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HANDBOOK OF
BIOLOLOGICAL
STATISTICS
T H I R D

E D I T I O N

JOHN H. MCDONALD
University of Delaware

SPARKY HOUSE PUBLISHING
Baltimore, Maryland, U.S.A.

 

©2014 by John H. McDonald
Non-commercial reproduction of this content, with attribution, is permitted;
for-profit reproduction without permission is prohibited.
See http://www.biostathandbook.com/permissions.html for details.


 

CONTENTS
 

Contents
Basics
Introduction ............................................................................................................................ 1
Step-by-step analysis of biological data ............................................................................. 3
Types of biological variables ................................................................................................ 6
Probability............................................................................................................................. 14
Basic concepts of hypothesis testing ................................................................................. 16
Confounding variables ....................................................................................................... 24

Tests for nominal variables
Exact test of goodness-of-fit ............................................................................................... 29
Power analysis ..................................................................................................................... 40
Chi-square test of goodness-of-fit ..................................................................................... 45
G–test of goodness-of-fit ..................................................................................................... 53
Chi-square test of independence ....................................................................................... 59
G–test of independence ...................................................................................................... 68
Fisher’s exact test of independence ................................................................................... 77
Small numbers in chi-square and G–tests ........................................................................ 86
Repeated G–tests of goodness-of-fit ................................................................................. 90
Cochran–Mantel–Haenszel test for repeated tests of independence ........................... 94

Descriptive statistics
Statistics of central tendency ............................................................................................ 101
Statistics of dispersion....................................................................................................... 107
Standard error of the mean .............................................................................................. 111
Confidence limits ............................................................................................................... 115

Tests for one measurement variable
Student’s t–test for one sample ........................................................................................ 121
Student’s t–test for two samples ...................................................................................... 126
Independence ..................................................................................................................... 131
Normality ............................................................................................................................ 133
Homoscedasticity and heteroscedasticity ...................................................................... 137
Data transformations......................................................................................................... 140
One-way anova .................................................................................................................. 145
Kruskal–Wallis test ............................................................................................................ 157
Nested anova ...................................................................................................................... 165
Two-way anova.................................................................................................................. 173
Paired t–test ........................................................................................................................ 180
Wilcoxon signed-rank test ................................................................................................ 186


 

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