Tests for nominal variables

Descriptive statistics

Tests for one measurement variable

Tests for multiple measurement variables

Multiple tests



Welcome to the Handbook of Biological Statistics! This online textbook evolved from a set of notes for my Biological Data Analysis class at the University of Delaware. My main goal in that class is to teach biology students how to choose the appropriate statistical test for a particular experiment, then apply that test and interpret the results. I spend relatively little time on the mathematical basis of the tests; for most biologists, statistics is just a useful tool, like a microscope, and knowing the detailed mathematical basis of a statistical test is as unimportant to most biologists as knowing which kinds of glass were used to make a microscope lens. Biologists in very statistics-intensive fields, such as ecology, epidemiology, and systematics, may find this handbook to be a bit superficial for their needs, just as a microscopist using the latest techniques in 4-D, 3-photon confocal microscopy needs to know more about their microscope than someone who's just counting the hairs on a fly's back.

You may navigate through these pages using the "Previous topic" and "Next topic" links at the top of each page, or you may skip from topic to topic using the links on the left sidebar. Let me know if you find a broken link anywhere on these pages.

I have provided a spreadsheet to perform almost every statistical test. Each comes with sample data already entered; just download the program, replace the sample data with your data, and you'll have your answer. The spreadsheets were written for Excel, but they should also work using the free program Calc, part of the suite of programs. If you're using, some of the graphs may need re-formatting, and you may need to re-set the number of decimal places for some numbers. Let me know if you have a problem using one of the spreadsheets, and I'll try to fix it.

I've also linked to a web page for each test wherever possible. I found most of these web pages using John Pezzullo's excellent list of Interactive Statistical Calculation Pages, which is a good place to look for information about tests that are not discussed in this handbook.

There are instructions for performing each statistical test in SAS, as well. It's not as easy to use as the spreadsheets or web pages, but if you're going to be doing a lot of advanced statistics, you're going to have to learn SAS or a similar program sooner or later.

Printed version

While this handbook is primarily designed for online use, you may find it convenient to print out some or all of the pages. If you print a page, the sidebar on the left, the banner, and the decorative pictures (cute critters, etc.) should not print. I'm not sure how well printing will work with various browsers and operating systems, so if the pages don't print properly, please let me know.

If you want a spiral-bound, printed copy of the whole handbook (293 pages), you can buy one from for $16 plus shipping. I've used this print-on-demand service as a convenience to you, not as a money-making scheme, so don't feel obligated to buy one. Note that I hope to have the third edition available by September 2012, so if you're going to buy a print copy, you should wait until then if possible.

You can also download a free pdf of the entire handbook and print it yourself. The pdf has page numbers and a table of contents, so it may be a little easier to use than individually printed web pages.

You may cite the printed version as:

McDonald, J.H. 2009. Handbook of Biological Statistics, 2nd ed. Sparky House Publishing, Baltimore, Maryland.

It's better to cite the print version, rather than the web pages, because I plan to extensively revise the web pages once a year or so. I'll keep the free pdf of the print version of each major revision as a separate edition on, so people can go back and see what you were citing at the time you wrote your paper. The page numbers of each section in the print version are given at the bottom of each web page.

Pitcher plants
Pitcher plants, Darlingtonia californica. This is an example of a decorative picture that will brighten your online statistics experience, but won't waste paper by being printed.

I am constantly trying to improve this textbook. If you find errors or have suggestions for improvement, please e-mail me at If you have statistical questions about your research, I'll be glad to try to answer them. However, I must warn you that I'm not an expert in statistics, so if you're asking about something that goes far beyond what's in this textbook, I may not be able to help you. And please don't ask me for help with your statistics homework (unless you're in my class, of course!).

Further reading

There are lots of statistics textbooks, but most are too elementary to use as a serious reference, too math-obsessed, or not biological enough. The two books I use the most, and see cited most often in the biological literature, are Sokal and Rohlf (1995) and Zar (1999). They cover most of the same topics, at a similar level, and either would serve you well when you want more detail than I provide in this handbook. I've provided references to the appropriate pages in both books on most of these web pages.

There are a number of online statistics manuals linked at If you're interested in business statistics, time-series analysis, or other topics that I don't cover here, that's an excellent place to start. Wikipedia has some good articles on statistical topics, while others are either short and sketchy, or overly technical.

Sokal, R.R., and F.J. Rohlf. 1995. Biometry: The principles and practice of statistics in biological research. 3rd edition. W.H. Freeman, New York.

Zar, J.H. 1999. Biostatistical analysis. 4th edition. Prentice Hall, Upper Saddle River, NJ.

Howard Hughes


Preparation of this handbook has been supported in part by a grant to the University of Delaware from the Howard Hughes Medical Institute Undergraduate Science Education Program.


Picture of Darlingtonia californica from one of my SmugMug galleries.

Banner photo

The photo in the banner at the top of each page is three Megalorchestia californiana, amphipod crustaceans which live on sandy beaches of the Pacific coast of North America. They are climbing on a slide rule. This illustration has been heavily photoshopped; to see the original, go to my SmugMug page.

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This page was last revised August 18, 2009. Its address is It may be cited as pp. 1-3 in: McDonald, J.H. 2009. Handbook of Biological Statistics (2nd ed.). Sparky House Publishing, Baltimore, Maryland.

©2009 by John H. McDonald. You can probably do what you want with this content; see the permissions page for details.