# Fundamental Statistics for the Behavioral Sciences

## David C. Howell

This page lists supplemental material that is available for Fundamental Statistics for the Behavioral Sciences, 9th edition. Much of the page will focus on the R computing language, including how to download and install R, code that relates to each chapter, and additional material that goes beyond the text but which is potentially useful for those wishing to go further. For some chapters there will be more content material that did not fit easily into the text but that may be useful.

## Supplements by Chapter

The following links are included here because they offer important additional information on the material in the text. In some cases the material goes well beyond the text, but I thought that it was appropriate to include them for completeness. I do not expect every user to be excited by every entry, but I thought that, in this case, occassional overkill was appropriate. Use your own discretion.

• ### Chapter One — Introduction

• No supplemental material
• ### Chapter Two — Basic Concepts

• No supplemental material

• ### Chapter Seven — Basic Concepts of Probability

• Binomial Distribution Calculator
• This link will allow you to enter the number of trials and the probability of success on any one trial, and calculate the probability of a specified number of success on those trials. You can also use either of the calculators referred to above.
• Multinomial Distribution Calculator
• This link will allow you to enter the number of different possible outcomes and the probability of success for each of those, and calculate the probability of a specified number of success on those trials. For example, with 3 outcomes the probabilities might be p(black) = .50, p(green) = .20, p(pink) = .30. We can now find the probability of 3 blacks, 2 greens, and 5 pinks.
• ### Chapter Eight — Sampling Distributions and Hypothesis Testing

• Jones and Tukey Table
• Andrew Waters, of Uniformed Services University of the Health Sciences, has suggested that a nice way to clarify the suggestion by Jones and Tukey is to present the decision process as in the attached table.
• ### Chapter Nine — Correlation

• Intraclass Correlation Coefficients
• This is a discussion that I wrote in the past about the intraclass correlation coefficient. It might ask something that you don't care to know, but it gives an important perspective. It bases much of the discussion on an understanding of the analysis of variance, which is not covered until the next chapter, but I put it here because that is where people are likely to look for it.
• Kinds of ICC coefficients
• The intraclass correlation is more complex that it might seem, depending mainly on how the data are collected. This document explains the various types. I believe that I wrote this, and a search of the Internet doesn't show that someone else did, but if I have taken someone else's work I apologize and would be happy to add an erratum.
• Reliability
• In looking again to see if I could find out if someone else wrote the previous entry, I came across an excellent page on reliability. No author is given, but it is on the Hanover College web site, so it was probably written by John Krantz.
• ### Chapter Ten — Regression

• Sampling distribution of the regression coefficient
• This is another answer to a question you probably never expected to ask. If we are going to use a t test on a regression coefficient (b), then we would hope that b is normally distributed. But is it?
• Useful Source for Regression and Correlation
• I have a Web page that contains a variety of examples on correlation and regression along with some other useful information. It may prove helpful for those seeking more information.

• ### Chapter Fifteen — Power

• Another Power Calculator
• Russ Lenth at the University of Iowa has created a very nice free power calculator. It does not have all the bells and whistles of G*Power, but it is quite useful. One trick is to notice that there are little square boxes on each slider that allow you to change the range.
• What About Power When we are Concerned with a Meaningful Difference.
• Several years ago I wrote a document on power when our null is not zero. We may want to reject the null only when the difference is sufficiently meaningful. This document raises important questions, though it does not attempt to answer all of them.
• Generating Data With a Specific Pattern of Correlations
• We sometimes want to generate a set of data that has a particular pattern of correlations. These correlations can either be exact in the sample, or they can refer to populations having those correlations and the data are simply a sample from those populations.
• Another Example of Multiple Regression
• It is always useful to look at multiple examples of a type of analysis, and the link here, from the Journal of Tropical Pediatrics--author unknown, contains an interesting and useful one related to crime rate.
• Multinomial Logistic Regression
• In Chapter 15 we considered logistic regression with only two possible levels of the dependent variable. That is the normal form of logistic regression. However suppose that you had three outcomes--"improved","no change", "worse." This is a case of what is called multinomial logistic regression. An example is given at the site linked above.
• Mediation and Moderation
• Some of the most important work on mediation and moderation has been done by David Kenny. These two links point to valuable pages that he has assembled on these topics.
• ### Chapter Sixteen — One-Way Analyses of Variance

• More on Multiple comparisons
• In the text I said that I would provide a copy of an older chapter that covers a wider variety of multiple comparison techniques in greater detail. If you really want that stuff, here it is. Much of the chapter is similar to the one in the 8th edition, but there is a lot that has been left out of the new version.
• Another View of the False Discovery Rate
• I could not afford the space to spend a lot of time on the False Discovery Rate in this chapter, but a more extensive discussion is available in a set of lecture notes by Bruce Walsh. I think that it nicely expands on what I said, but I still prefer the refernce to Maxwell and Delaney(2004).
• SPSS and the General Linear Model
• UCLA's Academic Technology Services maintains an excellent set of Web pages on a wide variety of statistical topics. The one on using SPSS to solve the General Linear Model is particularly good and will be helpful for those working with SPSS. It goes beyond what I have been able to cover in the text.
• ### Chapter Seventeen — Factorial Analysis of Variance

• Unequal cell sizes
• Unequal cell sizes can often make a significant difference in a factorial analysis of variance. There are alternative ways of treating unequal ns (see Type I II III.pdf), but the standard default, while generally appropriate, can sometimes give you misleading results.

• ### Chapter Nineteen — Chi-Square

• Alternative Research Designs
• This is a short entry that I wrote for the International Handbook of Statistical Sciences (2011), edited by Miodrag Lovric. It discusses the fact that we can construct contingency tables from a variety of different research designs, and these tables can be treated differently.
• Ordinal Categorical Variables
• The standard chi-square test on a contingency tables is not affected by the order of the categorical variable. But when the categorical variable you are using is ordinal, you can obtain significantly greater power for your test by taking that ordering into account.
• Testing Change Over Two Measurements in Two Independent Groups
• This entry addresses a question about two independent proportions of change. In other words, if Group A improved by 30% and Group B improved by 35%, is that difference significant. It started out as a simple question but soon became more interesting. I admit that I got a bit carried away.
• ### Chapter Twenty — Nonparametric and Distribution-Free Statistical Tests

• More (Much More) on Resampling
• It should be apparent from reading the text that I am a strong supporter of resampling procedures. Several years ago I put together an extensive set of pages on resampling--both bootstrapping and randomization tests. These pages have the advantage and disadvantage that I was aiming at looking at broader issues of hypothesis testing rather than simply at discussing how to perform the tests. I think that what I have here is more thorough that standard coverage.
• ### Chapter Twenty One — Meta-Analysis and Single Subject Designs

• A Broader View of Meta-Analysis
• Jamie DeCoster, at the University of Alabama, has compiled an excellent page on meta-analysis. His coverage differs from the one in this book because he spends more time in the beginning on discussing how to conduct, as opposed to how to analyze, a meta-analysis.
• What Does a Meta-Analysis Look Like
• In recent years online learning has become an important tool in education. This study is a complete meta-analysis looking at the effectiveness of online learning. I include it not for its statistical aspects, but to give students an idea of what a meta-analysis paper is all about.