will be either interpreting data analyzed by others or using statistical software to run statistical tests. In only a few places do I give enough details to compute the tests by hand. 
• Statistical tables. If you aren't going to be analyzing data by hand, there is very little need for statistical tables. I include only a few tables in places where it might be useful to do simple calculations by hand.
• Statistical distributions. You can choose statistical tests and interpret the results without knowing much about z, t, and F distributions. This book mentions them but goes into very little depth.

Excerpt from "Q and A about confidence intervals of "proportions (chapter 4, page 40). Q. Which is wider, a 95% CI or a 99% CI?
A. To be more certain that an interval contains the true population value, you must generate a wider interval. A 99% CI is wider than a 95% CI. See Figure 4.2.

Q. Is it possible to generate a 100% CI?
A. A 100% CI would have to include every possible value, so it would always extend from 0.0 to 100.0% and not be the least bit useful.

Q. How do CIs change if you increase the sample size?
A. The width of the CI is approximately proportional to the reciprocal of the square root of the sample size. So if you increase the sample size by a factor of four, you can expect to cut the length of the CI in half.  

Q. Can you compute a confidence interval of a proportion if you know the proportion but not the sample size?
A. No. The width of the confidence interval depends on the sample size.

Q. Why isn't the CI symmetrical around the observed proportion?
A. Because a proportion cannot go below 0.0 or above 1.0, the CI will be lopsided when the sample proportion is far from 0.50 or the sample size is small. 

Q. You expect the population proportion to be outside your 95% CI in 5% of samples. Will you know when this happens?
A. No. You don't know the true value of the population proportion (except when doing simulations), so you won't know if it lies within your CI or not.

 Excerpt from "Common mistakes: P values" (chapter 15, page 134)

The P value is not the probability that the result was due to sampling error. The P value is computed assuming the null hypothesis is true. In other words, the P value is computed based on the assumption that the difference was due to randomness in selecting subjects--that is, to sampling error. Therefore, the P value cannot tell you the probability that the result is due to sampling error.

The P value is not the probability that the null hypothesis is true. The P value is computed assuming that the null hypothesis is true, so it cannot be the probability that it is true.

The probability that the results will hold up when the experiment is repeated is not (1.0 minus the P value). If the P value is 0.03, it is tempting to think that this means there is a 97% chance of getting similar results in a repeated experiment. Not so. The P value does not itself quantify reproducibility.

A high P value does not prove that the null hypothesis is true. A high P value means that if the null hypothesis were true, it would not be surprising to observe the treatment effect seen in a particular experiment. But that does not prove that the null hypothesis is true. It just says that the data are consistent with the null hypothesis.

Excerpt from "An analogy to understand power" (chapter 20, page 170) 
  Here is a silly analogy helps illustrate the concept of statistical power (Hartung, 2005). You send your child into the basement to find a tool. He comes back and says, "It isn't there." What do you conclude? Is the tool there or not? There is no way to be sure, so the answer must be a probability. The question you really want to answer is, What is the probability that the tool is in the basement? But that question can't really be answered without knowing the prior probability and using Bayesian thinking (see Chapter 18). Instead, let's ask a different question: If the tool really is in the basement, what is the chance your child would have found it? The answer, of course, is: it depends. To estimate the probability, you'd want to know three things:

• How long did he spend looking? If he looked for a long time, he is more likely to have found the tool than if he looked for a short time. The time spent looking for the tool is analogous to sample size. An experiment with a large sample size has high power to find an effect, while an experiment with a small sample size has less power.
• How big is the tool? It is easier to find a snow shovel than the tiny screwdriver used to fix eyeglasses. The size of the tool is analogous to the size of the effect you are looking for. An experiment has more power to find a big effect than a small one.
• How messy is the basement? If the basement is a real mess, he was less likely to find the tool than if it is carefully organized. The messiness is analogous to experimental scatter. An experiment has more power when the data are very tight (little variation), and less power when the data are very scattered.

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